ISSN:0308-6003    

DOI:10.1039/PR97673FX001

出版商:RSC    

年代:1976

数据来源: RSC

ISSN:0308-6003    

DOI:10.1039/PR97673BX003

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

2 The Transfer of Vibrational and Rotational Energy By P.D. GAIT Physical Chemistry Laboratory South Parks Road Oxford OX1 302 1 Introduction It is several years since Annual Reports included a chapter devoted to the study of molecular vibrational energy transfer. This period has witnessed an enormous increase in our knowledge and understanding of this area of physical chemistry and a single review article covering even one year's work in this field is a practical proposition no longer. This short essay aims to do no more than paint a general picture and to consider a number of recent developments which seem to be of more than passing interest. As a matter of policy less emphasis than is usual is placed on certain aspects of the subject which have been treated in more detail and with greater authority el~ewhere.'-~ This and the need to keep the Report within reasonable bounds have meant that a great deal of valuable work has received no mention at all.Apologies are tendered in advance to any who may feel that their own particular area of interest has been neglected. It was felt that private communications and references to unpublished data are not appropriate in an article of this nature. Such references have not been included even though this has meant the exclusion of certain results which have become part of the established literature of the subject. 2 General Considerations of Molecular Energy Transfer The prime quantity in any discussion of molecular energy transfer is the Massey parameter 6 [equation (l)].6 = bE/hav (1) A,? here denotes the energy transferred between the internal degrees of freedom and translation z1 is the velocity of collision and a-l represents somewhat loosely the range of interaction between the colliding particles. The connection between this parameter and the probability (P)of a molecular collision causing a transition between molecular states is easily established. In terms of first-order time-dependent perturbation theory E. Weitz and G. Flynn Ann. Rev. Phys. Chem. 1974 25 275. * 'Molecular Energy Transfer' ed. J. Jortner and R. D. Levine Wiley 1976. 3 R. C. Amme Adu. Chem. Phys. 1975,28 171. 5 P.D.Gait for a transition between internal states rn and n and w = (Em-E,)/h (3) The time-dependent potential V(t,{c})depends on the internal co-ordinates {c},but if we make the assumption that the internal and translational motions are separable we obtain 00 li I Pmn= h -a dt ei"'V(t)(rn~V({c})ln)~2 (4) where (rnI V({c})ln)= V, is the time-independent inelastic matrix element.Consider interaction under an intermolecular potential V(r)=Vor-" (5) where r is the intermolecular separation. If n exceeds 2 (say) the potential can be said to vary strongly with r and the bulk of the contribution to-the integral in equation (4) will arise from interactions in the vicinity of the classical turning point the distance of closest approach lo. Under these conditions the potential may be expanded about the point ro retaining only terms linear in (r-r,,).The effective potential which determines the classical trajectory is written = ~b~/r'+ VeR(r) ~(r) (6) where the first term represents the centrifugal potential due to collision at an impact parameter 6. Two extreme cases may be visualized. Firstly if n is very large (i.e.the potential is of very short range) only low-impact parameter collisions need be considered. If b = 0 we may parametrize V(r)in terms of the time by solving the classical equation of motion The equation (4) then contains an integral of the form where [= (wro/uJn)and ro= nJ(V,/E). Although ro is strictly dependent on IJ it is clear that 4' has the form of the Massey parameter 6. If n is large we may associate the range parameter with (d/Jn)where d is the hard-sphere collision diameter.Alternatively should V(r)be of long range we will find it necessary to consider collisions of high impact parameter. Because V(r)varies more rapidly with r than the centrifugal potential we can visualize a limiting case in which the trajectory is determined solely by the latter potential. In this case the trajectory is a straight line and we may substitute in equation (8) ro= b and substitute V for E. (This latter change reflects the fact that the strength of the interaction is now independent of the collision energy.) After averaging over a thermal velocity distribution the high- and The Transfer of Vibrational and Rotational Energy 7 low-impact parameter probabilities vary as T-’and T+’respectively in the resonant limit (o= 0).In the other limiting case 6 >> 1 K,,(x) may be approximated by an exponential and the integration over velocity effected by the method of steepest descents. The dominant temperature variation is log P -3[2( &y] (9) So the Massey Parameter provides a useful general guide to the behaviour of the velocity-averaged probability if one replaces the velocity u in equation (1)with the thermally averaged value. It is apparent that when AE is large the transition will be dominated by short-range forces other things (the size of the inelastic matrix element V,,, included) being equal. Despite the rapid progress made during the past few years in the computation of accurate inelastic cross-sections the bulk of experimental work is still interpreted in terms of simple models which are based on arguments of the type set out above.On the basis of an exponentially repulsive interaction V(r)= V,e-‘” it is possible to obtain an expression similar to equation (8) characterized by a parameter l= (2wllu). Thermal averaging again gives a dominant temperature variation for log P of -3[801(rn/2kT)4]i,which is of similar form to the celebrated SSH formula for vibrational energy transfer under short-range forces. In the case of a resonant process as might arise for vibration to vibration energy transfer it is necessary to consider both short- and long-range interactions. The model of Sharma and Brau is widely used in the latter context. The interaction of prime importance is considered to be that between the molecular multipole moments; the probability of a transition depends directly on the strength of the transition multipole moment between the states concerned.In part this attitude is due to a feeling that neither the accuracy of the experimental data nor that of calculated intermolecular potentials warrants the use of more complex theoretical models. A comment on the current state of affairs is provided by those authors who after computing an accurate ab initio intermolecular potential for the C0,-N system conclude that ‘both the magnitude and the form of the inelastic intermolecular potentials are not well approximated4 by the elastic intermolecular potentials’. This result throws doubt on the only general procedure available for estimating the inelastic potential between complex molecules.The ‘classical’ techniques of measuring energy transfer using high-frequency sound or shock waves yield energy relaxation times r,defined from the equation dE/dt = (E-E)/T (1 0) where E is the internal energy undergoing relaxation and l? denotes the equilibrium quantity appropriate to the local temperature. In the case of relaxation of a set of harmonic oscillators T may be related to the rate constant (klo) for the transition v=l tov=O,by Y being the appropriate vibrational frequency. (We note in passing that k, may be converted into a ‘probability’ P by dividing by the gas kinetic collision rate P may be converted in turn into an inelastic cross-section by multiplying by the hard-sphere N. M. Witriol J. D. Stettler J.R. Sabin and S. H. Trickey Chem. Phys. Letters 1974 27 540. 8 P.D.Gait kinetic cross-section. A collision number z the reciprocal of P,is also sometimes used. These matters are discussed in more detail in ref. 3.) 3 Experimental Methods By far the most powerful and widely used technique of recent years has been laser-induced infrared fluorescence. As a rule a pulsed laser is used to excite a molecular vibration the course of the relaxation of the excited level being followed by monitoring the i.r. fluorescence intensity. The property of the laser employed in such experiments is that of providing short high-power pulses at the exciting frequency. The wavelength selectivity is of little importance if broad-band emission is to be used to follow the decay process.Houghton5 and Millikan,6 for example have dispensed with the laser source entirely obtaining their time resolution by modulation of the exciting radiation on the one hand and on the other by employing a flow system. In one of the earliest studies made of laser-induced i.r. fluorescence Moore employed a modulated low-power (mW) He-Ne laser to pump the u3 vibration of CH4;7by observing the phase shift of the u4fluorescence he was able to obtain information on the v3-v4coupling rate. In fact the highly monochromatic nature of laser radiation can constitute a limitation on the method. Laser fluorescence experiments are generally conducted at pressures of a few Torr (to facilitate time resolution of the relaxation process and to prevent excessive self-trapping of fluorescence) at which rotation-vibration linewidths are typically 0.01 cm-' with line separations of (say) 1cm-'.Given that the laser linewidth is of the order 0.01 cm-' it is clear that the matching of laser and molecular frequencies depends upon a happy coincidence. Those molecules which have been most intensively studied are those which can themselves be induced to undergo laser action; the hydrogen halides COz,and CO being particular cases in point. In part this excessive preoccupation with a few species stems from the interest aroused by technologically important laser systems. Equally it can be said to reflect the ease with which measurements can be made in these few cases. The use of genuinely tunable lasers has been limited but may be expected to increase during the next few years.Weitz and Flynn have given a discussion of this aspect of the field recently.' In certain cases laser-molecule coincidence has been effected by electric field shifting of molecular levels (NH,)8 or by collisionally broadening the molecular lines [CO (v~)].'This latter method is of general applicability but its use must give cause for concern. In general the effect of additional molecular species on the relaxation rate can be allowed for by considering all the effects to be additive. Such a picture can break down where the internal modes of the relaxer and additive are coupled. Recent studies of HF-HF and DF-DF relaxation have shown that even such an inert species as Ar can affect the aparent rate of the process DF (v = l)+DF (v = 0) -+ 2DF (v = 0) (12) by its effect on the rate of rotational equilibration of the vibrational states.J. T. Houghton Proc. Phys. SOC.,1967 91 439. 6 R. C. Millikan J. Chem. Phys. 1963,38 2855. J. T. Yardley M. N. Fertig and C. B. Moore J. Chem. Phys. 1970 52 1450 and references therein. M. Redon H. Gurel and M. Fourrier Chem. Phys. Letters 1975 30. 99. G. Inoue and S. Tsuchiya J. Phys. SOC. Japan 1975 39 479. The Transfer of Vibrational and Rotational Energy 9 Such criticisms apply in general to the much more widely used technique of collisional pumping. In general vibration to vibration (VV) transfer processes are very fast compared with vibration to translation (VT) processes. Excitation se- quences of the type HCl (u = O)+hv (HCl laser) 4 HCI (u = 1) HCl(u=l)+D2(~=0)4 HCI(u=O)+D2(t,=l) (13) have been used to extend the range of laser-induced fluorescence and to pump other inaccessible molecular states.Double-resonance methods have not been widely used in the study of vibrational energy transfer the reason being the need for two laser-molecule coincidences. The situation is very different where rotational relaxation is concerned and we enter the realm of the continuously tunable klystron microwave source. Microwave double and triple resonance has been widely used in the study of rotational selection rules in molecular collisions. The study of the absolute rates of relaxation (as opposed to relative rates) requires that the pumping source be modulated.Under such cir- cumstances the use of i.r.-microwave double resonance is more powerful and is being used increasingly. The i.r. pulse provides the time resolution producing excitation to a particular (v = 1,J)state and the microwave source monitors the J relaxation. Because of the lower thermal population of the upper vibrational level the sensitivity of the experiment is greatly enhanced. I.r.4.r. double resonance has been used to study HF rotational relaxation; a pulsed HF v = 1-+ 0 laser provides the excitation to v = 1,and a CW u = 2 -+1 source monitors the relaxation." Moving to the realm of visible and U.V. lasers we encounter the possibility of excitation to specific (u,J)levels of upper electronic states. Species studied in this way include HD I, NO Li, and Na,.The behaviour of such excited states under collision is usually very different from that of ground-state molecules. One of the limitations of the i.r. fluorescence experiment is that i.r. emission intensities are low as are i.r. detection efficiencies; this is the main reason for not attempting J selection of the emitted radiation. The intensities of allowed transitions between electronic states are considerably higher and observation of steady-state fluorescence of the electronically excited states referred to above has given valuable information on v,J selection rules. In a few instances U.V. absorption cr u.v.-excited fluorescence has been used to probe the population of states following i.r. laser excitation. In order to obtain sufficient signal from an excited level it is necessary to effect excitation from a thermally well populated level usually v = 0.The optical selection rules then effectively limit the accessible upper levels to the v = 1state. There are some exceptions to this where high laser power is available for example exciting the transition 00'0 -+ 02'0 in OCS using a doubled CO laser," but as a rule some other approach must be made to the question of higher-level excitation. Alternatively the products of chemical reactions can be observed either by flash photolysis or in reaction flow systems and the kinetics of the upper states followed. The CS+ 0-P CO* + S reaction can produce CO in states up to v = 15,and the behaviour of such states in both VV and VT processes has been measured down to 100K.' In 10 J.J. Hinchen and R. H. Hobbs J. Chem. Phys. 1976,65 2732. D. R. Siebert and G. W. Flynn J. Chem. Phys. 1976 64 4973. 10 P. D. Gait this respect the CO molecule is the best studied ground-state species. HF has been studied in similar fashion in a flow system using the reaction F+H2+HF(v) +H(v = 2-5) and in a novel laser fluorescence experiment. Osgood et al. used a pulsed HF laser to excite HF to 0 = 3 by means of successive one-quantum transitions.’* To an extent limited by the inherent improbability of multiple quantum transitions one can collisionally pump excited vibrational levels. This has been achieved with HZand D2 using excited sodium atoms as the source H2(v = 4) and D2(v = 6) were obtained.” Of course such considerations do not apply to the electronically excited levels which have been pumped from the ground electronic state.In 12B311&vibrational levels close to the dissociation limit have been populated directly and their novel kinetic properties well studied. l4 The spectrophone is in one sense one of the ‘classical’ instruments. The optico-acoustic effect has been known for over 100 years and used (although somewhat sparingly) in the study of energy-transfer phenomena for over thirty. However the technique has undergone something of a renaissance in recent years and in the words of one commentator ‘after decades of nonsense has begun to produce results’.’’ The principle of the method is that if modulated i.r.radiation is absorbed by a molecule it will be degraded subsequently to thermal energy by collisions and may be detected as sound of the same frequency. Both phase shift and amplitude of the sound contain inforyation on the kinetic pathway of energy degradation. The origins of the recent resurgence of interest in the spectrophone are to be found in basic improvements in experimental technique and no less important in a realization that only a realistic kinetic model can yield sensible data. The use of a two-state system comprising the excited state and the thermal reservoir is inade- quate. Conversely the sensitivity of the sound phase and amplitude to the form of the entire relaxation pathway means that there is available a great deal of information which cannot be obtained by any other technique.With this in mind the vast majority of recent studies have concerned themselves with the molecule C02 in an attempt to determine the pathway from the asymmetric vibration (v3)to ground. In particular the question of whether the initial stage in the v3 relaxation is (030) or (020) has been answered using this technique. Unmodulated excitation of a particular vibrational level may also result in a heating of the gas as the energy is degraded. Such local heating can result in defocusing of a laser beam this phenomenon being known as thermal lensing. Equally if the initial process following an exciting pulse is endothermic (as may occur in a rapid VV exchange) a kinetic cooling will be seen. Both magnitude and sign of the density change may be determined by probing the focus of the exciting radiation with a laser beam.This method has not been widely used but is capable of providing valuable information about non-resonant VV exchange rates within molecules. 12 R. M. Osgood P. B. Sackett and A. Javan J. Chem. Phys. 1974,60 1464. 13 D. A. Jennings W. Braun and H. P. Broida J. Chem. Phys. 1973 59 4305. 14 J. I. Steinfeld in ‘Chemical Kinetics’ ed. J. C. Polanyi M.T.P.International Review of Science Physical Chemistry Series 1 Vol. 9 1972 p. 247. 15 C. B. Moore Adv. Chem. Phys. 1973,23,41. The Transfer of Vibrational and Rotational Energy 11 Ducuing and co-workers have used the stimulated Raman effect to prepare i.r.-inactive molecules in excited vibrational states.I6 The relaxation of the excited state may be followed in principle by means of spontaneous Raman scattering but the favoured technique is to measure the density change following relaxation using a laser beam.Early results obtained for H relaxation using these two methods are not in agreement; the reason for this is not clear. By using two laser frequencies the threshold for stimulated excitation of vibrations is reduced and molecular vibrations may be selectively excited at the difference of the two frequencies. Nonetheless to ensure that the relaxation is faster than thermal diffusion (which will distort the form of the established density gradient) reactions are studied at high pressures of the order of atmospheres. Only a limited number of molecules undergo the stimulated Raman effect; in most cases stimulated Brillouin scattering occurs and sufficient vibrational excitation does not take place.Kovacs et al. have overcome this by using very short pulses (-10 ps) rather than the conventional 10 ns of a Q-switched ruby laser. l7 It is recognized that before an adequate understanding of vibrational relaxation can be obtained the way in which molecules undergo rotational and orientational relaxation must be known. Part of the answer to these questions comes from microwave studies of selection rules for rotational relaxation and from studies of rotational lineshapes. However relatively new and interesting information on orientation relaxation is being made available by the study of Rayleigh scattering line shapes and from the effect of electric and magnetic fields on transport properties the Senftleben-Beenakker effect.Just as Raman scattering linewidths and conventional transport properties are sensitive to energetically inelastic collisions these phenomena are primarily determined by the effect of collisions on molecular orientation. Energetically inelastic processes are important only in so far as they effect reorientation of the molecules. A more detailed discussion may be found in the reviews of Beenakker','' and in the following text. Although the more conventional techniques used in the study of relaxation times (ultrasonic absorption and dispersion shock-wave excitation impact tube etc.) continue to yield valuable information they have undergone relatively little development during the past few years and will not be discussed further at this point.Reference 3 contains detailed descriptions of these and other experimental tools. 4 Rotational Energy Transfer Because of the small energy-level spacing measurements of rotational relaxation times at normal temperatures refer to an average over a large number of populated J states. Indeed it is not always strictly correct to refer to a relaxation time in the sense of equation (lo) but as a rule departure from the single relaxation time model is not extreme and for heavy molecules it is customary to interpret experimental data in terms of a J-averaged collision number Zrot.[In part the adequacy of a single relaxation time model may be due to the existence of quasi-resonant reactions; for M.M. Audibert C. Joffrin and J. Ducuing Chem. Phys. Letters 1974 25 158. 17 M. A. Kovacs and M. E. Mack Appl. Phys. Letters 1972 20 487. 18 J. J. M. Beenakker Festkorperprobleme 1968 8 275. P.D. Gait example in normal H H2 (J=2)+H2 (J=3) -+ H2 (J=4)+H2 (J= 1) (14) may be more efficient in promoting excitation of J = 4 than the direct H2 (J=2)+H2 + H2 (J=4)+H2 (15) The outstanding features of rotational relaxation are the relatively weak depen- dence of Z,, on temperature T and on collision mass p (as compared with vibrational relaxation). The reason for this is in part that the parameter is generally small so that PJ,,is not strongly dependent on p cir T,and partly that an in- creasing temperature moves the rotational population distribution to higher J levels so that the average rotational quantum is larger.When kT>>B(the rotations€ constant) the most populous J level is J -and we may write 5-6 or -Jcclm (16) where m is the reduced mass of rotation. The important point is the lack of a temperature dependence which also appears in the more exact theory of Widom. The work of Prangsma et a/.gives results which are typical of rotational relaxation in heavy molecules. l9 They obtained Z,, from the frequency-independent excess absorption in an ultrasonic experiment. Over the range 77-300 K Z,, increases for N from 1.8to 5.6 for CO from 1.1 to 4.0 and for CH from 3.0 to 8.6. CD shows similar behaviour Z,, being consistently slightly lower than for CH (e.g.7.6 at 300 K). These results being out a number of important points; firstly Z,, shows a small but definite increase with temperature. The above analysis shows that the probability of the most populous transition does not change with temperature; the observed variation may be explained in terms of the form of the rotational envelope. At high temperatures the contribution of the most populous level to the overall relaxation falls and as a result attention must be paid to those transitions at J>J" which involve larger energy changes and so contribute more to the energy relaxation rate. The sequence of Z,, magnitudes CH > CD >> N2 or CO reflects the sizes of the rotational level spacings. An interesting question arises as to why N2 should relax more slowly than CO.These molecules possess very similar masses and rotational constants and it has been suggested that the difference lies in the restriction of transitions in N2 to AJ = *2 whereas AJ = f1is allowed in CO; thus the average quantum jump in N2is twice that in CO. Ultrasonic absorption measurements ofZ,, in isotopically substituted N and CO give the following data:*' I4N23.9 14N1'N4.1 lSN24.5 l2Cl602.8 and l2Cl80 2.7. This clearly shows that not only must AJ = *1 be possible but that the transitions must be kinetically accessible which depends on the form of the molecu- lar anisotropy. The intermolecular potential may be written in the form V(r)= Voe-"' C &,Pn(cos 8) (17) n where r is the intermolecular mass-centre separation and 6 is the angle between the molecular axis and the vector connecting the mass centres.In 14N2or 15N2Pn = 0 if n l9 G. J. Prangsma A. H. Alberga and J. J. M. Beenakker. Physica 1973 64 278. P. G. Kistemaker A. Tom and A. E. de Vries Physica 1970 48 414. The Transfer of Vibrational and Rotational Energy 13 is odd making the substitution 14N+ "N so that the mass centre is shifted by an amount S we find that p is non-zero and given (approximately) by2' p1= Gr-'(ar+~ap2r-312) (18) In l4NI5N S is very small (0.036 a.u.) and p1<< p,; in other words the alternate J levels are not strongly coupled because of the small P,anistropy. (This is in sharp contrast with HD which is discussed later.) From depolarized Raman and Rayleigh scattering in liquid N2 and CO it appears that the difference in the intermolecular potentials of CO and N resides in the molecular anisotropies rather than in the relative slope parameters The effect of inert gases provides some interesting contrasts.For CH and CD Z,, increases with reduced mass of collision for the series He Ne Ar Xe23 (that for CD being consistently the smaller). This trend may be understood simply in terms of the amount of energy transferred between colliding species of different mass; if we consider that collision occurs between an H or D atom at rest and a moving particle of mass rn,then the energy transferred to H in a collinear collision can be obtained by solving the classical conservation equations of energy and momentum to give where R = (m/mH)and AE has its maximum value when R = 1.This reflects the difficulty of transferring momentum between species of widely differing mass. Similar results exist for N,-inert gas colli~ions,~~ the most efficient inert gas being neon and the order of efficiencies in relaxing rotation is NeaAr>XeaHe. Surprisingly CH, CD4,and N appear to be slightly less efficient than expected on the basis of mass in promoting self-relaxation. This contrasts with vibrational relaxation where self-relaxing collisions tend to be unusually efficient. Hydrogen and deuterium have by virtue of their large rotational level spacing relatively long relaxation times (z,,~-300). At temperatures below 177 K for para-H, and 100K for ortho-D, these spin isomers behave as two-level systems.Jonckman et al. have made use of this to study the effects of collision partner and temperature on rotational relaxation uncomplicated by the effects of a varying average energy spacing.25 For para-H z,,~falls as the temperature increases as would be expected. At 170 K they find an order of efficiencies Ne> 'He-Ar -4He>Kr >Xe whilst at 90.5 K Ar -Ne >,He. They also found that para-H is less efficient than even xenon in causing relaxation whereas ortho-H (J= 1 level) is twice as efficient as para-H at 77 K. At these temperatures ortho-H is almost completely in the J= 1 state and would be expected to behave like an inert gas; because of the absence of a J =3 population quasi-resonant rotation to rotation (RR) processes may be safely ignored.Similar measurements in ortho-D at 90.5 K show efficiencies in order Ne -Ar >,He >ortho-Dz. Surprisingly Z,, varies but 21 P. M. Agrawal and M. P. Saksena J. Chem. Phys. 1976,65 550. 22 J. Bruining and J. H. R. Clarke Mol. Phys. 1976 31 1425. 23 P. G.Kistemaker M. M. Hanna and A. E. de Vries Physica 1974 78 457. 24 P. G. Kistemaker and A. E. de Vries Chem. Phys. 1975,7 371. 25 R. M. Jonkman G. J. Prangsma I. Ertas H. F. P. Knaap and J. J. M. Beenakker Physica. 1968 38 441 and following papers. 14 P. D.Gait slightly with temperature in ortho-D,-ortho-D collisions between 3 1 and 55 K and actually increases for ortho-D,-Ar between 77 and 90 K. Clearly hydrogen relaxa- tion does not fit in well with the classical model given above.Not surprisingly ortho-D 0-2 is relaxed more efficiently than the corresponding para-H transi- tion; however at higher temperatures when several J levels are populated the relaxation numbers are not greatly different. From the data of Sluijter etaf.26we may roughly correlate (Z,,)-' with the frequency of maximum ultrasound absorption (fl~)~~~: for normal H2 at 298K this is 8.52MHz atm-' for para-H 21.1 MHz atm-' for normal D2 14.7 MHz atm-' and for ortho-D 15.4 MHz atm-'. By contrast for HD(f/p),, lies above 100MHzatm.' even at 77K. Recently Prangsma et al. have extended measurements to 20-40 K for HD-HD and HD-He mixtures where HD is essentially a two-level system (J =0 +1).Over this tempera- ture range Zrotdoes not vary at all and HD is a more efficient collision partner than He in contrast to the results obtained for ortho-D2 and pa~a-H,.'~ The failure of Z,, to vary with temperature has been attributed to the effect of intermolecular attractions.An n.m.r. determination of the spin-lattice relaxation time from 28 to 100 K has confirmed these results but shows a rise of the rate for the J= O+ 1 transition above 40K.28These results agree well with calculations based on the H,-He p~tential.,~ On the basis of room-temperature measurements in para-H and normal H2 Valley and Amme attempted an analysis in terms of two rate processes each (the 0 +2 and 2 +4transitions in para-Hi, and in ortho-H the 1 +3 and 3 +5).30Their results agree with the low-temperature work discussed earlier in that for the 0 +2 transition the order of efficiencies is Ne >He >Ar >H, but for the 2 +4transition we have H2 >Ne bAr >He.If one ignores the unusual position of H2it is possible to correlate the relative efficiencies of these species with the size of the ratio hE/kT. When this is large (e.g. for 4+2 at 300K or 2+0 at 90K) Ne-ArB4He but when this is reduced (0+ 2 at 170 K or above) we find Ne> He >Ar. This cannot be simply an effect of the reduced collision mass on PJJrthrough the parameter 5 because in H,-M collisions the reduced mass is essentially fixed by that of H,. The unusually high efficiency of H at 300 K persists for the 1 +3 2 +4 and 3 +5 transitions. These results must be in doubt because of the failure of Valley and Amme to allow for the apparent J dependence of the H efficiency found by Jonkman and for the effect of RR quasi-resonant coupling.The latter process will relax para-H 4+2 and the ortho-H transitions in normal H2 quite readily. Measurements of zrOt for ortho-H2 between 230 and 293 K yield a value of about 520 this is significantly greater than the Valley and Amme result of 370 suggesting that their analysis may indeed have been affected by quasi-resonant proce~ses.~' In the measurement of TIfor HD Fisher and Riehl were concerned to know the effect of various collisions on the spin reorientation; both elastic (AJ =0 AM #0) and inelastic (AJ #0 AM #0) processes had to be considered. The former were esti- mated from work on H2 on the grounds that only the even-symmetry anisotopy can 26 C.G. Sluijter H. F. P. Knaap and J. J. M.Beenakker Physica 1965,31 915. 27 G.J. Prangsma J. P. J. Heemskerk H. F. P. Knaap and J. J. M. Beenakker Physica 1970 50 433. 28 C. J. Fisher and J. W. Riehl Physica 1973,66 1. 29 S.Green Physica 1974 76 609. 30 L.M.Valley and R.C. Amme J. Chem. Phys. 1969,50 3190. 31 G.J. Prangsma L. J. M. Boorsborn H. F. P. Knaap C. J. N. van der Meijdenberg and J. J. M. Beenakker Physica 1972,61 527. The Transfer of Vibrational and Rotational Energy 15 cause AJ = 0 transitions (in a single transition at least) which will be comparable in HD and in H,. The nature of molecular reorientation can be studied from n.m.r. spectral line- broadening and transport properties and throws a great deal of light on the related phenomenon of energetically inelastic processes.Recent n.m.r. measurements on H2 relaxation at 298 K have been interpreted in terms of the Bloom-Oppenheim model which introduces a parameter R,the ratio of inelastic to elastic collisions in promoting changes in M.32The conclusion reached was that R,,> RHe> RAr> RN2; unfortunately theory does not distinguish between non-resonant quasi-resonant and resonant processes in effecting AJ # 0 AM # 0 transitions. However the large value of RH2suggests the possible importance of quasi-resonant or resonant RR collisions. This is clearly shown in measurements of the depolarized Raman scatter- ing from ortho-para-H mixture^.^' The general trend is that linewidths decrease as J increases; this can be understood in terms of the increase in energy-level spacing with J and in the resistance of a rapidly rotating system to reorientation.However in normal H2 the ortho-H lines are consistently broader than expected on the basis of the para-H2 linewidths; the authors attributed this to a resonant RR transfer. In normal H about $ of all molecules are in the J= 1state which resonantly couples with J = 3 alone. Studies of the variation of linewidth with the ortho-para H ratio confirmed this hypothesis; as the J = 1-P 3 linewidth decreased with increasing para-H concentration resonant RR processes must be more important in causing reorientation than quasi-resonant processes. The Raman scattering linewidth is sensitive to both inelastic and elastic processes and significantly the HD linewidth is 10times as large as those of D2 and H,.Rayleigh scattering can be used to explore reorientation collisions alone (i.e.inelastic scattering is important only in so far as it causes AM# 0 processes). The Lorentzian Rayleigh lineshape of normal H2 and para-H shows the existence of a single relaxation time in contrast to the behaviour found in energy rela~ation.~~ Differences between energy and orientation cross- sections are also seen in the monotonic increase of the Rayleigh linewidth of N with collision mass35 and the similarity of N and CO cross-sections. On the basis of their study of the decay ofthe J-resolved chemiluminescence of the reaction H+C1 -+ HCI(u,J)+Cl Polanyi and Woodall postulated a general relationship PJJ,= Aexp (-BAEJJ9/kT) (20) where A and B depend on the molecule and on the size of AJ.36 The relaxation of a rotational distribution peaked at high J in HCl occurs by the appearance of a second peak at lower J;this is due to the decreasing probability of transition with increasing J such that at some intermediate level the rate of decay greatly exceeds the rate of formation.AJ = 1transitions sufficed to explain the HCl data and the hypothesis has 32 R. L. Armstrong K. E. Kisman and W. Kalechstein Canad.J. Phys. 1975,53 1. 33 R.A. J. Keijser J. R. Lornbardi K. D. van den Hout B. C. Sanctuary and H.F. P. Knaap Physica 1974 76,585. 34 R. A. J. Keijser K. D. van den Hout M. de Groot and H.F. P. Knaap Physica 1974,75,515. 35 R.A. J. Keijser K. D. van den Hout and H. F. P.Knaap Physica 1974,76 477. 36 J. C.Polanyi and K. B. Woodall J Chern. Phys. 1972,56 1563. 16 P.D. Gait been made that selection rules AJ = 1(or 2) hold in light systems but not in heavy ones; when kT >> AE energy rather than angular momentum considerations are most important. On the other hand in Li’ scattering from CO and N2 at energies of 4eV and above the total AJ is large (above 20) and very similar for both CO and N2. (Clearly at such energies equivalent to a temperature of over 4000K energy considerations are dominant.),’ Evidence in favour of the existence of selection or ‘propensity’ rules comes from microwave and i.r. double-resonance studies associated chiefly with the name of Oka who has recently reviewed the field.,’ The main conclusions are that in for example NH and CH,OH (the two best studied systems) the selection rules are essentially of the dipolar type AJ = 0 f1 AK = 0 *l.By contrast in collisions with inert gases much larger Af are allowed the probability of transition decreasing slowly as AJ increases. Clearly several factors are determining the selection rules here; probably in NH,-NH inelastic collisions can occur at large impact parameter owing to the strong dipolar interaction. By way of contrast collisions with inert gases will be inelastic only at small b,where multiple rotational transitions may take place. Recent work in this field includes the study of AK selection rules in CH,OH by Lees and Haque.AK = 0 collisions are preferred in inert-gas collisions but less so in collisions with H and D2.39The M dependence of transitions has been studied in CH,OH with M states split by an electric field.,’ The AM=0 ;tl transitions seen for pure CH,OH strengthen the view that dipolar processes are important whilst IMl>1 seen in He and H2 collisions again strengthens the views obtained from observations of J changes alone. Cross-sections for rotational relaxation have also been obtained from oxygen e.p.r. linewidths; as usual the cross-section decreases as J increases. Only a slight M dependence was found.,’ In general two relaxation times may be distinguished TI,related to the ‘dephas- ing’ of the radiation from a coherently excited sample and T2,a population decay time.The assumption has been often made that for rotational relaxation TI= T2. However recent experiments on NH and OCS suggest that T2may be significantly greater than TI.42,43 The results obtained for the hydrogen halides are frequently in conflict one with another. Analysis of rotational distributions of HF produced in a flow system from the F+ H2 reaction shows that PJ,J-Idecreases as J increases.44 Furthermore xenon exceeds helium in efficiency as a relaxer (contrast this with CH and CD,). These results have been confirmed by studies of HCI far-i.r. line-br~adening.~’ However in quantitative terms the latter results are not in accord with calculations based on the accurate potential of Nielsen and Gordon. The cross-section was found to increase as the temperature fell which is in accord with the behaviour of other molecules but not with results obtained from thermal conductivity meas~rernents.~ 37 R.Bottner U. Ross and J. P. Toennies J. Chem. Phys. 1976 65 733. 38 T. Oka Adu. Atom. Mol. Phys. 1973 9. 127. 79 S. S. Haque and R. M. Lees Canad. J. Phys. 1975 53 2617. 4O R. M. Lees and L. J. Retallack Chem. Phys. Letters 1976 41 583. 41 W. C. Gardiner H. M. Pickett and M. H. Proffitt J. Chem. Phys. 1975,63 2149. 42 W. Hoke J. Ekkers and W. H. Flygare J. Chem. Phys. 1975 63 4075. 43 S. L. Coy J. Chem. Phys. 1975 63 514.5. 44 I. V. Lebed V. D. Perrninov and S. Ya. Umanski Chem. Phys. Letters 1975 36 626. 4s P. M. van Aalst J. A. Schuurman and J. van der Elsken Chem.Phys. Letters 1975 35 558. The Transfer of Vibrational and Rotational Energy 17 Hinchen and Hobbs studied HF rotational relaxation in an i.r. double-resonance experiment using the pulsed v = 1-+0 HF laser emission as pump and a CW LI = 2 +1line as probe of relaxation of J levels in v = 1.” The anaiysis allowed for resonant RR exchange by means of reactions of type HF(u = 1,J)+ HF(u = 0 J’) -* HF(u = 0,J) + HF(u = 1 J’) but assumed a Polanyi-Woodall relationship with neglect of W restrictions in contrast to the analysis of Lebed eta1.44 where W = 1was assumed. Not surprisingly the results are not in agreement Hinchen and Hobbs obtaining AJ = 1-3 only for the levels J = 2-3. They also saw a slower decay attributed to momentum transfer from the initial &like velocity distribution formed by the narrow exciting pulse.This implies a cross-section for rotational inelasticity which is greater than gas-kinetic; such a situation is not uncommon for polar molecules where inelastic collisions can occur at high impact parameter.46 Related results based on the probing of a thermal velocity distribution of a vibration rotation transition with a narrow-band laser have been obtained for H2C047 and NH,.48 The principle of the method is to measure the change in the form of the velocity distribution produced by optical perturbation of the population of a related rotational level. In H2C0,where the levels concerned were -12 cm-’ apart changes in the shape of the Doppler profile were interpreted as reflecting the change in translational energy needed to effect the rotational transitions.This result also implies that the RT process is at least as fast as momentum transfer. Molecular beam work in general has not produced a great deal of new information. Very large cross-sections for low-angle (high b) scattering in polar molecules have been interpreted in terms of rotationally inelastic scattering induced by dipolar Toennies has performed experiments on CsF which differ little from the earlier TIF results.49 The order of efficiencies in inducing the transition J = 3 +2 is symmetric top >asymmetric top >linear molecule which reflects the decreasing range of the spherically averaged interaction between CsF and its collision partner. There exist a number of measurements on relaxation in electronically excited states; frequently the behaviour in such states departs markedly from that encoun- tered in the ground state.Akins et al. have observed large rotational changes in relaxation of the B’C; state of HD excited by zrgon resonance lines. AJ = hl transitions were most probable in HD-HD collisions whereas for HD-inert gas collisions W = *2 transitions were more probable.” Propensity rules for transitions between different A doublet states of Li B’II excited by an argon ion laser have been found and interpreted in terms of a charge density model of the Similar results have been obtained for Na2.’Ib The B311&,state of I2has been studied in a variety of highly excited rotation-vibration states (v = 35-50).In such states it 46 H. A. Rabitz and R.G. Gordon J. Chem. Phys. 1970 53 1831. 47 M. Takami and K. Shimoda Japan J. Appl. Phys. 1973,12,934. 48 S. M. Freund J. W. C. Johns A. R. W. McKellar and T. Oka J. Chem. Phys. 1973,59 3445. 49 U. Borkenhagen H. Malthan and J. P. Toennies Chem. Phys. Letters 1976 41 222. E. H. Fink D. L. Akins and C. B. Moore J. Chem. Phys. 1972 56 900. 51 (a)C. Ottinger R. Velasco and R. N. Zare J. Chem. Phys. 1970,52 1636; (6)K. Bergmann and W. Demtroder J. Phys. (B),1972 5 1386. 18 P.D. Gait appears that selection rules break down completely; transitions involving AJ = f12 have been seen. (Large vibrational quantum jumps also occur.)52 Kato el al. have J-resolved the emission spectrum of 1 after exciting the B'n& state using circularly polarized light;" the process of J-reorientation was followed observing the circularly polarized emission.MJ persists for many elastic collisions and also appears to persist in inelastic processes involving large J changes. A similar investigation has been made of the Li2 ('nu) 5 Vibration-Rotation Energy Transfer The energy deficit of a vibration_translation (VT)transfer process may be reduced by simultaneous rotational transitions. The extent of rotation-vibration (VR) coupling will depend on the position of balance struck between the favourable energy change and unfavourably large angular momentum changes. The largest energy gain for a fixed W will occur for those molecules with the smallest moments of inertia.In fact the only cases in which VR coupling is clearly implicated involve collisions of hydrides. The phenomenon is well known in the hydrides and deuterides of Groups IV-VII (although in certain cases the effect is complicated by the polarity of the species involved). 1535 Considering the parameter for H and its isotopes we see that for the ZI = 0 + 1 transition 6 varies as (collision mass/reduced mass of vibration) which is essentially independent of the molecular mass. On this basis we would expect all the vibrational transition probabilities to be equal but high-temperature shock-tube measurements show that in the range 1700-1900 K HD relaxes twice as fast as H2 and D256(with PYj'==P?$). The situation is similar to that which exists in rotational relaxation of H2 HD and D2.We can consider two extreme cases in which VR coupling occurs (a)that in which VR is fast and RT rate limiting and (b)the reverse situation It is usually assumed that the latter is the case on the grounds that a substantial portion of the energy still goes to translation (i.e.the coupling process is far from resonant) and that the RT relaxation is known to be much faster than the overall vibrational relaxation. Nevertheless there are a number of considerations which may serve to modify this view somewhat. The first is that the rotational energy-level spacing increases with J so that coupling to high J levels will cause an increased relaxation rate; this must be balanced against the decreasing thermal population. The relaxation time of such a high-energy J state may be significantly longer than the J-averaged Z,, would suggest.Case (b)will generally apply and the case (a)limit will only be approached when the moment of inertia is very small so that (i) the rotational relaxation is relatively slow and (ii) the rotational energy can absorb a substantial fraction of the vibrational quantum for a modest angular momentum change. Thus case (b)can only be expected to apply to the relaxation of hydrogen and its isotopes. Pritchard has gone so far as to suggest that in the vibrational relaxation and dissociation of H2 the rate-limiting step is the slowest step in the rotational relaxation sequence prior to 52 R. B. Kurzel J. I. Steinfeld D. Hatzenbuhler and G. E. Leroi J. Chem. Phys.1971 55 4822. 53 H. Kato R. Clark and A. .I.McCaffery Mol. Phys. 1976. 31,943. S4 J. Bormann and D. Poppe 2.Naturforsch. 1976 31a 739. 55 C. B. Moore J. Chem. Phys. 1965,43,2979. 5h C. J. S. M. Simpson T. J. Price and M. E. Crowther Chem. Phys. Letters 1975 34 181. The Transfer of Vibrational and Rotational Energy 19 a fast near-resonant VR process.57 This amounts to ignoring the large AJ involved in the VR coupling. In para-H this model implies that the following processes are import ant VRH2(v = 1 J=O) + H2(v=O,J=8) fast RTH2(u=0,J=8) + H2(v=0,J=6) slow H2(v = 0 J = 6) -+ H2 (v = 0,J = 4) fast efc. If true this means that the J = 6,8 levels of H would be significantly perturbed from their equilibrium values and the vibrational and (in part) rotational degrees of freedom would show a common relaxation time.Dove et al. have claimed evidence for this from high-temperature shock-tube studies of D2 rela~ation.~~ Using a Schlieren technique they measured the total post-shock density change and found that it corresponded to a larger relaxing heat capacity than was attributable to molecular vibration alone. Employing Pritchard's criterion the rate-limiting pro- cesses in H2 and its isotopes are para-H (1,O) -+ (0,8) AE (J= 6-8) = 1637.2 cm-' ortho-H2 (1,3) -+ (0,9) AE (J=7-9) = 1814.7 cm-' para-D (1,5) -+ (0 11) A€ (J = 9-1 1) = 1158.0 cm-' ortho-D (1,O) -+ (0,lO) AE (J= 8-lo)= 1062.7 cm-' HD (1,O) -+ (0,9) AE(J=8-9) = 735.5cm-' On this basis we can understand the existence of an anomalously rapid HD relaxation.Ducuing and co-workers have measured the relaxation times of ortho- and para-H from 50 to 400 K and find that above 300 K the relaxation rates of the two isomers are at lower temperatures they find that ortho-H is significantly faster relaxing. This cannot be reconciled with the Pritchard scheme unless we also consider a less nearly resonant VR process ortho-H (1 1) + (0,7) AE (J= 5-7) = 1347.4 cm-' but in this case A,!?"'= 1087 cm-I compared with the alternative process where hEVR = 170 cm-' and the VR process must be very slow. Clearly qualitative models of this type are of limited value in predicting the relative rates of vibration-rotation relaxation. The most striking features to emerge from the low-temperature measurements of Ducuing et al.are the failure of the Landau- Teller model below 300 K; at these low temperatures the transition probability tends to a limiting value which can be attributed to the effect of attractive interactions. (A similar effect is seen in COY C02 and the rotational relaxation of HD.) In addition the differences in relaxation rate between ortho-H and para-H, and between H2 and DZ become more pronounced as the temperature is lowered. At sufficiently low /T~~ temperatures the ratio T~~becomes very large indeed an effect not predicted by 57 H. 0.Pritchard in 'Chemical Kinetics' ed. P. G.Ashmore (Specialist Periodical Reports) The Chemical Society London 1975 vol. 1 p. 281. 58 J. E. Dove D. G. Jones and H. Teitelbaum Proceedings of the 14th Combustion Symposium The Combustion Institute Pittsburgh 1973 p.177. 59 M. M. Audibert R. Vilaseca J. Lukasik and J. Ducuing Chem. Phys. Letters 1976 37 408. 20 P.D.Gait simple theoretical models.60 Ducuing et al. are of the opinion that the rate-limiting process is VR if we confine attention to Av = -1 AJ =6 transitions in the de- excitation step we come to the conclusion that the most nearly resonant processes are (1,3)+(0,9) hE = 170 cm-' and (1,2) +(0,8) hE =447 cm-' in ortho- and para-H respectively. Similarly for AJ =4and AJ = 8 we obtain (1,7) + (0 11) hE=55cm-' (1,8) + (0 12) AE= 291 cm-' (1 1) -+ (0,9) hE=728 cm-' (1,O) -B (0,8) AE=llOcm-' At small AJ resonance can only occur at high J where thermal populations are very small.McGuire and Toennies have interpreted the low-temperature He-H data of Ducuing theoretically and conclude that in para-H the transitions (1,O) + (0,4) or (0,6) are the most significant decay processes from (1,O) [they did not consider other (1,J) If we assume that AJ = 4,6 are dominant decay processes then for decay of (1 1) we note that the (1 1)+(0,5)and (0,7)processes are significantly closer to resonance. Thus in contradiction of Pritchard's hypothesis it seems that even in H the VR process is rate limiting. Similarly in the relaxation of CH and CD at 300 K the former is significantly faster despite the higher frequency of its vibrational modes;55 in contrast the rotational relaxation rates are very similar (Z,,,= 8.6 and 7.6 respectively).The hydrogen halides all relax more rapidly than their deuteriated analogues;' in addition the relaxation rate is only weakly dependent on the reduced collision mass in HX(DX)-inert gas collisions. Both facts suggest that the primary step is a VR coupling in which hE is small. This has been confirmed by a classical trajectory study of HF-Ar collisions.62 (It is easily seenfrom the dependence of P on 6 that if hE is small dependence on mass of collision will be weak.) At room temperature these rates are very much less than occur in HX-HX collisions; the latter are extremely large as shown by the fact that CO with a vibrational frequency half that of HF relaxes lo7times more slowly. It appears that the unusually rapid self-relaxation is not due to the ability of the partner to take up the rotational deficit Chen and Moore analysed HCl and DCl relaxation rates and using very qualitative arguments came to the conclusion that the rotational state of the collision partner was largely unimpor- tant.3 Similarly no difference was found in the efficiencies of normal H and para-H in relaxing HBr HCl and DCl on the basis of which it is argued that the rotational degrees of freedom of H2play no part.63 Nonetheless it must be said that as the VR process is non-resonant VR coupling could occur without any apparent isomer effect.Spin-isomer effects are seen in CO relaxation where the J =2 +6 para-H transition is resonant with the CO vibrational frequency; on the other hand CO cannot itself take up much rotational energy whereas the hydrogen halides can.The order of efficiencies in HX (DX) relaxation is H >HD >D, which is the expected order on the basis of mass. Yet the effect of mass as such in HX-inert gas encounters 60 J. Lukasik Chem. Phys. Letters 1976 44 219 and references therein. 6' P. McGuire and J. P. Toennies J. Chem. Phys. 1975,62 4623. 62 G. C. Berend and R. L. Thornmarson J. Chem. Phys. 1973 58 3454. 63 B. M. Hopkins and H.-L. Chen J. Chem. Phys. 1973,59,1495. The Transfer of Vibrational and Rotational Energy 21 is known to be small (for example KDFWHe =r KDF-Ar= 30 s-' Torr-'; KHF-Ar-1.5KHF-He = 60 s-' Torr-' at 295 K). Clearly if the hydrogen isotope effects are put down to pure mass effects we are forced to the unlikely conclusion that AE in HX-H collisions must be significantly greater than in HX-M collisions.Also in favour of VR transfer to H are th_e observations that in efficiency HD > 3He and D2> 4He; on the basis of the normal H,-para-H results Hopkin and Chen were forced to conclude that such differences reflected a steeper potential in H,-HX collisions compared with HX-He collision^.^^ Hancock et al. measured the rate of VT relaxation of CO between 109 and 630 K and found that D and 4He showed almost equal efficiency in relaxing the CO vibration whereas H and HD were considerably more efficient.64 It is not clear how these results fit in with the general picture given above nor is it known if VR relaxation occurs in HD-CO as well as in para-H,-CO. The VT relaxation of CO by normal D and ortho-D from 340 to 110K shows no sign of a spin-isomer effect.65 Thus far the experiment of exciting a single high J level and looking for direct transfer to vibration has not been done.The conclusions that can be drawn from the indirect evidence discussed above are limited and rather depend on which of the conflicting pieces of evidence one chooses to afford most weight. HF-HP6 and DF-DF6' self-relaxation are found to be catalysed by the addition of a large excess of argon. The explanation of this is that self-relaxation proceeds through collisions of the type HF (v = 1,small J)+ HF -+ HF (u = 0 largeJ)+ HF The efficiency of this mechanism depends on subsequent rapid rotational relaxation of the v = 0 state. The VR coupling is very fast and the addition of a large argon excess speeds UP the rotational equilibration.Unfortunately direct observation of J-level population perturbation is again lacking. Hancock and Sanders6' have extended the DF relaxation measurements to low temperatures and observe a markedly non-linear dependence of VT relaxation rate on the DF concentration. This effect increases as the temperature decreases and is attributed to polymer formation. Shin has offered a model of HFV-V transfer involving dimer formation,68 but the VTR relaxation appears to involve hexamers and a convincing theoretical interpretation will pose considerable problems. DF shows greater non-linearity than HF in line with the known polymerization equilib- rium constants. This tendency to hydrogen-bond also shows itself in the decrease in rate as the temperature increases resulting in a maximum in the relaxation time at a temperature of 1000 K for HF 400 K for HCI.(At higher temperatures normal processes showing a log PI,-T-1'3behaviour dominate the relaxation.) HX-inert gas relaxation probabilities show a straightforward T1I3 variation. Flynn Ronn and co-workers have studied the molecular series CH3X CD3X (X = F C1 Br or I) in some detail.69 Here again we have a series of molecules in e4 W. S. Drozdoski R. M. Young R. D. Bates and J. K. Hancock J. Chem. Phys. 1976,65 1542. 65 C. J. S. M. Simpson A. J. Andrews and T. J. Price Chem. Phys. Letters 1976,42,437. 66 J. K. Hancock and W. H. Green J. Chem. Phys. 1973,57,4515. 67 J.K. Hancock and A. W. Saunders J. Chem. Phys. 1976,65 1275. H. K. Shin and Y. H. Kim J. Chem. Phys. 1976,64 3634. 69 L. A. Gams B. H. Kohn M. I. Pollack and A. M. Ronn Chem. Phys. 1976 18 85 and reference therein. 22 P.D. Gait which V-R transfer is expected and found. This VR coupling manifests itself in an unusually rapid relaxation of hydride as compared with deuteride and also in a very weak dependence of deactivation probability of the lowest mode on the reduced mass of collision. This last factor as in HX is interpreted as evidence for a small energy change in the deactivation step. Moore and Hess have also recently measured CH relaxation times and find a similar effect.” An interesting similarity can be found between vibrational deactivation rates of hydrogen halides and of hydrogen itself.Thus at 300 K we find HCl-HCl> DCl- HCl >DCl-DCl and HBr-HBr >DBr-HBr >DBr-DBr in transition prob-abilities. According to L~kasik,~’ D2-H2 == H,-H >D2-D2 in this respect. The possibility of having significant VR coupling in heavy diatomic molecules is clearly much reduced. Because of the relatively small value of B a significant rotational energy change can only be produced by either very large AJ or by transitions involving high-J (therefore thermally unpopulated) levels. Clear exam- ples of VR coupling in anything other than hydrides and deuterides are lacking. Bauer and Liska claim to have obtained evidence for this in C0,-He mixtures where the total relaxing heat capacity exceeded that for CO vibration alone7’ (cf.Dove’s results on D,).(Significantly the excess ultrasonic absorption was found at high He concentrations and has not been confirmed by dispersion studies. At very high sound frequencies the contribution to the absorption from viscothermal relaxation is high and where the species involved have very different masses the thermal diffusion ratio in particular is difficult to estimate.) Bauer and Liska interpreted their results in terms of rotational transitions occurring simultaneously with the vibrational change such as to reduce the energy deficit. Eckstrom and Bershader conducted a shock-tube study at 1000K of CO, measuring the relaxation time of the (10’0) level as a function of J,, using a tuned CO laser.73 Their initial claim that the relaxation time depended on the rotational level was remarkable and does not appear to have been confirmed by later measurements.It may well be that when the vibrational relaxation is very slow the amount of energy absorbed by rotation has a significant effect on the relaxation time. A case in point is N,; the rotational transition J = 8+10 would absorb about 70 cm-’; when one considers that CO and N2 differ in relaxation times at room temperature by about three orders of magnitude although their vibrational frequencies differ by less than 200 cm-’ it is clear that the effect of such a rotational change may be far from trivial. Intermolecular VR coupling has been seen in many systems nearly all the data refer to relaxation of molecules possessed of low-energy vibrational modes by hydrogen.The best studied examples are C02(v’2)-H274 and CO-H,.75 In the former system at low temperatures (<700 K) normal H2relaxes the v2 mode more rapidly than para-H,; in the latter the reverse is true. These phenomena are attributed to the 70 P. Hess and C. B. Moore J. Chem. Phys. 1976,65 2339. 71 J. Lukasik and J. Ducuing Chem. Phys. Letters 197 27 203. 72 H. J. Bauer and E. Liska Z. Phys. 1964,181 356. 73 D. J. Eckstrom and D. Bershader J. Chem. Phys. 1972 57 632. 74 C. J. S. M. Simpson P. D. Gait and J. M. Simmie Proc. Roy. Soc. 1976 A348 57 73. ’5 A. J. Andrews and C. J. S. M. Simpson Chem. Phys. Letters 1976 41 565 and references therein. The Transfer of Vibrational and Rotational Energy 23 reactions COz(O110)+H2(J= 1) + CO (OOOO)+H,(J= 3) AE= 80.5 cm-' CO (U = 1)+H (J = 2) + CO (U = O)+H (J = 6) AE =88 cm-' It is well known that the probabilities for these processes are too large to be explicable in terms of short-range forces and Sharma has offered an explanation in terms of long-range dipole (CO,)-quadrupole (H,) interaction^,^^ and a similar dipole-hexadecapole interaction has been put forward for the latter pro~ess.'~ The long range of these interactions means that Plois particularly sensitive to AE,which explains the strong spin-isomer effect.Furthermore the CO,-H relaxation time is found to increase as the temperature rises which has been taken to imply confirma- tion of the long-range-force model in general.However as Simpson et al. have shown the separation of VR and VTcontributions is complex and the magnitude and temperature dependence of the VR probability is uncertain. In fact two theoretical models of these systems have been offered recently which employ short-range forces and appear to give as good agreement with experiment as does Sharma's m~del.~'.~~ Thus the question of the nature of the forces involved must remain open at present. Simpson et al. also found that HD was unusually efficient (more so that H2) in relaxing CO,. This was attributed to the fact that the VR process is as fast as the rotational relaxation in H,; as a result the critical J-level population in H is reduced to a value below the thermal one and the observed relaxation rate due to VR coupling is less than expected.In HD the RT rate is so great that a true measure of the coupling rate is obtained. Rather more direct evidence that VR coupling occurs is provided by the impact-tube measurements of Huetz-Aubert and Chevalier." They measured the relaxation times of CO,-H mixtures up to large mole fractions -~~ of H (xH2)and found that 7-l varied linearly with x~but showed a fall off at high x~-~~. The former could imply either the absence of VR coupling or that such coupling is slow compared with rotational relaxation. This latter explanation is not compatible with the observed curvature and higher rate for normal H,. Taken together these results imply VR exchange in normal H, none in para-H, and a VR coupling rate close to the RT rate as indicated by the results of Simpson.For CO, D2 and HD are more efficient than the isobaric helium isotopes and this is commonly taken to imply VR exchange the mass-dependent VTterm being the same for both hydrogen and helium isotopes. However as noted earlier some authors believe that He-D differences simply reflect differing intermolecular potentials. The work of Klein and Hess on CF does not appear to be explicable in terms of either of these models;" they found that He is more efficient than D in relaxing the CF v mode. By contrast the normal behaviour is seen for CH,. Frenkel et al. have also observed VR coupling between the lowest mode of BCl and HC1.82 Above 250 K Sharma's dipole-dipole model fits these results very well but the rate greatly exceeds the theoretical estimates at lower temperatures.76 R. D. Sharma J. Chem. Phys. 1969 50 919. 77 R. D. Sharma and C. W. Kern J. Chem. Phys. 1971,55 1171. 78 J. Stricker J. Chem. Phys. 1976 64 1261. 79 C. I. Nelson and R. E. Roberts Chem. Phys. 1973,2 445. 80 M. Huetz-Aubert and P. Chevalier Compt. Rend. 1973 276 B 211. 81 R. Klein and P. Hess Acustica 1975 33 198. 8* D. Frenkel J. I. Steinfeid R. D. Sharma and L. Poulsen Chem. Phys. Letters 1974 28 485. 24 P.D. Gait The rate of the transition ZJ = 1+0 in the A ’Z+ state of OH has been found to decrease as the angular momentum quantum number increase^.'^ It is supposed that rapid molecular rotation hinders the orientation of molecular axes necessary for efficient vibrational relaxation.If so it may prove to be rotational rather than translational hindrance of orientation which produces the unusual low-temperature behaviour of polar molecules such as SO,. 6 Vibration-Vibration Energy Transfer Transfer of energy between vibrational degrees of freedom is known to occur in both intra- and inter-molecular processes. The salient features of W transfer are well known. In an early paper Moore and co-workers examined the transfer of energy from the v3mode of CO to a variety of molecules chosen such that the energy deficit varied over a wide range.” It was found that the probability showed a T’ dependence when AE was small and an e~p(-AT-l/~) variation at large hE. This is in full accord with the theoretical picture described in Section 1; at resonance long-range interactions are important giving rise to a characteristic T’ dependence and large cross-sections (often approaching gas-kinetic).The T1l3 behaviour of log P is equally characteristic of VTtransfer where the dominant interactions are of the short-range repulsive variety; however it should be noticed that this type of behaviour is found for both long- and short-range interactions in the non-resonant limit. The real reasons for believing that short-range forces are operative in any given case is that the long-range force contribution falls off very much more rapidly with increase in A23 than does that due to short-range forces. At sufficiently high temperatures a process showing a T-’ dependence of probability will pass over to a positive gradient (in the resonant limit varying as T+l) thereby exhibiting a minimum in the plot of P as a function of temperature.The importance of the strength of the multipole moment responsible for the coupling is clearly shown by for example the experiments of Smith and co- worker~.~~ Although to a large degree the rates of resonant VV processes are in good agreement with the predictions of the Sharma-Brau model there exist a number of cases in which agreement is not ~btained.~’ An interesting example is the process HCl (u = 2)+HCl (u = 0) -P 2HC1 (v = 1) where the observed rate greatly exceeds that calculated. The rate appears to be too large to be accounted for by short-range interactions and it has been suggested that quadrupole forces may be important.86 This may well be true but a situation in which agreement between theory and experiment can be assured by inclusion of succes-sively higher terms in a multipolar expansion is hardly satisfactory this is particularly true when the higher transition moments in question are not known with any certainty.Furthermore when interactions of range shorter than dipole-dipole are concerned it has been argued that the T’dependence is an artifact of the model used and that the true temperature dependence should be somewhat ~eaker.~’ A 83 R. K. Lengerl and D. R.Crosley Chem. Phys. Letrers 1975 32 261. *4 I. W. M. Smith ref. 2 p. 85. 8s H. Gueguen F. Yzambart A. Chakroun M. Margottin-Maclou L. Doyenette and L. Henry Chem. Phys.Lefters 1975,35 198. 86 R. D. Sharma H.-L. Chen and A. Szoke J. Chem. Phys. 1973,58,3519. 87 P. D. Gait Chem. Phys. Letters 1976.41 236. The Transfer of Vibrational and Rotational Energy 25 more reasonable suggestion has come from work on exciton splitting in solid HCl lattices; these are too large to be explicable in terms of free molecular dipole moments but are explicable in terms of the values measured in the solid phase. It is suggested that the transition dipole moment may vary during the course of a collision." Bott has measured rates of energy transfer from DF to other hydrogen halide^;'^ the rates fall remarkably slowly with increase in the energy deficit AE which might suggest the operation of short-range forces. However the rates are known to decrease with increasing temperature.These results are compatible if part of the deficit is taken up by rotational energy. Rotational effects are frequently implicated in VV transfer involving hydrogen-containing species. A system to which much attention has been paid involves transfer of energy from C02 (v3) to hydrogen halides e.g. co2(00~1) +HF(V=0) -+ co2(OOOO) +HF(U= 1) Probabilities of these processes may be orders of magnitude larger than calculated. It has been suggested that the reaction may be brought closer to resonance by relaxation of the J quantum number selection rule in the halide. Calculations in high order of perturbation theory allowing for large ATchanges in HF and using accurate classical trajectories yield substantial improvement on the simple Sharma-Brau However it has been suggested that a large part of this improvement is due to the use of the correct trajectory;" spiralling trajectories can give rise to very large inelastic cross-sections in the non-resonant case.It has also been found that the relaxation of OH and HCl in an i.r. chemiluminescence experiment proceeds through A V= -1 AJ= 0 transition^.^^ The W transfer process is apparently 'tuned' to resonance through J changes in the heavier species which in the experiment referred to were NO2,NOCl and ICl. W coupling of D to CO exhibits a spin-isomer effect para-D being the more efficient isomer over the temperature range 340-240 K.65 The rate shows a positive temperature gradient but this may reflect the change in the thermal population of a critical J state rather than the molecular forces involved.There is some indirect evidence to implicate rotational effects in VV exchange between two non-hydrogenic molecules. Agreement between observation and the predictions of Sharma-Brau-type calculations is obtained for such systems as COz-NZ only if correct allowance is made for simultaneous rotational-vibrational transition^.^^ The form of the calculated temperature dependence is affected strongly by the changing shape of the rotational envelope. This strong dependence on the populations of particular J states which are capable of bringing a reaction to resonance will only exist if the forces are of the long-range variety. VV transfer in processes of the type CO (v)+CO(0) + CO (v -1)+CO(1) AE =-26.3(~-1)cm-' 88 J.E. Cahill Chem. Phys. Lerters 1975 31 228. 89 J. F. Bott Chem. Phys. Letters 1974 23 335. 90 T. A. Dillon and J. C. Stephenson J. Chem. Phys. 1973,58 2056 3849. 91 P. D. Gait Chem. Phys. Letters 1975 35 72. 92 M. A. Nazar J. C. Polanyi W. J. Skrlac and J. J. Sloan Chem. Phys. 1976 16,411. 93 R. D. Sharma and C. A. Brau J. Chem. Phys. 1969,50,924. 26 P.D.Gait are of considerable interest in that they provide unique tests of theories of energy transfer the only significant difference between one reaction and another being the size of the energy term hE. At 300 K the rates of the above reaction fall less rapidly with increasing u than the Sharma-Brau model predicts suggesting that when v is large contributions from short-range interactions should be ~onsidered.~~ Indeed calculations which allow for both types of interaction obtain excellent agreement with observations for this reaction but it must be said not for the analogous CO-N reaction.Smith and Wittig found that in reducing the temperature to 100K the rates increased for reactions involving large 0.94 It might be that as in the HF-CO system the AJ selection rule is being relaxed. Similar processes have been investi- gated (over a more limited quantum-number range) in HCl HF and DF.84The HF system is unusual in that above 300 K the rate increases with the vibrational quantum number. Shin and Kim have interpreted this in terms of energy flow within a non-rigid dimer.68 Legay has examined the related sequence co (v)+CO (v') -D co (v -1)+CO (u'+ 1) where both u and u' are large by perturbing the vibrational distribution in a CO-He discharge with a' laser.95 It appears that the subsequent time evolution of the distribution can be understood only if Av = 2 transitions are reasonably efficient.No quantitative estimates of the importance of such processes are given however. Flynn Ronn and co-workers measured intramolecular VV coupling in methyl halides by means of laser-induced fluorescence. For the most part confirming the rapidity of VV coupling they have nevertheless obtained evidence' for relatively slow relaxation of certain modes. For example excitation of the v6 mode in CH3Br is followed by equilibration with the vl v, v4 and v5modes in 60 collisions (at room temperature); however the v3 mode requires 170 collisions.All modes VT relax together in 335 collisions. By way of contrast CH3F and CH3Cl show single W relaxation times. Such instances of relatively slow coupling can be explained in terms of the absence of a nearly resonant energy-transfer process amongst the levels involved. An extreme case of slow VV exchange is SO which is one of those rare molecules which exhibit 'double dispersion' in an ultrasonic experiment. Laser fluorescence experiments have confirmed the existence of a slow v2 -+ (v1/v3) step.96 This may be related to the kinetic cooling found in a thermal lensing experiment where the energy flow from the vl mode was primarily upwards in an endothermic pro~ess.~' Similar effects have been found in the relaxation of 03 where v2 + v1/v3coupling is and in OCS where the slow step is vl + v exchange." This last result may throw doubt on the interpretation of bulk OCS relaxation data where the existence of a single relaxation time was assumed.99 The v1 + v2exchange in N20 has been shown to be very fast (with a relaxation time of 0.06 ps atm at 300 K compared with -1 ps atm for the v2mode).loO This would be 94 I.W. M. Smith and C. Wittig J.C.S. Faraday II 1973 69 939. 95 Ph. Brechignac G. Taieb and F. Legay Chem. Phys. Letters 1975 36 242. 96 R. C. Slater and G. W. Flynn J. Chem. Phys. 1976,65 425 and references therein. 97 D. R. Siebert F. R. Grabiner and G. W. Flynn J. Chem. Phys. 1974,60 1564.98 K. K. Hui D. I. Rosen and T. A. Cool Chem. Phys. Letters 1975 32 141. 99 C. J. S. M. Simpson P. D. Gait and J. M. Simmie J.C.S. Faraday ZZ 1976,72 417. 100 R. T. V. Kung J. Chem. Phys. 1975,63. 5305 5313. The Transfer of Vibrational and Rotational Energy 27 expected from the nearly resonant nature of the process. It is therefore all the more remarkable that H20 should catalyse this process so well; H,O is 100 times more efficient than N in promoting the coupling. Perhaps the rotational energy of H,O is able to take up the remaining energy deficit. Of considerable importance to an understanding of the CO laser is the nature of the state immediately following the collisional deactivation of the (00'1) level. Fluorescence experiments although capable of distinguishing between different modes cannot resolve the possible states corresponding to one two or three bending quanta.This information is now available from the work of Cannemeijer and de Vriesl'' and of Huetz-Aubert and Lepoutre.'02 In light inert gas collisions (e.g.with neon) the (100,020) level is preferred whilst the heavier inert gases tend to the (1 10,030) level. For low-mass collisions the dependence on hE is not strong so that the reaction involving the smaller quantum number change is preferred. CO also induces relaxation to (030 110). An i.r. double-resonance study of energy flow in SF has shown that the v3 mode loses its energy to levels 1000cm-' above rapidly and apparently in the absence of collision^.'^^ The v4 mode is relatively slowly populated by collision.A tentative explanation invokes the high-level density at the high energies involved. 7 Vibration-Translation Energy Transfer By and large the vibrational relaxation of most simple molecules has been well studied over a wide range of temperatures by the classical techniques. If one ignores those cases of vibrational relaxation in which rotational or vibrational degrees of freedom are clearly implicated only the moderately heavy non-hydrogenic molecules remain. In this realm the most recent work has been concerned with the extension of measurements to low temperatures. Using the stimulated Raman technique 0 and N2have been investigated at room temperature relaxing alone and in mixtures with helium.lo4 These relaxation times correlate surprisingly well with high-temperature shock-tube data.The relaxation time of N2 is the largest known being about 10 s at 300 K. CO has also been studied at low temperatures by means of fluorescence quenching (using both laser and flame radiation sources). At temperatures of 100-200 K the CO-He probability shows remarkably non-Landau-Teller behaviour decreasing very slowly with falling temperature. lo5 This is interpreted as being due to the attractive portion of the intermolecular potential. Carbon monox- ide and oxygen have also been studied using the 'transient' stimulated Raman method of KOV~CS." Similar low-temperature behaviour has been observed for the u2mode of CO,.'O6 Allen et af.have pumped CO (v3)using laser-excited CO; the v2 mode is populated by v3 decay.The effect of intermolecular attraction is felt in C02-C02 collisions even at 300 K. In C0,-Ar the effect is less strong. lo1 F. Cannemeijer and A. E. de Vries Physicu 1972,64 123. lo2 M. Huetz-Aubert and F. Lepoutre Physicu 1974,78 435. '03 D. S. Frankel J. Chem. Phys. 1976,65 1696. Io4 R. Frey J. Lukavsik and J. Ducuing Chem. Phys. Letfers 1972,14 514. Io5 D. J. Miller and R. C. Millikan J. Chem. Phys. 1970,53 3384. 106 D. C. Allen T. J. Price and C. J. S. M. Simpson Chem. Phys. Letters 1976 45 1. P.D.Gait The effect of attraction found in these systems must be distinguished from that found in the relaxation of certain polar molecules (e.g.SO and the hydrogen halides) where the rate shows a distinct minimum.This is attributed to the possibility of orientation under long-range forces. In the case of non- or weakly polar species the effect of the attractive well is essentially to provide a limiting collision velocity at low temperatures. A distinct relaxation-time maximum has been found in the C02(v3)-C02 and C02(v3)-C0 systems at 250 K.'07 Above this temperature the relaxation rate of the asymmetric stretch shows typical SSH-type behaviour. Similar results have been obtained for the N20 v3vibration. An interesting problim is provided by the effect of inert gases on vibrational relaxation. The spectrophone measurements of Cannemeijer and de Vries'" on relaxation of C02(v2) suggest that the rate of decrease of probability with increasing mass is less than expected on the basis of SSH-like behaviour.They find that Kr and Xe are of equal efficiency and suggest that for slow collisions reorientation can occur to a favourable 'side on' position. However other workers find Kr more efficient than Xe as is expected. An argument against the theory of Cannemeijer is that CF4 which is spherically symmetric shows similar behaviour at high collision mass.81 Toennies has found that although N2and CO are so similar Li' scattering at 7 eV produces very different vibrational inelasticity. The 0 -+ 2 transition in CO is of intensity comparable to that of =O -+ 1 whereas N shows only a 0 -+ 1 tran~ition.~' (At the energies involved the effect of the CO dipole moment must be negligible.) 8 Vibrational Relaxation in Potentially Reactive Systems In the discussion given earlier of the theory of vibrational energy-transfer processes the assumption was made that only one electronic state of the system was accessible i.e.motion was considered to be electronically adiabatic. When dealing with collisions between particles which possess closed electronic shells this assumption is justified under normal conditions. If this condition is not satisfied we must consider the following processes which are capable of effecting vibrational relaxation (i) electronic-vibrational energy transfer; (ii) relaxation by chemical reaction; (iii) the effect on relaxation of the potentially reactive intermolecular potential. That relaxation in open-shell systems is in some degree unusual is shown by the data for relaxation of molecular vibrations by free atoms; such rates are often orders of magnitude larger than corresponding rates for relaxation by molecules or by inert gases of comparable mass.84 V -+ E transfer is a potentially efficient mechanism for vibrational relaxation.It is known for example that Br2Pl is efficiently deactivated by HBr and HCl in an E -+ V process.'08 Nevertheless the reverse process will only be an efficient means of quenching vibrational energy if Br2P4 is quenched efficiently. Leone et al. studied HCI relaxation by Br2P$ and concluded that the Br2PJ is not quenched sufficiently to make V -+ E an important channel; the unusually rapid relaxation of HCI by Br must have a different origin.'" Similarly Karny and Katz have rejected V -+ E processes in HBr-Br relaxation."' However Quigley and lo7 D.F. Starr and J. K. Hancock J. Chem. Phys. 1975 63,4730. Io8 S.R.Leone and F. J. Wadarczyk J. Chem. Phys. 1974 60 314. Io9 S. R.Leone R. G. MacDonald and C. B. Moore J. Chem. Phys. 1975.63.4735. 110 Z. Karny and B. Katz Chem. Phys. 1976,14 295. The Transfer of Vibrational and Rotational Energy 29 Wolga have observed a double-exponential decay of HFfluorescence in the presence of Br2Pg which they attribute to a resonant process fast HF (v = 1 J= 5)+Br2Pg +HF (v =0 J= 6)+Br2P4 hE = -9 cm-' followed by a slow VT or E+T relaxation.'" In cases where resonant V-bE transfer is impossible such double decay is not seen. Unfortunately no analysis of the subsequent slow relaxation was given.An interesting laser fluorescence study has been made of C02(v3) relaxed by F C1,0 H D and N." The former three species have a marked effect on the rate of relaxation atomic oxygen for example relaxing the v3mode with an efficiency 100 times that of neon. By way of contrast the species H D and N had immeasurably little effect the authors estimating that their efficiencies did not exceed those of inert gases of comparable mass. It was suggested that the difference lay in the P character of the former species as opposed to the S character of the latter; it appears that the order of efficiencies C1> F>0correlates with the size of the spin-orbit splitting. The possibility of strong bonding between CO and these atoms was ruled out by the absence of significant broadening of the atomic e.s.r.lines. However Benson et al. in a flow-tube study of 'C02(v3) de- excitation have shown that Li Na K and Cs are as efficient as atomic oxygen although in ,S ~tates."~They also demonstrated that the measured rates are orders of magnitude smaller than predicted on the basis of an ionic-atomic curve crossing model. In the absence of V +E transfer one must consider that unusually rapid relaxation occurs by reaction or by virtue of some unusual feature of the potential energy surface. Smith and Ward have performed classical trajectory studies on the H-HCl and Cl-HCl systems and come to the conclusion that in the former case relaxation by atom exchange is the dominant mechanism whereas in the latter system it contri- butes only 50%.'14 The H+H system also falls in to this category of relaxation by atom exchange.Smith's conclusion of 50% reaction in Cl-HCl was based on earlier measurements of relaxation rate which have since been disputed on the basis of two independent sets of measurements by Moore et ~1."~These workers find signifi- cantly larger rates suggesting that the contribution of reactive collisions must be smaller than 5'/o. The question of the relative contributions of reactive and non-reactive pathways is a difficult one particularly as the rates of reaction are often strongly enhanced by vibrational excitation so that vibrational ground-state reaction rates are no guide to the rate in the v = 1 level. Moore et al. have also measured the rates of relaxation of HCl by Br to be 2.8~ cm3s-'molecule-' for v = 1 and 1.8x lo-' cm3s-' molecule-',for v =2.They believe that the latter process occurs mainly by reaction. The former rate is similar to that found for HBr +Br relaxation. In view of the expressed belief that C1+ HCl relaxation does not proceed by reaction it is interesting to note that the HC1-Cl rate is significantly greater of the order lo-'' cm3s-' molecule-' for Y = 1. Other systems in which reaction was believed to G. P. Quigley and G. J. Wolga J. Chem. Phys. 1975,62 4560. 112 M. I. Buchwald and G. J. Wolga J. Chem. Phys. 1975,62 2828. 113 R.C.Benson D. J. Bernard and R. E. Walker J. Chem. Phys. 1974,61 1652. 114 I. W. M. Smith and P. M. Wood Mol. Phys. 1973 25 441.R. G. MacDonald C. B. Moore I. W. M. Smith and F. J. Wodarczyk J. Chem. Phys. 107,62 2934. 30 P.D. Gait play a part included HCl +0. Recent work by Karny et al.' l6 has confirmed that the rate of reaction of 0with HCl (v = 1)is rapid [lo0 times that with HCI (u =O)] but indicates that direct deactivation is the dominant relaxation mechanism. Karny and Katz have distinguished between the efficient relaxation of HCl by Cl and Br,'I7 on the grounds that in the former (as in relaxation by 0 and H) 'chemical' forces are operative. It is not clear why reaction is impossible in the latter case and this explanation also seems to ignore the relatively low rate found for HBr-Br which is potentially reactive. Nor does it appear to agree with the results of Quigley on HF relaxation."8 Here HF is rapidly relaxed at 300 K by 0 and F (KHF-o KHF-F) whereas H has no apparent effect.This has been disputed by Kwok and Wilkins"' and by Heidner and Bott'20 who find rates of -cm3 molecule-' s-' for H-HF. As calculated barriers to reaction of HF with F and H are large (23 kcal mol-' and 40 kcal mol-' respectively) it appears that relaxation must be essentially non-reactive. HF-F relaxation has been studied up to 4000 K and the efficiency of F relative to HF increases with temperature showing an exp (ATf)type of behaviour. Low- temperature studies of the relaxation of HCI by 0and Br show a similar dependence of rate on temperature. Brown et al.showed that DCl is relaxed more efficiently than HCI at room temperature by both Br and 0.121s122 This is interesting in view of the reverse relationship found in relaxation of these isotopes by the inert gases where VR coupling is important.The opposite behaviour was found for relaxation of HF and DF by H atoms.'20 DF is relaxed more efficiently than HF by 0,C1 and F. There is no correlation of order of efficiencies (0>C1> F) with the magnitude of spin-orbit ~p1itting.l~~ High-temperature shock-tube studies of the relaxation by 0 of COY 02,and N2 have been made. Eckstrom has noted that although the latter is relaxed rapidly the rate is much less than that for CO and 02,which suggests the possible importance of atom exchange.'24 Center has made similar measurements on C02(~2).125 At 2000K 0 is ca.4 times as efficient as neon and 10 times as efficient as argon in deactivating the bending mode. There is some disagreement about the temperature dependence of the high-temperature processes; on the basis of sho~k-tube'~~ and ~-~ flowing afterglow experiments'26 it seems that T~ changes only by 10 between ~-~ 3000 and 300 K. T~ varies by only a factor of three from 4000 to 3000 K,127and ~-~ T~ according to the most recent results does not change between 1000 and 3000 K.'28 It is interesting to note that the N2-0 rates show a less steep temperature dependence and at 300 K a considerably smaller magnitude than predicted on the Ild Z. Karny B. Katz and A. Szoke Chem. Phys. Letters 1975 35 100. Z. Karny and B. Katz Chem. Phys. Letters 1976 38 382.G. P. Quigley and G. J. Wolga Chem. Phys. Letters 1974 27 276. 119 M. A. Kwok and R. L. Wilkins J. Chem. Phys. 1974,60 2189. 120 R. F. Heidner and J. F. Bott J. Chem. Phys. 1975,63 1810. R. D. H. Brown 1. W. M. Smith and S. W. J. van der Merve Chem. Phys. 1976 15 143. 122 R.D. H. Brown G. P. Glass and I. W. M. Smith Chem. Phys. Letters 1975,32 517. 123 G. P. Quigley and G. J. Wolga J. Chem. Phys. 1975 63 5263. 124 D. J. Eckstrom J. Chem. Phys. 1973,59 2787. 125 R. E. Center J. Chem. Phys. 1973 59 3523. 126 G. R. Cook M. E. Whitson and R. J. McNeal Trans.Amer. Geophys. Union 1973.54 403. 12? R. E. Center J. Chem. Phys. 1973 58 5230. 12x J. E. Breen R. B. Quy and G. P. Glass J. Chem. Phys. 1973 59 556. The Transfer of Vibrational and Rotational Energy 31 basis of a curve-crossing model [cf.CO,(v,)+metal atoms). A recent study of O3(u = 1) relaxation by 03P shows a rate two orders of magnitude larger than expected; however reactive and non-reactive channels were not disting~ished.”~ It has long been recognized that NO undergoes self-relaxation with a rate several orders of magnitude larger than expected on the basis of the vibrational quantum involved (1876 cm-l). The 211f-21-Q electronic splitting of 120 cm-’ is very much less than the vibrational quantum so that efficient V +E transfer is ruled out. Nikitin has explained such efficient transfer in terms of splitting of these electronic states in collisions;*3o when the size of the splitting is comparable to the vibrational energy efficient VHE coupling can occur.This process is characterized not only by the size of the rate in NO-NO relaxation but also by the weaker dependence on temperature compared with ‘normal’ VT processes and with the predictions of the SSH model. In NO-Ar similar splittings may be expected and Andreev has interpreted shock-tube measurements on this system in terms of non-adiabatic coupling. 13’ However Stephenson’s room-temperature measurements of NO relaxation by a variety of species show that NO does not differ greatly from CO (allowance being made for the different sizes of vibrational quanta). 132 Similar conclusions have been arrived at for the VV coupling of CH and CH3F to NO; a short-range-force model appears to describe the coupling adequately. 133 The reaction 2NO(v=1) -+ NO(v=2)+NO(u=O) proceeds at a rate almost identical with that of C0.13’ It is difficult to reconcile this work with the calculations of Andreev; the experimental work on which his arguments are based show that TNO-A~varies more slowly with temperature than predicted by SSH theory.However it must be said that the SSH model does tend to overestimate the temperature dependen~e,~ and we conclude that the NO-Ar question has yet to be settled. 9 Relaxation in Condensed Phases Liquid- and solid-state relaxation processes are of interest both in their own right and for the light they shed on related gas-phase processes. Two vibrational relaxation times may be distinguished and measured the energy relaxation time T’,which measures the decay of vibrationally excited-state popula- tions and the dephasing time T,associated with the relaxation of coherently excited Ultrasonic absorption and dispersion have been used to measure 7’but the limitations of the method are considerable partly because the high densities of the liquid phase produce very high relaxation rates.Brillouin scattering can be used to extend absorption and dispersion measurements into the hypersonic region above loloHz.’~~ Recent results obtained in this way include the observation of double 129 G. A. West R. E. Weston and G. W. Flynn Chem. Phys. Letters 1976 42 488. ‘30 E. E. Nikitin and S. Ya. Umanski Comments Atom. Mol. Phys. 1973 3 195. I3l E. A. Andreev S. Ya. Umanski and A. A. Zembekov Chem. Phys. Letters 1973 18 567.132 J. C. Stephenson J. Chem. Phys. 1973 59 1523. 133 S. M. Lee and A. M. Ronn Chem. Phys. Letters 1974,26 497. 134 A. Laubereau L. Kirschner and W. Kaiser Opt. Comm. 1973 9 182. 135 J. S. Rowlinson and M. Evans Ann. Reports (A) 1975 72 5. 32 P.D. Gait dispersion in liquid benzene the lowest mode relaxing independently of the higher- frequency modes.136 Independent studies of relaxation in liquid N and 0 using stimulated Raman excitation have been made by Renner and Maier and by Calla~ay.'~' The relaxation times are very long 1ms for 0 and 1.5 s for N, reflecting the very large vibrational quanta and the low temperatures involved. Sedlacek has compared the relaxation times of liquid- and gas-phase CCl at 300 K determined by ultra- and hyper-sonic abs~rption.'~~ After allowing for the differing densities he obtained values for the probability of vibrational deactivation of the molecule P(gas) =3.8 x lop3and P(liquid)= 2.6 X which agree well with the theoretical expression P(liquid)/P(gas) = (1+S,/ T)e-E'kT where S,.is Sutherland's constant and E the intermolecular potential well depth. The greater probability in the gas phase is attributed to the accelerating effect of the attractive well. The relaxation times of organic liquids are very short typically of the order 1-loops. Laubereau Kaiser and co-workers have studied a number of such liquids exciting molecular vibrations using both transient stimulated Raman scatter- ing and i.r. abs~rption.'~~ Relaxation of vibrational levels is followed using spon- taneous Raman scattering or optically induced fluorescence.Excitation of the CH vibrations of ethanol at 2900 cm-' relaxes with T' =22 ps; Raman spectra taken shortly after the exciting pulse show equilibration of vibrational energy amongst near-resonant CH levels in times less than 1ps.',' A study of the composition dependence of the relaxation time in CH3CC13-CC1 suggests that energy is transferred to other vibrational modes in termolecular rather than bimolecular collisions. Dephasing times (T) have also been measured following stimulated Raman excitation of coherent vibrations by probing the coherence using Raman scattering under phase-matching conditions. 14' (This is to be contrasted with the measurement of T' by spontaneous incoherent scattering.) It is generally true that T' >T although the ratio varies from 4 for CH3CC13 to 10" for N,.14 This last figure reflects the very large energy relaxation time of N (the dephasing time is 75 ps).The dephasing time essentially measures the loss of coherence amongst molecular vibrations and is attributable to fast near-resonant vibrational energy transfer. Similar information is obtainable from Raman linewidths. Interestingly a composition dependence study of the linewidths in CH,CC13-CC14 mixtures gives no indication of termolecular collision processes.134 Unusual results have been obtained by Allamandola and Nibler who studied the C,- ion in Ar and N lattices using optical double re~onance.'~~ Relaxation times in 136 K.Takagi P. K. Choi and K. Negishi Acustica 1976 34 336. I37 G. Renner and M. Maier Chem. Phys. Letters 1975 35 226. I38 M. Sedlacek Z. Phys. (A) 1975 274 99. l39 W. Kaiser and A. Laubereau 'Laser Spectroscopy,' Vol. 43 of 'Lecture Notes in Physics' Springer 1975 p. 380. I4O A. Laubereau G. Kehol and W. Kaiser Opt. Comm. 1974 11 74. 141 A. Laubereau D. von der Linde and W. Kaiser Phys. Rev. Letters 1972 28 1162. 142 A. Laubereau Chem. Phys. Letters 1974 27 600. 143 L. J. Allamandola and J. W. Nibler Chem. Phys. Letters 1974,28 335. The Transfer of Vibrational and Rotational Energy both lattices are 1.3ms for the u = 2+ 1decay and 0.3ms for u = 1+0. This is the opposite of what would be expected on the basis of a harmonic oscillator model.Despite these odd results behaviour of vibrational relaxation in solids closely parallels that of the gas phase. In a study of W transfer from ND(A 'XI) to l2C0 and 13C0in solid Ar Goodman and Brus found excellent correlation of rate of ND relaxations with energy deficit.', Significantly the hydride NH relaxed much faster than expected on the basis of the energy deficits involved suggesting that rotational degrees of freedom may be important in reducing the deficit. Vibration-vibration energy exchange has also been seen in solid N2,145 in CO-doped N2,146 and in CO in inert gas lattices studied by i.r.-induced fluores~ence.'~' Transfer from N to l2C0 depopulated the v =6 of N2 primarily which after allowance has been made for the phonon state density at 4 K correlates with the most resonant possible W process.In CO dilute in Ne or Ar the CO-CO distances are large and transfer is believed to occur by resonant dipole-induced transitions. The transfer rate from the pumped v = 1 level of CO decreases with increasing average CO-CO distance. An interest- ing parallel with CO-CO gas-phase transfer can be found here.148 If one considers a process of type co (v)+CO(v') $ co (0-1)+CO (v'+ 1) where u' >u,then k/k' =eAE'"* where AE >0 is the energy transferred to the lattice. Although hE is small at T =8 K the forward process is greatly favoured and energy is rapidly pushed to high u levels. In this experiment emission u =7+6 was observed after pumping u = 0 +1. Because of the anharmonicity population inversion is also possible and was observed for u = 2 +1.Legay et al. observed relaxation of the NH v mode excited by a Q-switched CO laser in an N lattice at 8 K.14' A 2 ps fluorescence decay time was observed. In Ar and CH lattices this decay was too fast to measure. This was interpreted as being due to molecular inversion which has been invoked to explain the very fast gas-phase relaxation time. In the N lattice it is believed that inversion cannot occur. Unfortunately theoretical work on NH has suggested that NH inversion is not an important mechanism. 150 144 J. Goodman and L. E. Brus J. Chem. Phys. 1976,65 1156. 145 K.Dressler 0.Oehler and D. A. Smith Phys. Rev. Letters 1975 34 1364. 146 W. W. Daley 0.Oehler and D. A. Smith Chem. Phys.Letters 1975 31 115. 147 H.Dubost and R. Charneau Chem. Phys. 1975,12,407. 148 J. W.Rich and C. E. Treanor Ann.Rev. Fluid.Mech. 1970,2 355. 149 L. Abonaf-Marguin H. Dubost and F. Legay Chem. Phys. Letters 1973 22,603. 150 D. F.Starr and J. C. Decius J. Chem. Phys. 1975,62 2808.

ISSN:0308-6003    

DOI:10.1039/PR9767300005

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

3 Newer Methods of Measuring Diffusion Coefficients By H. J. V. TYRRELL and P. J. WATKISS Department of Chemistry Chelsea College Manresa Road London SW3 6LX 1 Introduction Considerable advances have been made in the past thirty years in the methods available for the accurate determination of diffusion coefficients. Interfsrometric techniques of measuring changes in refractive index (e.g. by Rayleigh inter- ferometry’) or of refractive index gradients (e.g. by Gouy2 or by Savart plate interferometry3) have been developed to give precise (-0.1 O/O) values of differential interdiffusion coefficients in binary and in multi-component systems provided that they are not too dilute. Improvements based primarily on the work of stoke^,^ in the long-established diaphragm cell method have enabled comparable levels of precision to be attained by this method both for inter- and intra-diffusion coefficients.” Similar developments of the closed-end capillary method first proposed by Anderson and Saddington’ have also made this into a potentially accurate technique especially for intradiffusion studies.These together with other special techniques such as Harned’s conductometric method6 for very dilute electrolyte solutions provide a range of methods capable of handling most diffusion problems their principal disadvantages being the specialized skills required for these experiments and particularly the time involved in them. They are unsuited for rapid surveys of the diffusion properties of a wide range of solutions and can only be used for the study of stable species.Intradiff usion coefficients can be measured rapidly though with limited precision by the n.m.r. spin-echo techniq~e,~ which can be applied even to very slowly diffusing e.g.J. St L. Philpot and G. H. Cook Research (London) 1948,1,234;H. Svensson Acta Chem. Scand. 1949,3 1170; 1950,4 1329; 1951,5 72; E. Calvet and H. Patin J. Chim. Phys. 1951,54 910; L. G. Longsworth Rev. Sci. Instr. 1950 21 524; Analyt. Chem. 1951 23 346. e.g. L. J. Gosting and L. Onsager J. Amer. Chem. SOC.,1952,74 6066. ’ M. FranGon J. Opt. SOC.Amer. 1957 47 528; E. Ingelstam ibid. 1957 47 536; 0.Bryngdahl Acta Chem. Scand. 1957 11 1017. R. H. Stokes J. Amer. Chem. SOC. 1950 72 763. For a summary of modern technical aspects of diaphragm-cell studies see R.Mills and L. A. Woolf ‘The Diaphragm Cell’ Australian National University Canberra 1968. J. Anderson and K. Saddington J. Chem. SOC.,1949 S381. H. S. Harned and R.L. Nuttall J. Amer. Chem. SOC.,1947,69 736; 1949 71 1460. e.g. H. Y. Carr and E. M. Purcell Phys. Rev. 1954,94,630;K. J. Parker C. Rees and D. J. Tornlinson in ‘Diffusion Processes’ ed. J. N. Sherwood A. V. Chadwick W. M. Muir and F. L. Swinton Gordon and Breach New York 1971 Vol. 1 p. 101. * The terms ‘interdiffusion coefficient’ and ‘intradiffusion coefficient’ introduced by Mills (R. Mills,J.Phys. Chem. 1965,69,3116) and by Albright and Mills (ibid.,p. 3120) have been used throughout in preference to ‘mutual diffusion coefficient’ ‘tracer diffusion coefficient’ etc.35 36 H. J. V.Tyrrell and P. J. Watkiss species"and to multi-phase systems such as those found in many biological speci- mens. In recent years two other rapid methods have been developed the one being suitable for rapid surveys (particularly of interdiffusion coefficients) and the other being particularly suitable for the study of dilute polymer solutions including solutions of relatively unstable biological polymers. The first is based on the techniques of liquid chromatography. A solution is allowed to flow at low Reynolds number through a long narrow tube. A pulse of a solution of different composition is injected into the flowing stream at the entrance to the tube and the shape of the resulting chromatographic peak is examined at the exit of the tube.The second method depends on the extent to which the Rayleigh component of monochromatic light is broadened when scattered quasi-elastically by a dust-free solution. This broadening arises from the Brownian motion of the molecules and modern photon- correlation techniques make its detection and analysis relatively simple. This Report is concerned with the principles and some of the applications of these two methods. 2 Diffusion Coefficients from Chromatography When a pulse of dye solution is injected into a slow stream of solvent that is confined within a narrow bore tube the patch of colour is found to move along the tube as a symmetrical column of slowly increasing length. This was first observed by Griffiths,' but it was not until 1953that Taylor" commented on and explained the apparent discrepancy between this observation and the fact that for a liquid in laminar flow through a tube there is a parabolic distribution of velocities over any cross-section normal to the tube axis the fluid near the centre moving at twice the mean speed of flow.Fluid flow alone should distort the patch of colour into a parabolic form. Taylor recognized that the reason why this does not occur is that mass transport by convective flow along the tube is supplemented by diffusion both along and perpendicular to the axis of the tube. The first is unimportant in comparison with convective transport but the second has been shown by Taylor,10-12 and in a more general way by Aris,13 to be responsible for the phenomena described by Griffiths.They and other^,'^-^^ have shown that provided certain conditions are fulfilled the concentration distribution within the solute column as it passes down the tube can be used to determine the interdiff usion coefficient of a two-component solution. The most convenient arrangement to consider theoretically is that where a 6 -pulse of a solution is introduced into a stream either of pure solvent or of a solution of different composition flowing in a straight tube. The injected pulse is carried along with a velocity u (r),where r is the distance measured perpendicularly to the axis of the tube radius R. If the ratio r/R is written as z and the average velocity equal to * B. D.Boss E. 0.Stejskal and J. D. Ferry J. Phys. Chem.1967 71 1501. 9 A. Griffiths Proc. Phys. SOC.Lond. 1911 23 190. lo G. Taylor Roc.Roy. Soc. 1953 A219 186. 11 G. Taylor Roc. Roy. Soc. 1954 A223 446. G. Taylor Proc. Roy. Soc. 1954 A225,473. l3 R. his Roc. Roy. SOC.,1956 A235,67. l4 0.Levenspiel and W. K. Smith Chem. Engineering Sci. 1957,6 227. 15 R. J. Nunge R. S. Lin and W. N. Gill J. Fluid Mech. 1972 51 363. '6 E. van Andel H. Kramers and A. de Voogdt Chem. Engineering Sci.,1964,19,77;M. E. Erdogan and P. C. Chatwin J.Fluid Mech. 1967 29,465; D. J. McConalogue Roc. Roy. SOC.,1970 A315 99. Newer Methods ofMeasuring Diffusion Coefficients 37 half the maximum velocity u(O) as U,then u(r)= 2~(1-z2) (1) This velocity is measured relative to the laboratory frame and it is convenient to measure the concentration distribution relative to an axial co-ordinate x which moves with the mean fluid velocity U.The flow velocity relative to this new frame of reference ~(r), is from equation (1) v(r)=u(r)-U= ~(1-2z2) (2) The flow density along the tube axis relative to this reference plane J, is made up of a diffusive term and a convective term J = -D dc/ax + cU(1-222 (3) where D is the diffusion coefficient and c the concentration in units of mass per unit volume. The radial flow density solely diffusive is given by J = -D ac/ar = -DR ac!az (4) The concentration distribution is symmetrical about the tube axis and the correct form for the diffusion law (‘Fick’s second law’) can be found by considering the rate of accumulation of solute in a ring-shaped element of volume of inner radius r outer radius (r +dr) and thickness dx.Application of equations (3)and (4) to the rate at which solute enters and leaves this ring by mass transport along the x and r axes with the assumptions that diffusion is isotropic and that D is independent of concentra-tion gives -+-+R2-=-+__(1-2~2)_ a2C 1 ac a2c R2ac R~U ac az2 z az ax2 D at D ax (5) The operator d/dt is taken at constant x ie. at planes fixed in a frame of reference moving with velocity U relative to the laboratory. The term d2c/dx2 represents axial transport by diffusion and Taylor’’-12 has shown that this can be neglected when the pulse shape is examined after passage through a tube of length L provided that L/U >> 2R2/(3.8)2 D (4) The diffusion equation (5)then reduces to The simplest parameter to measure experimentally is the mean concentration (c,) at any selected plane in the mean-velocity reference plane.This is defined by c = 2 I,’CZ dz and Aris13 have shown that when condition (6) is fulfilled this mean concentration obeys the following differential equation ac,/at = K a2c,/ax2 (9) 38 H.J. V.Tyrrelland P.J. Watkiss This is identical with the usual form of the Fick equation for diffusion in one dimension with the diffusion coefficient replaced by the quantity K. ArisI3 proved that K =D +R2U2/48D (10) Equation (9)can be solved for the case of the injection of a 8-pulse into the flowing stream to give" (c in units of solute mass per unit volume) M C = 7rR2(27r)f (2Kt) exp [-x2/2(2~t)] where M is the mass of solute injected in the pulse.The co-ordinate x is measured relative to a frame moving with the reference velocity U.If the time taken for this reference frame to move from the point of injection a distance L down the tube to the point at which the mean concentration is being measured is denoted by <then x = u(t-ij (12) where U(t)is the corresponding co-ordinate in the laboratory-fixed frame. Equation (11)can then be transformed to M C = 7rR2(27r)4 U(2Kf/U2)i exp [-(t -7)'/2(2~t/~~)] In terms of the cross-section average mole fraction X this can be written as N X = n7rR2(27r)4U(2Kt/U2)texp [-(t -f)2/2(2Kt/U2)] where N represents the number of moles of solute injected in the pulse and n is the molar density of the flowing solution.Equations (13) and (14) are products of constant terms and a normal error curve with variance (02) of (2Kt/U2)(cf. ref. 14). Provided that all the conditions implicit in the derivation of these equations are fulfilled then the mean concentration across the tube cross-section recorded at a laboratory-fixed point should vary with time according to a Gaussian curve with the above value of the variance. Combining this with equation (10) gives u2= 2Dr//u2 +R2?/24D = [2D(ij3/L2]+[R 2F/24D] (15) The use of ;rather than t in equation (15) assumes no dispersion of the pulse through the detection point; possible effects of this are considered below. The variance skewness and kurtosis of the experimental curve can readily be determined if the concentration-time data are recorded digitaIly in a form suitable for the calculation of the first four moments of the curve;17 the last two parameters provide a method of detecting any deviations from the true Gaussian shape.This technique was first applied to the measurement of gaseous diffusivities (D-m2s-') using either packed or unpacked columns and the normal vapour chromatographic techniques.'8-21 Ouano22 seems to have been the first to use it with l7 K. C. Pratt and W. A. Wakeham. Roc. Roy. SOC.,1974 A330.393. l8 J. C. Giddings and S. L. Seager J. Chem. Phys. 1960,33 1579. l9 J. Bohemen and H. J. Purnell J. Chem.SOC.,1961,360. 2o W. A. Wakeham and D. H. Slater J. Phys. (B),1973 6 886. 21 V. R.Maynard and E. Grushka Adv. Chromatog. 1975 12 99. 22 A. C. Ouano Ind. and Eng. Chem. (Fundamentals) 1972 11 268. Newer Methods of Measuring Diffusion Coefficients 39 liquid systems. It has since been used quite extensively for the determination of interdiffusion coefficients for solutes at high dil~tion~~-~~ though as Pratt and Wakeham have ~hown,'~,~~,~~ injection of one solution into another of slightly different composition permits the determination of differential interdiff usion coeffi- cients as a function of solution composition. In principle intradiffusion coefficients can also be measured if the practical problems of detecting the distribution of an isotopically labelled species can be overcome. The interdiffusion coefficient of HDO in water has been obtained by injecting a pulse of pure D,O into a flowing stream of water and measuring the variance of the resulting chromatographic peak by differen- tial refractometry;28 values obtained over a temperature range compared well with those in the literature.Diffusion coefficients in gases (-lo-" m2s-I) are much larger than those found in liquids (-lo-' m2s-' or less). If the following values of the experimental variables (cf ref. 17) are selected L = 15 m R =4x lo-" m t=5 ks together with the above values for diffusion coefficients then the ratios of the first and second terms in equation (15) are -3 x lo5 and -3 X for gases and liquids respectively. The observed variance is therefore proportional to the diffusion coefficient for gaseous systems and inversely proportional to it for liquid systems where equation (15) can be simplified to a'= R2i/24D (16) Equations (15)and (16)were derived on the assumption that the tube was straight.This is difficult to realize in practice because of its length and it is either necessary to bend the tube into a U-shape (Ouano,22 Ouano and Carothers26) or to wind it in the form of a helix (e.g.Pratt and Wakeham'7*29). In the helical case two additional but opposing modes of mass transport need to be con~idered.'~ At different radial positions in the tube the fluid traverses different path lengths in its passage through the tube an effect which tends to increase the dispersion. In addition the helical form sets up secondary flows which decrease the dispersion.The net effect of these additional mass-transport mechanisms is that a correction term must be added to equation (10) to give (r2U2/2t=K =D +R2U2[1+ 192f(A,NRe Ns,)]/48D (17) The correction term is a function of A the ratio of the helix radius to the tube radius and NRe,N, are respectively the Reynolds and Schmidt numbers defined by NRe =2URPlr) (18) Nsc =r)/PD (19) In these equations 7 is the viscosity and p the density of the flowing liquid. As before the first term on the right of equation (17) can be omitted to give the 23 H. Komiyama and J. M. Smith J. Chem. and Eng. Data 1974 19,384. 24 E. Grushka and E. J. Kikta J. {hys. Chem. 1974,78 2297. z5 E. Grushka and E. J. Kikta J. Phys. Chem. 1975 79 2199. z6 A. C. Ouano and J.A. Carothers J. Phys. Chem. 1975 79 1314. 27 E. Grushka and E. J. Kikta J. Amer. Chem. SOC.,1976,98,443. 28 K. C. Pratt and W. A. Wakeham J. Phys. Chem. 1975,79,2198. z9 K. C. Pratt and W. A. Wakeham Proc. Roy. Soc.,1975 A342,401. H.J. V.TyrrellandP.J. Watkiss following modified version of equation (16) uz= R F[ 1 + 192f(A,NRe,N,)]/24D (20) An apparent diffusion coefficient D" can be calculated from the experimental variance [using equation (16)] that is valid for a straight tube and the proportional difference between this and the true diffusion coefficient D is from equations (16) and (20) (Da-D)/D"=-192f(A NRe,Nsc) (21) The function f tends to zero at low Reynolds numbers and an approximate form that is valid at high Reynolds numbers has been given by Nunge Lin and Gill." This form has been shown to fit remarkably well with experimental data obtained by Pratt and Wakeham on an isopropyl alcohol-water mixture (mole fraction of isopropyl alcohol = 0.3207).29For dispersion times >3 ks in their apparatus the function f was so small that it could be neglected i.e.a suitable choice of experimental variables permits the use of equation (15),even with a helical tube. A similar effect appears to have been present in the work of Ouano and Carothers with a U-shaped tube; they found the experimental values of D derived from equation (15)to vary slightly with flow rate.26 A source of error which becomes significant for systems with very low diffusion coefficients is associated with the finite volume occupied by the detection system.Even if the mean concentration across a section of the tube is normally distributed in time the signal from the concentration sensor will not be so if there is a detectable dispersion of the pulse as it passes through the sensing chamber.14 This signal will be skewed and the peak signal time twill no longer be exactly L/U,but will be slightly larger r =(L/U)(1 +2K/L U)= (L/U>(1 +2P) (22) where P is defined as K/LU. In addition the variance of the observed pulse is modified to uz=2(L/u)2P(1 +4P) (23) Equations (22) and (23) can be combined to give u2= (;)2c2~(1+4~)/(1+2p12] (24) For liquids P<<1 and equation (24) can be expanded to give [if equation (16) is used] g2=R2$24D +(R2r/24D)2 when terms of order P3or higher are neglected.Equation (25) is a quadratic in D with one physically significant real namely D =(R2~/48u2){1+[1+402/(~)2]t} (26) The correction term 4a2/(T)2can be calculated approximately from equation (16). Under normal experimental conditions it is very small when D = m2s-l but it becomes significant if D is an order of magnitude less than this. Another possible source of error is the assumption in the theoretical treatment that the injected pulse Newer Methods ofMeasuring Diffusion Coefficients is a 6-function a condition never realized in practice. Levenspiel and Smith14 have shown that the error arising from this is negligible provided that the injection sample does not exceed 1%of the volume of the diffusion tube.In practice the injected volume is usually considerably less than this. Pratt and Wakeham'7'29 estimate that the overall error in their diffusion coeffi- cients is -2.5% while Grushka and Kikta27 claim a precision of between 1and 3% depending on the system studied. The largest contribution to the experimental error lies in the determination of the ~ariance.'~.~~.~~ Pratt and Wakeham" have com- pared their values for the limiting diffusion coefficients of ethanol in water and of water in ethanol at 25 "Cwith those obtained in other ways. As can be seen from Table 1 the agreement is good in the first case and slightly less good in the second. Table 1 Limiting interdiffusion coefficients in the ethanol-water system at 25 "C (lo9D/m2s-') Ethanol1 Pram and Hammond and Dullien and mol Wakeham" Stokes Shemilt' 0.0 1.23 1.24 1.22 1.o 1.08 1.13 1.22 a K.C. Pratt and W. A Wakeham Proc. Roy. SOC.,1974 A330 393;b B. R. Hammond and R. H. Stokes Trans. Faraday SOC.,1953,49,890; F. A. L. buIlien and L. W. Shemilt Canad.J. Chem.Eng.,1961,39 242. However the literature values require to be extrapolated to obtain the limiting values and this extrapolation is less reliable in ethanol-rich Other comparisons of data derived from this chromatographic method with those derived from more conventional techniques are available for a series of phenones in benzene and in n-he~tane,~~ for benzene in chloroform,26 and for benzene and toluene in n-hexane n-heptane cycloheptane and The method clearly has great promise as a method for rapid survey and that is of moderate accuracy.It can be used even for systems in which the diffusion coefficients are lower than those normally encountered in liquid systems. Examples are the isopropyl alcohol-water where the lowest diffusion coefficient recorded was -2 X lo-'' m2s-' and for solutions of benzene and carbon tetrabromide in pr~panediol,~~ for which values as low as 5 x lo-'' m2s-' were found in agreement with those obtained by a refractometric meth~d.~~,~~ The method has the added advantage that the apparatus required can be readily adapted from the standard high-pressure liquid chromato- graphic equipment that is available in many laboratories. 3 Diffusion Coefficients by Light Scattering When a monochromatic beam of light passes through a dielectric medium there is some scattering by the molecules of the medium.The major component of the scattered light (Rayleigh scattering) has a Lorentzian intensity distribution that is 30 B. R. Hammond and R. H. Stokes Trans. Faraday SOC.,1953,49,890. 31 F. A. L. Dullien and L. W. Shemilt Canad.J. Chem. Eng. 1961 39 242. 32 P. J. Watkiss Ph.D. Thesis Univ. of London 1976. 33 M. Mitchell and H. J. V. Tyrrell J.C.S.Faraday IZ 1972,68,385;C. J. Skipp and H. J. V. Tyrrell J.C.S. Faraday I 1975,71 1744. 42 H.J. V.TyrrellandP.J. Watkiss centred on a frequency identical with that of the incident light the half-width of the band being dependent on the Brownian motion of the molecules. This motion which gives rise to local fluctuations in the dielectric susceptibility (i.e.the refractive index) that are associated with local changes in the temperature (entropy fluctuations) and in the case of multi-component systems of concentration also (diffusion fluctua- tions) is too small to be detected by conventional spectroscopic techniques.It can be studied by interferometry at the limit of performance of conventional spectroscopic technique~,~~ or by the newer techniques of photon-correlation Diffusion coefficients (especially of macromolecules in dilute solution) and thermal diffusivities can be obtained from the results. Other spectral features also occur in the scattered light (Brillouin lines Raman lines) but they are not currently of importance in connection with transport processes.Light-beating spectroscopy central to photon-correlation spectroscopy was first reported in 1955,36and its principle can easily be appreciated. Consider an optical spectrum consisting of two sharp lines with frequencies v and (v +Av) respec-ti~ely.~~ The increment Av is taken as 1O-"v where n is an arbitrary number. If these lines are to be resolved in a conventional spectrometer the optical path length Lowithin it must be large enough for the difference in path length between the two frequencies to be about one wavelength. If the wavelength corresponding to the frequency is A written as 10-"Lo this will be resolved from the wavelength A' corresponding to the frequency (v +Av)when Lo=lO"A =(10"+1)A' (27) These two frequencies will interfere the beat frequency being Av.The time (T) between successive beat maxima will be l/Av or 10%. At a given wavelength both Lo and T increase as the required degree of resolution increases i.e. as the parameter n increases. For example with A = 0.5 pm (5000A) Lo= 0.05 m T = 2 x lO-'Os when n = 5 (resolving power 1 lo5). For a resolving power of 1 lo8 however Lo= 50 m and T = 2 X s. At high resolution it is obvious that the physical dimensions required for a conventional spectrometer become unacceptably high while the time T comes into a range accessible to modern photon-counting techniques. Each component of the Doppler-broadened Rayleigh line can beat against another and the intensity of the light reaching the detector fluctuates with time (self-beat technique).An alternative is to allow the scattered light to beat against radiation from another source usually derived directly from the laser which acts as the source of the scattered light (heterodyne technique). The two methods give different information about the scattering system and the choice between them depends on circumstance^.^^ The simplest form of light-scattering theory assumes that the incident light interacts with the electrons in the system this interaction being described in terms of 34 cf.C. J. Oliver E. R. Pike and J. M. Vaughan in 'Coherence and Quantum Optics' ed. L. Mandel and E. Wolf Plenum Press London 1973. 3* 'Photon Correlation and Light Beating Spectroscopy' ed. €3. Z. Curnrnins and E. R. Pike NATO Advanced Study Institutes Series Plenum Press New York London 1974.36 A. T. Forrester R. A. Gudmundsen and P. 0.Johnson Phys. Reu. 1955 99 1691. 37 E. R. Pike ref. 35 p. 5. 38 cf. E. R. Jakeman ref. 35 p. 90. Newer Methods of Measuring Diffusion Coefficients small local changes A&(r,t) in a linear electronic dielectric susceptibility which relates fluctuations in the local polarizability @(r t) to the incident field Ei(r,t). All three quantities are functions of position (r)and time (t),and are related by 47rP(r,t) = AE(r t)Ei(r,t) (28) The total scattered field E from incident light of frequency vo is assumed to be the sum of contributions (Ej)from a number of small scattering volumes each of which scatters independently of the others so that E =CEj =CAj exp (i4j)exp (-ivot) (29) J J Ajis the amplitude of the scattering from the volume elementj at position rj,and c$~ is the phase angle between light scattered from the volume element at the arbitrary origin and that from the element centred on rj.Let the incident and the scattered fields be represented respectively by the wave-vectors ki k,. Then 4j= (ki-k,) rj =-K -rj (30) where K,the scattering waue uector is defined as (k,-ki). The wavelength change on scattering is very small and the vector magnitudes lkil lksl can therefore be written as lkilz lksl =~.~~cLIAO (31) where p is the mean refractive index of the medium and ho is the (vacuum) wavelength of the incident light. Simple vector addition shows that since lkil and lksl are almost equal then for a scattering angle of 8 IKI = 21kil sin 812 (32) Hence from equations (31) and (32) 1KI = (4wp/Ao) sin 8/2 (33) Equation (29) can be re-written using equation (30) as Es=C A exp (-iK -r,)exp (-ivot) (34) I The scattering amplitudes Aj change with time if the scattering element jchanges its structure or if anisotropic its orientation.The phase factor exp (-iK -rj),will change with time because of the motion of the centre of mass of the scatterer. Various functions of the scattered field E are accessible to experimental measure- ment as follows (i) The time-averaged intensity I,,defined as I =(Ez)= (AjAj.exp [-iK * (rj-rj.)]) (35) (ii) The field autocorrelation function G(')(T), defined as G(')(T)(Et(t)E,(tf 7)) (36) = where E is the conjugate of E,.A normalized field autocorrelation function is defined as (37) H.J. V.TyrrellandP.J. Watkiss (iii) The optical spectrum I(v) a function of the frequency v defined as I(v) = (1/27r) G(l)(r) exp (ivt) dr (38) I It can be seen that I(v)is the Fourier transform of G'~)(T). (iv) The intensity autocorrelation function G'2'(~), defined as =(E$(t)E,(t)E$(t+T)E,(~ G'2'(~) +r)) (39) A normalized intensity autocorrelation function g(2)(T)is defined as g'2'(T) = G'2'(Tj/G'2'(0)= G'2'(r)/[G'''(0)]2 (40) The time-averaged intensity I is the quantity measured in conventional measure- ments of light ~cattering.~~ For dilute solutions of identical small spherical particles measurements of I,can give the molecular weight of the scattering species.Methods have been developed to study size and shape factors; inter-particle interactions to obtain second virial coefficients and radii of gyration in addition to molecular weights. However since the experimental data are time-averaged information on transport processes is lost. The field autocorrelation function does however contain this kind of information which can in certain instances be extracted in useful form from experimental data on G(~)(T). The simplest case is that of N identical spherical scatterers each with the same time-independent scattering amplitude A. Then from the definition of G(~)(T) equation (36) and equation (34) N G(~'(T) 1A exp [iK rj(0)] A exp [-iK -rj,(7)])exp (-ivoT) (41) =(" j=l j'= 1 The positions of the scattering centres are uncorrelated if they are relatively far apart and the cross-terms in the ensemble average of equation (41) will then disappear; this will be the case for a dilute solution of strong scatterers in a dielectric medium when the following equation holds = N(AI2(exp{-iK [r(~)-r(O)]}) G")(T) exp (-ivoT) (42) If G,(R,t)is the probability that a particle located at the origin at zero time will have moved to a point R at time t (the 'self' part of the van Hove space-time correlation function) the ensemble average in equation (42) can then be written as I (exp {-iK [r(T) -r(O)]})= G,(R,t) exp (-iK R)d3R (43) The manner in which the space-time correlation function G varies with time is a fundamental question.It is always assumed that it varies in the same way as the appropriate macroscopic variable namely temperature in the case of entropy fluctuations and molar concentration in the case of composition fluctuations. Consequently for entropy fluctuations a thermal diffusivity K is defined by aG,/at =KV~G (44) 39 e.g. G. Oster Chem. Rev. 1948 43 319; J. Gen. Physiol. 1950 33 215. Newer Methods of Measuring Diffusion Coefficients 45 and this thermal diffusivity is identified with that defined by Fourier’s Law. Similarly for composition fluctuations a diffusion coefficient DT is defined by a similar equation dG,/dt =D~V~G (45) The relationship of this diffusion coefficient to inter- and intra-diffusion coefficients defined in terms of Fick’s Law is an interesting one which is discussed later.With these definitions it is possible to relate G(’)(T) either to K or to D,. For concentration fluctuations it follows from equations (42) (43),and (45) that =NIAI2exp (-DT(KI2~) G(~)(T) exp (-ivoT) (46) From equations (37) and (46) it follows that Methods for finding g(”(7) have been described by for example Jakema~~,~~ but this route is not the most convenient one for finding DT or K. The optical spectrum I(v) is defined in terms of G(’)(T) by equation (38). If this is combined with equation (46) it follows that I(v) is a Lorentzian of half-width at half-height (Avj) given in the case of concentration fluctuations by Av; =D,IKj2 =(16DTw2p2/hE)sin2 8/2 (474 In the case of entropy fluctuations the same equation applies but with DT replaced by the thermal diffusivity K.These half-widths are very small. For A. = 500 nm p = 1 and typical values of D m2s-’) and of the thermal diffusivity K (l.0-7m2s-l) for the liquid state they are respectively Concentration fluctuations 6 x lo5sin2 8/2 Hz Entropy fluctuations 6 x lo7sin2 8/2 Hz Even with a scattering angle close to 180”and a shorter wavelength the broadening due to entropy fluctuations is close to the detection limit by normal interferometric technique^,^^ and this Doppler broadening of the Rayleigh scattered line can be studied more effectively by light-beating spectroscopy. For example Berge Cal- mettes Dubois and Laj40 measured the thermal diffusivity from the Rayleigh linewidth in pure carbon disulphide where only a single Lorentzian component was observed.When about 10%of acetone was added the experimental contour of the Rayleigh line needed to be resolved into two Lorentzian components a narrow one characteristic of concentration fluctuations (from which a value of D.r could be calculated) and a broad one from which the thermal diffusivity of the mixture could be calculated albeit with a rather low precision. The normalized intensity autocorrelation function g‘2’(r) defined by equation (40) is of particular importance for two reasons. For those systems where there is a sufficiently large number of particles in the scattering volume the Siegert relationship3* is valid. This gives a simple relationship between g‘2’(T) and the normalized field autocorrelation function g(”(r),which in the form appropriate to the present model is g(*’(T)= 1 +lg‘”(T)12= 1 +exp (-2~~J~j~r) (48) 40 P.Berge P. Calmettes M. Dubois and C. Laj Phys. Rev. Letters 1970 24 89. H. J. V.Tyrrell and P. J. Watkiss Furthermore a quantity related to g"'(7) can be obtained readily from photon- correlation experiments. Equation (48) shows that if g"'(T) can be found as a function of 7,then In [g(')(T)-11 should be a linear function of T,with a slope of -2D,JW2if the simple model used here is applicable. The value of IKI' is a function of scattering angle and can be obtained from equation (33). To obtain a suitable plot it is necessary to select a suitable scattering angle i.e.a suitable value of IKI,and time intervals T in an appropriate range.The most appropriate ranges for these two parameters will differ depending on whether concentration or entropy fluctuations are being studied. Developments in the technology of integrated circuits and experience gained in the field of microwave radar4' have made it possible to design equipment now available commercially for the rapid determination of a quantity closely related to g"'(7). A block diagram of a typical digital auto~orrelator~~ used for this purpose is shown in Figure 1. The sample cell is irradiated by a monochromatic laser beam (e.g. I I Figure 1 Block diagram of a single-clipped digital autocorrelator (Redrawn by permission from Nature 1970 227 242) from a He/Ne laser) and the light that is scattered by the solution in the cell from within a small solid angle defined by two apertures falls on a photomultiplier.The resultant signal is amplified and then standardized in the discriminator to give a train of pulses corresponding to the intensity fluctuations of the light falling on the detector. The number of pulses reaching the detector in successive short time 41 For a brief popular account see E. R. Pike Physics Bulletin 1974 25,522. 42 R. Foord E. Jakeman C. Oliver E. R. Pike R. J. Blagrove E. Wood and A. R. Peacocke Nurure 1970 227 242. Newer Methods of Measuring Diffusion Coefficients intervals will vary because of the ‘self-beating’ phenomenon. If n(ti,T) is the number of photo-events detected in a time interval T centred at a time ti and n(ti +T,T)is that detected in the same time interval after a fixed period T has elapsed the product n(ti T)n(ti +T T) can be calculated and stored.If this process is repeated M times then the average value of the product namely is an estimate of the ensemble average (n(O)n(T)); cf. equation (39). For an ideal source free from all correlations this ensemble average is fi2,where ii is the average number of photons reaching the detector in the time interval T. The ratio is identical with the normalized intensity autocorrelation function g‘2’(T)defined by equation (40). It would be prohibitively expensive to obtain this function from photon counts but an almost equivalent quantity the single -channel clipped autocorrelation function gf)(7),can be obtained using simple binary The following quantities can be defined for integral values of the ‘clipping level’ q n,(ti T)= 1 if n(ti,T)>q (5la) n,(t, T)=0 if n(ti T)sq (51b) The new autocorrelation function gF)(T)is defined as gj12)(7)= nq(ti T)n(ti +T T)/(nq)(n) (52) In practice the train of pulses reaching one channel is passed through a limiter (Figure l) which only gives an output if more than the pre-set ‘clipping level’ q of photons arrive in the sampling time T.The clipped signal nq(0)is then moved sequentially down the shift register by a clock which determines the sample time T and is cross-correlated with the original signal. The information is stored in such a way that the content of the channel number S of the store is the product n,(O)n(ST).The counting process is repeated M times and at the end of the operation the contents of channel S will be M2(nq(Oh (ST)) (53) The total number of photon events is M(n),and the total number of clipped counts is M(n,). Both these are recorded and the product M2(nq)(n)is calculated. The ratio of the contents of channel S to this product is from equations (52) and (53),equal to gF’(ST). For the model of a dilute solution of identical spherical scatterers it can be that the following modified form of equation (48) is valid gy’(ST)= 1+a exp [-~D,JK~~(sT)] (54) where a is a quantity that is independent ofthe product ST i.e. independent of T. H.J. V.Tyrrell and P.J. Watkiss Equation (54) shows that a plot of In [gF’(ST)-13against the channel number S should be linear with a slope of (-2DTIKI2T).However both the sample time T and IKI,which is a function of wavelength refractive index and scattering angle need to be chosen with care.Equation (54) demonstrates that gf’(ST) varies between (1+a),when the exponent of the exponential term is small and 1,when it is large. If the product (2DTIKl2T) is either very small or very large the experimental autocor- relation function will not be a sensitive function of channel number. This can be seen from curves (i) and (ii) in Figure 2. If 2D,T is of the order lKl-2,then &’(ST) will Channel number S Figure 2 Variation of clipped autocorrelation function with channel number. Curve (i) 2DTT very small Curve (ii) 2DTT= l/lK(* Curve (iii) 2DTT very large vary rapidly with channel number as can be seen from curve (ii) in Figure 2.If for example a dilute protein solution is under study the diffusion coefficient will typically be about 10-’om2s-’. If the scattering angle is 90° the refractive index about one and the wavelength of the light is 500 nm then IKI is 1.78X lo7m-* or IKI’ is 3.2 x 1014 m-2. To obtain a regression line of unit slope in the logarithmic plot equation (54) shows that for this particular experiment it would be necessary to choose T to satisfy the relationship 2~~y3.2 = x 101~)1 The appropriate value of T is therefore ca. 16ps. As the scattering angle is reduced from 90° the optimum interval for any given value of DT increases.This example refers to scattering caused by fluctuations in the local concentration of a dilute solution of strongly scattering solute molecules. In principle it should also be possible to detect entropy fluctuations whose rate would be determined by the thermal diffusivity of the medium. Equation (54) would apply with the diffusion coefficient DT replaced by the thermal diffusivity K. For dilute aqueous solutions this Newer Methods of Measuring Diffusion Coefficients 49 is about 140times the value of DT used in the above calculation and the appropriate time interval would be reduced to 30 ns at a scattering angle of 90". This is rather below the practical limit (in currently available instruments T can be varied upwards from 50ns) but could be made longer simply by reducing the scattering angle.Oliver Pike and Va~ghan~~ have successfully measured the thermal diff usivity of carbon tetrachloride by Rayleigh scattering using the photon-counting technique described here but with heterodyne beating. A suitable time interval was selected and the scattering angle was varied. The principal problem in work of this kind is the weak scattering associated with entropy fluctuations and the need for reducing unwanted scattering by dust particles etc. to a very low The method does however show some promise for the rapid measurement of thermal diffusivities free from many of the problems associated with conventional methods. The thermal diff usivity and diffusion coefficients obtained from light-scattering experiments are defined by equations (44)and (45)in terms of the rate of regression with time of the microscopic variable G,(R,t).This refers to the probability of the movement of a particle relative to a laboratory-fixed frame of reference. The idea that macroscopic variables such as concentration and temperature regress with time according to the same phenomenological laws as microscopic variables such as G,(R,t) is central to Onsager thermodynamic^,^^ and the Onsager mobility coeffi- cients can be related precisely to intra- and inter-diffusion coefficients defined in an unequivocal manner.45746 The model used in the form of light-scattering theory discussed above corresponds to a dilute solution of a strongly scattering solute in a solvent medium.For such a solution the distinction between the interdiffusion coefficient of the binary system and the intradiffusion coefficient of the solute becomes unimportant because both coefficients then tend to the same value.46 If the simple model used in the theory is adequate for the solution being studied the experimental quantity In [g(2)(7)-11 should be a linear function of 7. The parameter DTobtained from the slope of this regression plot should be independent of scattering angle. If so it can be identified as the normal diffusion coefficient for a dilute solution. The question of whether it is an inter- or an intra-diffusion coefficient does not arise since in this example they are indistinguishable. The most obviously attractive field of application of photon-correlation tech-niques to diffusion is to systems containing macromolecules especially where these are of biological origin and equation (54)has been found to be valid (within the limits of experimental error) for many of these including for example preparations of virus particle^.^"^^ C~mmins~~ has summarized work in this field up to the middle of 1973and the method clearly has real advantages.Provided that the molecule can be regarded as spherical so that equation (54)should apply the method is reasona- bly precise. The maximum precision obtainable for DT is f1'/o if the error in the scattering angle is $*0.5". When dilute solutions are used the results are not 43 M. Corti and V. Degiorgio J. Phys. (C) 1975,8 953.44 S. R. de Groot and P. Mazur "on-Equilibrium Thermodynamics' North Holland Amsterdam 1962. 45 D. G. Miller Chem. Rev. 1960,60 15; J. Phys. Chem. 1966,70 2639. 46 H. J. V. Tyrrell 'Diffusion and Heat Flow in Liquids' Butterworth London 1960. 47 P. N. Pusey ref. 35 p. 389. 4R P. N. Pusey D. E. Koppel D. W. Schaefer R. D. Camerini-Otero S. H. Koenig Biochemistry 1974,13 952; R. D. Camerini-Otero P. N. Pusey D. E. Koppel D. W. Schaefer and R. M. Franklin ibid. p. 960. 49 H. Z. Cummins ref. 35 p. 312. 50 H.J. V.TyrrellandP.J. Watkiss usually quite as good as this but even in the worst cases the error range in DTdoes not exceed *4% if the sample number A4 is sufficiently large i.e.,if the experiment is continued for a sufficiently long time.For example the diffusion coefficient of lysozyme at a concentration of 3 mg ml-’ in O.1M-NCl buffered with O.OlM- phosphate was measured to this precision in two In less dilute solutions the experiment times that are required are much less; a particular advantage if relatively unstable substances are to be examined. The total amount of material needed is small since the diffusion cells which are very simple in design require only 1 or 2 ml of solution. There are no problems associated with the production of a sharp initial diffusion boundary at some definite zero of time as in the usual optical methods and there is no need for stringent temperature or vibration control. Concentration fluctuations can be detected in solutions of smaller molecules. For example autocorrelation functions have beeri measured for approximately molar solutions of aqueous zinc sulphate manganous sulphate and caesium fluoride which can be interpreted in terms of ‘effective diffusion coefficient^',^^*^^ using equation (54).These represent weighted averages of the diffusion coefficients (not closely defined) of all the scattering species present (ions ion-pairs and possibly neutral salt molecules) and cannot be related to the diffusion coefficients of the individual species. This is an inherent weakness of the method. Equation (48) and consequently equation (54) can break down for several reasons. If the solution is not dilute the motions of the molecules become correlated and in this event the cross-terms in the ensemble average of equation (41) do not disappear.In physical terms the motion of a scattering molecule is only partly due to random Brownian motion; part must arise from the interactions with others. Application of equation (54) to the light-scattering data should in principle lead to values of DTwhich depend upon the magnitude of the scattering vector IKI though this dependence is very small in normal circ~mstances.~~ A more important cause of the failure of equation (48) especially where macromolecules are being studied is polydispersivity. The scattering from each solute component in the mixed solution will provide a separate exponential term in the decay rate of the normalized field autocorrelation function g(l’(7). In dilute solutions each solute component can be regarded as contributing a decay rate independently of the others but this is no longer true in more concentrated solutions just as it is incorrect to define an independent Fick Law diffusion coefficient for each solute in such a mixed solution (cf.ref. 46 p. 40). This has been clearly demonstrated by PhilliesS2 for a three- component solution (A+B +solvent). Two exponential decay modes are present even if one of the solute components (B) has a zero scattering intensity because of the correlation of the motions of molecules of A with those of B. In practice the interpretation of quasi-elastic light scattering from polydisperse solutions is not easy since the number of species present is usually unknown and may be hard to define. A detailed discussion of possible approaches has been given by P~sey,~’ who recommends the following technique.For a single solute equation 50 J. H. R.Clarke G. J. Hills C. J. Oliver and J. M. Vaughan J. Chem. Phys. 1974 61 2810. 5l G. D. J. Phillies J. Chem. Phys. 1974 60 976. 52 G. D. J. Phillies J. Chem. Phys. 1974,60 983. Newer Methods of Measuring Diffusion Coefficients 51 (54) can be re-written as [gj12)(7)-11' = at exp (-11~1~1~7)=a;exp (-rT) (35) where r =DTIKl2.For a polydisperse system the exponential term in equation (55)is expanded about a mean value (I;)of r?defined as where G(T)is the appropriate normalized distribution of decay rates. Equation (55) then becomes [gF)(T)-11' =a' eXp (-rT[1 +.4,T2/2!-.k3T3/3! +&4T4/4!. . . I} (57) where Aiis the ithmoment of the distribution G(T) about this mean r -.h!/~,(f'T)~/3!(T)~+(.h!4-3&3(TT)~/4!(1;)~ (59) For many systems providing that TT,, <4,equation (59)is rapidly convergent and a three- or four-term polynomial will suffice to fit the data.Pusey4' recommends an empirical approach assuming first a linear then a quadratic then a cubic equation etc.,testing the fit of each in turn. Other methods are possible but that outlined here requires a minimum of a priori assumptions. With particularly complex systems some form of initial separation of the fractions by electrophoresis by sedimentation or in other ways can be helpful. The mean that is defined by equation (56)can be related to a mean diffusion coefficient DTby defining this as r/lK12.For non-interacting particles that are small in comparison with l/lKl the mean intensity of light scattered by Ni molecules of mass Mi, is N,M?,53and hence G(T,)=N,M?/C NiM? (60) each species being assumed to have the same refractive index increment.Since Ti can be written as DilK12,where Di is defined as the diffusion coefficient of species i it follows that DT =C N,M?Di/(C NiMT) (61) This is the z-average diffusion coeficient which can be combined with the Svedberg sedimentation coefficient to give a weight-average molecular weight. The second moment A2is a measure of the polydispersivity of the system but a meaningful estimate of this parameter can only be obtained from experimental data of very high precision. For non-spherical scatterers which are small enough for the scattering amplitude A [equation (29)]to be independent of orientation and which at the same time are 53 C.Tanford 'Physical Chemistry of Macromolecules' John Wiley New York London 1961 p. 278. H.J. V.Tyrrell and P.J. Watkiss optically isotropic the theory developed for spherical scatterers is valid. In other cases the scattered spectrum depends on rotational as well as translational diffusion. For certain specific models such as rod-like molecules the relationship between the experimental scattering function and the rotational and translational diffusion coefficients can be deduced,49 but much experimental and theoretical work remains to be done if the light-scattering behaviour of systems other than simple ones is to be fully understood.It has already been stated that the problem of the relationship of the light- scattering diffusion coefficient DT to inter- and intra-diff usion coefficients defined in terms of Fick’s Law is unimportant in practice for experiments with dilute solutions. However even for a solution of a single solute concentration fluctuations arise and disappear not by the movement of the solute alone but by co-operative movement of both solute and solvent molecules. Phillie~~~ has shown theoretically that the decay rate for scattering by solute molecules is affected by the presence of non-scattering molecules of another species and has argued cogently that DT is equivalent to an interdiff usion coefficient. In an attempt to check this conclusion experimentally Phillies Benedek and have compared light-scattering diffusion coefficients measured for solutions of bovine serum albumin with solute intradiffusion coeffi- cients (D;),determined inde~endently.~~ A quite different concentration depen- dence was found for the two coefficients indicating that DT is not to be identified with the solute intradiffusion coefficient.They also argued that if D can be identified with the interdiffusion coefficient it should be related to the solute intradiffusion coefficient by In this equation T is the osmotic pressure c2 and 42 are respectively the molar concentration and volume fraction of solute and y2 is the solute activity coefficient on the molar scale. Equation (62) is not strictly and the claim54 that the data obtained provide firm evidence for the identification of DT with the Fick Law interdiffusion coefficient is not well substantiated.Similar studies on a simpler solute-solvent system would be useful but it is essential to remember that there are three independent diffusion coefficients (one inter- and two intra-diff usion coeffi- cients) for a two-component solution and that there is no generally applicable relation between them.57 54 G. D. J. Phillies G. B. Benedek and N. A. Mazer J. Chem. Phys. 1976 65 1883. 55 K. H. Keller E. R. Canales and S. I. Yum J. Phys. Chem. 1971,75 379. 56 R. W. Laity J. Phys. Chem. 1959 63 80; P. J. Dunlop ibid. 1964,68 26. 57 H. J. V. Tyrrell J. Chem. Soc. 1963 1599.

ISSN:0308-6003    

DOI:10.1039/PR9767300035

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

4 Chiral Systems By S. F. MASON Depaflment of Chemistry Kings College London WC2R 2LS Dissymmetric molecules are characterized by two sets of distinctive properties. The first group is made up of the various types of chiral discrimination displayed by enantiomeric and diastereomeric substances and the second group relates to the several aspects of optical activity. As yet there are only tenuous relations between the two sets of properties although significant connections have been indicated in theoretical studies of chiral discriminations. These studies and related experimental investigations have been reviewed recently’ and they are only briefly summarized here. The present Report is devoted mainly to recent advances within the individual fields of optical activity and chiral differentiations.In general the studies of chiral systems discussed are complementary to those covered in Annual Reports over recent years notably the application of chiroptical methods to organic stereochemistry . PARTI Chiral Discriminations 1 Enantiomeric Interactions Up to the time of Pasteur enantiomers were termed ‘physical isomers’ as they appeared to be chemically identical and were distinguishable only by the sign of their optical rotation. By 1860Pasteur had identified three types of dissymmetric discrimi- nation.* These were (i) the discovery of diastereomeric substances (+)-A(+)-B and (-)-A( +)-B with different solubilities and other properties affording a general chemical procedure for the isolation of optical isomers; (ii) a biochemical selectivity between enantiomers was established by the degradation of specifically (+)-tartaric acid from the racemate by Penicillium glaucum; (iii) it was found that while the majority of racemates crystallize as such a small proportion form optically pure enantiomorphous crystals which are separable by hand-picking.Subsequent studies have shown that stabilizing d-1 enantiomeric interactions in the solid state are strongly preferred and that of the numerous racemates investi- gated there are only some 200 cases known of spontaneous resolution by crystalliza- tion either from the melt or from ~olution.~ Spontaneous resolutions by crystalliza- tion are represented notably by the amino-acids and their derivatives4*’ in the D.P. Craig and D. P. Mellor Topics Current Chem. 1976,63 1. S. F. Mason Topics Stereochem. 1976,9 1. M. Leclercq A. Collet and J. Jacques Tetrahedron 1976,32 821. R. M. Secor Chem. Rev. 1963,63,297. 5 H. Nohira K. Watanabe and M. Kurokawa Chem. Letters 1976 299. 53 54 S. F. Mason organic field and in co-ordination chemistry by the ethylenediamine complexes cis-[M(en),X,]Y (M= Cr'" or CoIII X =NO2-or X2=oxalate and Y =halide).6 A recent thermodynamic study3 shows that the free energy change AG* in the formation of racemic crystals from an equimolecular mixture of the crystals of the corresponding (+)-and (-)-antipodes lies in the range 0 to -8 kJ mol-' and is proportional to the difference between the melting point of the racemate and that of the antipodes rR-FAfor a wide range of organic compounds.The formation of the racemate from the enantiomers is generally exothermic and in the majority of cases the racemate crystal is theoretically in equilibrium with the conglomerate of active crystals only at a virtual transition temperature To,i.e. To>FR. The theoretical transition temperature Tois represented approximately by the ratio of the enthalpy to the entropy for the formation of the solid racemate from the corresponding conglomerate of active crystals (AHe/AS*) and in the rare cases where To<rRand the substance is optically labile crystals of a single enantiomer are afforded by judicious seeding of the melt. A notable example studied in detailY7 is 1,l'- binaphthyl where the eutectic of active crystals melts at 158 "C and the racemate is metastable from the transition temperature To-76 "C to the melting point rR= 145"C.Seeding of the melt at 150°C with S-(+)-or R-(-)-1,l'-binaphthyl provides yields of up to 100% of the (+)-or the (-)-antipode re~pectively.~ In the study of crystallization from the melt it was assumed that the ther- modynamic properties of a racemate and of the corresponding enantiomers are effectively equivaknt in the fluid phase^.^ Enantiomeric interactions in solution are substantially weaker (-J mol-') than in the solid phase (-kJ mol-') and in some cases exhibit a converse discrimination. Measurements of the heat of mixing of aqueous (+)-and (-)-tartaric solutions give an enthalpy of mixing at 25.6 "C of +1.9J mol-' showing that the d-1 contacts are energetically less stable than the d-d or 1-1 contacts in solution.8 In the tartaric acid crystal however the racemic d-1 contacts are preferred.In contrast the mixing of aqueous solutions of (+)-and (-)-threonine is exothermic* (AHM= -5.4 J mol-' at 25.6 "C) but again the prefer- red contacts in solution (d-1) are the converse of those for the solid state (d-d and 1-Z) since (& )-threonine crystallizes from aqueous solution as a conglomerate of individual (+)-and (-)-cry~tals.~ The influence of antipodal interactions in solution upon the product ratio of reaction has been discussed recently.' The LiAlH reduction of (+)-camphor and of (*)-camphor under the same conditions yields isoborneol and borneol in the ratio of 9.20 and of 7.85 respectively.' Similar discriminations are found in the ratios of geometrical isomers produced in the dimerization reactions of an enantiomer and of the corresponding racemate.' The equilibrium ratios of the Eel to ob isomers of the tris-complexes formed by cobalt(II1) with (-)-trans-l(R),2(R)-cyclohexanediamine and with the corresponding racemic diamine also differ significantly the ratios having the values" of 13.72 and 14.37 respectively for aqueous solution at 100 "C K.Yamanari J. Hidaka and Y. Shimura Bull. Chem. SOC.Japan 1973,46 3724. 7 K. R. Wilson and R. E. Pinock J. Amer. Chem. SOC.,1975,97 1474. 8 S. Takagi R. Fujishiro and K. Amaya Chem. Comm. 1968,480. 9 H. Wynberg and B. Feringa Tetrahedron 1976 32 2831. lo S.E. Harnung B. S. S~rensen,I. Creaser H. Maegaard U. Pfenninger and C. E. Schaffer Inorg. Chem. 1976 15 2123. Chiral Systems with a charcoal catalyst. The interconversion of the isomers is essentially a 'racemiza- tion' reaction involving the transformation A-lel,~A-ob3 in the case of the [Co{(-)-chxn),l3+ complexes. A possible basis for the observed discrimination is provided by a study of the racemization rate of aqueous (+)-[Co(en),]I catalysed by carbon black," showing that the surface reaction follows the third-order rate law with k =3.5 X dm6 molW2 s-' at 40 "C. k[C~(en),~']~[I-] 2 DiastereomericInteractions It has long been recognized that the discrimination between diastereomers (+)-A(+)-B and (-)-A( +)-By is generally more considerable and complete than that differentiating like from unlike pairs in enantiomeric interactions.Dias- tereomeric discrimination energies in solution are commonly of the same order (-kJ mol-') as those differentiating d-l from d-d or 1-1 enantiomeric pairs in the solid state e.g. the differentiation between the antipodes of a chiral ammonium ion by a dissymmetric crown ether in solution.'2 The basic model for diastereomeric discriminations remainsI2 the 'key-and-lock hypothesis of Fi~cher'~ in which it is postulated that a more compact fit is sterically allowed between the two chiral species in one of the diastereomers than in the other. The model is supported by recent X-ray crystal structure analyses14 of the less soluble diastereomers formed by racemic ethylenediamine transition-metal complexes with (+)-tartaric acid (+)-Li[Cr(en),][( +)-tart],,3H20; (+)-[Co(en),]Br[( +)-tart],SH,O; (+)-H[Co(en),][( +)-tartI2,3H2O; and (+)-[Co(en),(ox)][( +)-tart],H,O; together with (f)-[Co(en),],[( ~)-tart],,lOH,O.In all of these cases the two glycollic hydroxy-groups and one of the carboxylate groups of a tartrate ion hydrogen-bond to three ligand atoms forming an exposed triangular face of the co-ordination octahedron in the neighbouring complex ion while the second carboxylate group acts as a chiral steric discriminator. For the (+)-tartrate ion the discriminating carboxylate group is sterically conformable only with the left-handed propellor isomer of the complex ion the A-configuration the non- bonding contact repulsions being prohibitive for the A-isomer.l4 The diastereomeric discrimination between the optical isomers of [Co(en),l3' and related complexes by (+)-tartrate and its derivatives extend with attenuation to the liquid phase. The ion-association constant [ML]/[M][L] of the (+)-tartrate ion (L) with the complex ion (M) in aqueous solution has the value" of 26 and 22 1-' mol for A-( +)-and A-( -)-[Co(en),l3+ respectively and the mobility of the A-( -)-isomer from conductivity studies is 1.7% larger than that of the A-(+)-complex ion in 3X M aqueous sodium (+)-tartrate.16 The viscosity coefficient of aqueous [Co(en),]CI containing 0.5 M (+)-diethyltartrate is 8% larger for the A-(+)-than the A-( -)-complex ion and in the neat liquid (+)-diethyltartrate the solubility ratio A-(+)-isomer/A-(-)-isomer of the complex salt has the value" of 4.2 at 25 "C and P.D. Totterdell and M. Spiro J.C.S. Faraday Z 1976,72 1477. l2 M. Newcomb R. C. Helgeson and D. J. Cram J. Amer. Chem. Soc. 1974,96,7367. l3 E. Fischer Chem. Ber. 1899 32 3617. l4 Y. Kushi M. Kuramoto and H. Yoneda Chem. Letters 1976 135 339 663 1133; Abstracts XVII I.C.C.C.,Hamburg 1976 p. 320. l5 B. Norden Acta Chem. Scand. 1972,26 11 1; K. Ogino Bul. Chem. Soc. Japan 1969,42,447. l6 L. J. Parkhurst and R. W. Kunze J. Amer. Chem. Soc. 1964,86 300. M. Yarnamoto and Y. Yamamoto Znorg. Nuclear Chem. Letters 1975 11 833. 56 S. F. Mason of 3.5 at 35 "C. The preferred association in solution between (+)-diethyltartrate or (+)-tartrate and the A-isomer of a tris-chelate co-ordination compound indicated by these data for [Co(en),13' extends more generally to anionic neutral and other cationic complexes,'8 notably the oxalates K3[M(ox),] (M =Cr'" or Co"') the pentane-2,4-dionates [M(pd),] (M =Cr"' Co'" Rh'" or Ru"') and the 2,2'- bipyridyl and the 1,lO-phenanthroline complexes [Ni(bipy),]Cl and [Ni(phen),]Cl,.A steric model has been proposed" for the preferred A-(-)-diastereomer formed by [Ni(phen),12' with (-)-2,3-butanediol in the neat glycol as solvent. 3 Origins of Chiral Discriminations The dispersion energy between two enantiomeric molecules randomly oriented in the gas phase was shown to be non-equivalent for a d-d and a d-1 pair by Mavroyannis and Stephen." More recently Craig and co-workers' have extended the investigation to fixed and semi-locked orientations of chiral systems and to electrostatic inductive and resonance interactions.21*22 While these interactions are important at moderate and long range outside the contact region the non-bonding repulsions dependent on R-12 are dominant at short range and govern crystal packing determining whether the racemic crystal or the conglomerate of active crystals is the more stable.The short-range contact interactions have been studied in two ways. First the enantiomeric interactions between the d-1 groups of meso -butane-2,3-dinitrile and between the d-d or the 1-1 groups of the active isomer have been calculated ab inirio as a function of the dihedral angle between the two groups in order to afford a measure of the short-range forces which provide the chiral intramolecular discrimi- nation between the meso and the active isomers.23 The results of the calculations which support those of a simpler pairwise additivity procedure suitable for general appli~ation,'~ show that the meso form is more stable than the racemic isomer by 3.1 kJ mol-' at 0 K or 3.6 kJ mol-' at 300 K.That is the short-range forces favour the intramolecular d-1 pair in the meso-isomer of butane-2,3-dinitrile just as the intermolecular analogues generally favour by a comparable energy the racemic crystal over the corresponding active conglomerate. In a second approach to the problem of chiral discrimination by the short-range forces the differential packing of d-1 and d-d assemblies of enantiomeric systems in a confined volume has been analysed in terms of contacts between hard surfaces in order to determine the effective volume occupied by each type of assembly.' The analysis at present limited to a 'flatland' model in which two-dimensional projec- tions of enantiomers form assemblies confined to a bounded area shows that the d-d or 1-1 assembly is the more compact with an excluded volume or excluded area in projection some 0.1-0.3% smaller than that of the corresponding d-E assembly.' 18 S.F. Mason R. D. Peacock and T. Prosperi J.C.S. Dalton 1977 in press; and unpublished results. 19 B. Bosnich and D. W. Watts Inorg. Chem. 1975,14 47. 20 C. Mavroyannis and M. J. Stephen Mol. Phys. 1962,5 629.21 D. P. Craig E. A. Power and T. Thirunamachandran Proc. Roy. SOC.,197I A322 165. 22 D. P. Craig and P. E. Schipper Proc. Roy. SOC.,1975 A342 19. 23 D. P. Craig L. Radom and P. J. Stiles Proc. Roy. SOC.,1975 A343 1 11. Chiral Systems 57 The analysis is supported by recent crystal structure determination^.^^ The (+ )-isomer of 2,2,5,5-tetramethyl-3-hydroxypyrrolidinenitroxide forms quasi-ideal solid solutions with the (-)-isomer the melting point remaining 126 "C throughout the composition range.24 The (+)-isomer and the pseudo racemate crystallize in the related orthorhombic space groups p2,2,2 and Cmcrn respectively with nearly identical unit cells which contain four molecules in each case. However the crystal of the (+)-isomer is slightly more compact with a unit cell volume of 926 A3,compared with the corresponding volume of 938 for the pseudo racemate solid In the gas phase chiral discriminations originating from dispersion inductive and electrostatic interactions are expected to be significant.' For a d-d pair of enantiom- ers randomly oriented in the gas phase and separated by the distance R the discriminating dispersion energy term is given by equation (1),20.21where Ron refers to the rotational strength of the electronic transition $, -+$, with the energy Eonin each of the molecules a and b.Equation (1) is restricted to a single excited state and in general a sum is taken over all excited states. If the molecules a and b are a d-d or 1-1 pair the rotational strengths have the same sign but for the corresponding d-Z pair the signs are opposed and the chiral discrimination energy is double the quantity given by equation (1).Thus like enantiomers repel whereas the corresponding unlike antipodes attract.The discrimination is small representing some 10-3-10-4 of the total dispersion energy.2' For the semi-locked case where two dipolar enantiomers adopt a preferred mutual orientation with the dipoles head-to-tail but rotate about the orientation axis the chiral discrimination energy due to dispersion forces becomes an order of magnitude larger. In the fixed orientation case the discrimination becomes still larger,l attaining values -J mol-' with a total dispersion energy -kJ mol-'. Electrostatic chiral discriminations require in an enantiomer of rotational sym- metry C,,a charge distribution corresponding to a minimum of two multipoles (2"-poles) one of order n and the other of order (n+ l),e.g.the dipole pzand the quadrupole components (& f&) afford antipodal charge distributions in a molecule of Cl symmetry.22 Two such molecules randomly oriented in the gas phase give a negligible chiral discrimination but with fixed mutual orientation or semi- locked with a common z-axis arising from the head-to-tail attraction of the two dipoles the electrostatic chiral discriminoation energy attains values22 of -300 J mol-' for quadrupole moments -1e A* and an intermolecular separation of -5 A. 4 Photo-discriminations The photochemical discrimination between enantiomers by circularly polarized light predicted by Le Be1,2 has been recently reviewed.25 The optical or the chemical yield of the discrimination is generally small being essentially bounded by Kuhn's dissymmetry factor g given by equation (2) where E is the extinction coefficient Z4 B.Chion J. LajzCrowicz A. Collet and J. Jacques Actu Cryst. 1976 B32 339. 25 0.Buchardt Angew. Chem. Internut. Edn. 1974,13 179. 58 S.F. Mason and Ronand Donare respectively the rotational strength and the dipole strength of an electronic transition in the enantiomer with a frequency vOnat or within the band-width of that of the radiation. In randomly oriented assemblies the g-factor is commonly of the order of lop3for electric-dipole transitions giving strong absorp- tion and the factor rarely exceeds 10% in the most favourable case of a weak absorption due to a magnetic-dipole transition.For the photoresolution of a racemate proceeding to a photostationary state or to photostable chiral products the maximum optical yield expected is g/2 but in the corresponding photodecomposi- tion reaction the optical purity of the residual enantiomer increases towards 100%as the photolysis goes to completion i.e.,as the chemical yield decreases to zero.25 g = (&L-ER)/E '4R0n/Don (2) In the multistage dissymmetric photosynthesis of chiral helicenes from 1,2-diarylethylene derivatives optical yields up to 2% and chemical yields of some 85% have been rep~rted.~~,~~ The photoresolution of tris-chelate complexes of chromium(II1) has been extensively ~tudied,*~.~~ particularly the P-diketonates which are generally photostable in aromatic solvents and have a g-factor of some 10% at 500 nm.Irradiated with an argon ion laser the latter complexes attain the photostationary state of partial resolution in a few minutes.28 Methods have been developed for deriving the c.d. spectrum of the optically pure enantiomer from the corresponding spectrum of the partly resolved racemate in the photostationary ~tate,~~.~' and the treatment has been extended to the differential photolysis of the enantiomers in a racemate employing the c.d. spectrum of maximum amplitude observed during the course of the photodecomposition as a basis.29 PART 11 Optical Activity 1 New Fields The study of optical activity by absorption (c.d.) and dispersion (0.r.d.) measure- ments over the visible and quartz U.V.region has been augmented over the past few years by extensions of the spectral range covered to the vacuum ultraviolet (v.u. c.d.) and to the infrared (Lr. c.d.) regions and by the development of techniques for the measurement of circular polarization in the emission of radiation by chiral molecules (c.p.e.) and of the circular intensity differential (c.i.d.) in the Rayleigh and Raman scattering. The substantial progress achieved in the development of both the theoretical and experimental aspects of Raman c.i.d. has been re~iewed,~' as have V.U. c.d. and the general theory of optical acti~ity.~',~~ The theory of two-photon optical activity has been discu~sed,~~,~~ including that of a coupled 26 A.Moradpour H. Kagan M. Baer G. Morren and R. H. Martin Tetrahedron 1975 31 2139. 27 K. L. Stevenson and R. L. Baker Znorg. Chem. 1976 17 1086. 28 H. Yoneda U. Sakaguchi and Y. Nakashima Bull. Chem. SOC. Japan 1975,48 1200. 29 R. Blume H. Rau and 0.Schuster J. Amer. Chem. Soc. 1976,98 6583. 3" L. D. Barron and A. D. Buckingham Ann. Rev. Phys. Chem. 1975,26 381. 31 E. S. Pysh Ann. Rev. Biophys. Bioengineering 1976 5 63. 32 A. D. Buckingham and P. J. Stiles Accounts Chem. Res. 1974 7 258. '3 J. A. Schellman Chem. Rev. 1975,75 323. 34 E. A. Power J. Chem. Phys. 1975 63 1348; G. G. Adonts and L. M. Kocharyan Optics and Spectroscopy 1976 40 410. '5 I. Tinoco jun. J. Chem. Phys. 1975 62 1006. Chiral Systems 59 two-chromophore system.36 The effect is expected to be detectable3' both by direct c.d.absorption and by an indirect method which uses fluorescence as a measure of c.d. ab~orption.~~ The measurement provides three new structure-related polariza- bility parameters which contribute to the c.d. with weights dependent upon the relative polarization and propagation direction of the two 2 Luminescence Studies In the fluorescence-detected c.d. technique a sample is irradiated with modulated left and right circularly polarized radiation and the total fluorescence emitted at 90" to the excitation direction isolated from scattered light by a cut-off filter is moni- t~red.~~ The ratio of the fluorescence intensity differential at the modulation frequency to the total fluorescence intensity for dilute solutions is proportional to the dissymmetry factor [equation (2)] of the fluorescent species in the electronic ground state and the excitation spectrum is equivalent to the c.d.g-factor spectrum of that specie^.'^ The method is useful for c.d. studies of mixtures containing a single chiral fluorescent species or macromolecules containing a particular fluor~phore.~~ In the c.p.e. technique,3840 on the other hand the exciting radiation is unpolarized and the circular intensity differential of the luminescence (IL-1,) is monitored as a function of wavelength to afford the c.p.e. spectrum and the dissymmetry factor g, of the enantiomer in the excited electronic state [equation (3)]. In order to avoid linear polarization artefacts the luminescence is generally collected in the forward direction at 180" to the excitation ray,38*39 although the theory of collection at 90" has been ~onsidered.~' The effects of photoselection and of rotatory Brownian motion in the lifetime of the excited state have been discussed and it is concluded that the g,-factor is insensitive to these effects in the cases where the excitation and emission transition moments are ~arallel.~'-~~ While the g-factor obtained from the c.d.spectrum refers to the molecular geometry of the enantiomer in the ground electronic state the g,-factor is related to the equilibrium nuclear configuration of the molecule in the excited state and the c.p.e. spectrum affords complementary rather than redundant information.If an enantiomer undergoes no change in shape or size on electronic excitation the c.d. and c.p.e. spectra are expected to bear a mirror-image relationship to one another across the band-origin position on the frequency scale and to give the same g-factors. The carbonyl n -P T* c.d. and c.p.e. spectra of a range of chiral ketones show substantial differences of bandshape and of g-factor including changes of sign in a number of conformationally non-labile cases such as (+)-camphor.41 The differences are attributed to a change in the shape of the carbonyl chromophore from planar to pyramidal in the excited state of the n +T* transition as is established for 36 D. L. Andrews Chem. Phys. 1976 16 419. 37 I. Tinoco jun.and D. H. Turner J. Amer. Chem. SOC.,1976,98 6433. 38 I. Z. Steinberg and B. Ehrenberg J. Chem. Phys. 1974,61 3382. 39 J. Snir and J. A. Schellrnan J. Phys. Chem. 1974 78,387. 40 J. P. Riehl and F. S. Richardson J. Chem. Phys. 1976 65 1011. 41 H. P. J. M. Dekkers and L. E. Closs J. Amer. Chem. SOC.,1976,98 2210. 60 S. F.Mason the case of formaldehyde and to a linear variation of the rotational strength I?,,* with the normal co-ordinate Q of one or more of the vibrational modes due mainly to the change with Q of the electric dipole transition rn~rnent.~' The c.p.e. spectra of a number of chiral lanthanide complexes have been found to be sensitive to pH and to the H20-D20 solvent composition and in non-aqueous solution to the co-ordinating properties of the An unusual induced c.p.e.effect has been noted in the case of fluorescein dissolved in (+)-or in (-)-1- phenylethylamine the solutions giving no induced c.d. ab~orption.~~ 3 Vibrational Optical Activity The optical activity arising from the vibrational modes of randomly oriented chiral molecules at present is more readily accessible through Raman spectros~opy~~ than by infrared absorption measurements. The largest Raman c.i.d. effects with g- factors of -4 X are observed for low-frequency modes,30 such as the methyl torsion vibration between 200 and 300 cm-' although the degenerate antisymmet- ric deformation mode of the methyl group near 1450cm-' shows a small but prominent c.i.d. couplet for which a sector rule has been and a Raman c.i.d.effect has been detected in carbon-halogen stretching modes.45 The majority of Raman c.i.d. studies refer to the Stokes region at frequencies lower than that of the excitation source but anti-Stokes Raman optical activity has been discovered recently in (+)-3-methylcyclohexanone.46 The vibrational optical activity detected by i.r. c.d. absorption is confined at present to X-H stretching modes at frequencies higher than -2000 cm-' the main limitations being the decrease in energy from black-body radiation sources and the general relative decline in detector performance with increasing wa~elength.~~'~~ The reported g-factors are low -or less both for the and for the overtone^.^^ Calculations of the i.r. c.d. expected in the amide I and amide I1bands of chiral polypeptides near 1660and 1535 cm-' respectively predict a relatively large g-factor -for the a -helix conformation and smaller values for p 4 The Optical Activity of Crystals The dissymmetry factor circumscribing measurements of optical activity is approxi- mately proportional to the ratio of the molecular dimensions or of those of the repeat unit in a periodic structure such as the a-helix to the wavelength of the radiation employed in the study.Thus the g-factor for the absorption bands of a given chiral molecule is expected to decrease generally on proceeding from the ultraviolet and visible to the infrared region. If the dimensions of the molecule or of 42 H. G. Brittain andF. S. Richardson Znorg. Chem.,1976,15,1507;J. Amer.Chem.SOC.,1976,98,5858. 43 H. G. Brittain and F. S. Richardson J. Phys Chem. 1976 80 2590. 44 W. Hug S. Kint G. F. Bailey and J. R. Scherer J. Amer. Chem. SOC.,1975,97 5590. 45 M. Diem M. J. Diem B. A. Hudgens J. L. Fry and D. F. Burow J.C.S.Chem. Comm. 1976 1028. 46 L. D. Barron Mol. Phys. 1976 31,1929. 47 G. Holzwarth E. C. Hsu H. S. Mosher T. R. Faulkner and A. Moscowitz J.Arner. Chem. Soc. 1974,% 251 252. 48 L. A. Nafie T. A. Keiderling and P. J. Stephens J. Amer. Chem. SOC.,1976,98 2715. 49 H. Sugeta C. Marcott T. R. Faulkner J. Overend and A. Moscowitz Chem. Phys. Letters 1976,40,397. 50 T. A. Keiderling and P. J. Stephens Chem. Phys. Letters 1976,41 46. 5l J. Snir R. A. Franke! and J. A. Schellman Biopolymers 1975 14 173. Chiral Systems 61 the repeat unit in a periodic structure are increased to match the wavelength of the radiation the g-factor is increased towards its maximum value of 2.The pitch-length of a cholesteric liquid crystal is readily adjustable by the addition of a chiral guest molecule to a nematic mesophase and for axial propagation of radiation in a cholesteric plane texture g-factors of the order of 10% are readily obtained even under the adverse conditions of i.r. c.d. spectroscopy at -1000cm-'.52*53Further an achiral solute even an optically isotropic molecule with 0 or Td displays an induced c.d. absorption in a cholesteric or twisted nematic mesophase s01vent.~~*~~ In the plane texture formed by a thin film 5-50pm thick of a cholesteric mesophase between sodium chloride or silica windows the long axes of the con- stituent molecules are statistically oriented along the local nematic director which forms a helix with the helix axis perpendicular to the end plates.The preparation is isotropic for radiation propagated along the helix axis but it has a strong circular birefringence (0.r.d.) and a substantial c.d. at absorption frequencies whether electronic or vibrational and additionally at a wavelength hocorresponding to the pitch-length of the helix P(ho= nP n being the mean refractive index) where the dissymmetry factor attains its maximum value (g -2) one circular component of the radiation being transmitted and the other reflected. Two contributions to the c.d. at absorption frequencies of guest or of host molecules in a cholesteric mesophase have been disting~ished.~~-'~ First the host molecules are necessarily anisotropic with a linear birefringence An and a linear dichroism (1.d.) in absorption which are directly observable for the corresponding nematic mesophase or may be estimated for the cholesteric system.At an electronic or vibrational absorption wavelength hj of the host molecules or of anisotropic guest molecules statistically aligned in the cholesteric solvent the assembly of transition- moment vectors forms a helical array with a dissymmetry factor gj (l.d.) related to the linear dichroism given by equation (4). The degree of statistical alignment of the transition moment vector is measured by the order matrix element Sjj= (1/2) <3 cos2 t? -1 >,where 0 is mean angle between the transition moment direction and the local nematic director.Values of S for the average alignment of the molecular axes are available e.g. from n.m.r. spectroscopy so that c.d. studies of cholesteric solutions provide the polarization of an electronic or vibrational transition moment relative to the molecular axe^.'^-'^ The linear dichroism contribution is zero for an isotropic solute in a cholesteric solvent but the large circular birefringence of the solvent affords a second and more general contribution.52 Left and right circular radiation incident with equal field amplitudes upon a chiral solvent have different effective field strengths in the medium and give rise to c.d. in the absorption of a solute.The dissymmetry factor 52 R. J. Dudley S. F. Mason and R. D. Peacock J.C.S. Chem. Comm. 1972,1084;J.C.S.Faraday ZI 1975 71,997. s3 G. Holzwarth I. Chabay and N. A. W. Holzwarth J. Chem. Phys.,1973 58 4816. 54 E. Sackmann and H. Mohwald J. Chem. Phys. 1973,58,5407. 55 F. D. Saeva and G. R.Oh J. Amer. Chem. SOC.,1976,98 2709. 62 S.F. Mason contributed by the effective Lorentz field gj (L.f.) is expressed by equation (5) which reproduces the g-factors observed for 0,solutes in a cholesteric The expectation that the g-factor changes sign on shifting the cholesteric reflection pitch-band hofrom wavelengths longer than to shorter than hi is also realized. g,(L.f.)=Ai(An)2/[2Aj(Ai -A;)(n2 +2)] In helical polymers and uniaxial ionic or molecular crystals with a screw-axis of symmetry the repeat unit generally is only a small multiple of the monomer or of the molecular dimension at most and the optical activity has more of a single-molecule character particularly in the case of weak absorption bands where the intermolecu- lar coulombic coupling between the electric transition moments is usually insignific- ant.Thus the c.d. spectrum over the visible region of the trigonal {A-( +)-[CO(~~),]C~~),,N~C~,~H,O for radiation propagated along the optic axis of the crystal is virtually identical to the corresponding spectrum of A-( +)-[Co(en)J3+ as a guest ion in the lattice of the transparent isomorphous crystal of the analogous rhodium(r1r) or iridium(rI1) complex ion The axial single-crystal c.d.spectra of all of the tris-diamine cobalt(II1) complex ion salts with a known crystal and molecular struetures6 and crystallizing in a trigonal tetragonal or hexagonal system have now been measured.” Single-crystal c.d. studies have been largely confined to axial propagation in uniaxial systems on account of the large artefacts arising from .linear birefringence and linear dichroism for the propagation of radiation perpendicular to the optic axis of a uniaxial crystal or for all propagation directions generally in biaxial crystals. Recently a method has been devised for minimizing and correcting these artefact^,^^ and c.d. spectra have been reported for ortho-axial propagation in the trigonal crystal5’ 2[Ir(en),]C1,,NaC1,6H20 doped with A-( +)-[Co(en),13’ and for the orthorhombic crystal6’ of [CUR-pn(pd),] [R-pn(pd) =4,4’-(R-(-)-1,2-propanedi-iminato)di(3-pentene-2-one)].The method employs a modulator giving half-wave retardation for the measurement of l.d. or quarter-wave retardation for the determination of c.d. At a given wavelength the 1.d. is measured and the crystal is then rotated about the direction of propagation as an axis until the 1.d. is zero when the c.d. is determined with a minimum of interference from linear polarization effe~ts.~~ General theoretical analyses of the optical activity of uniaxial crystals61 and of all of the non-centrosymmetric classes6 have been reported. 5 Co-ordination Compounds Until recently general treatments of the d-electron optical activity of the simpler chiral co-ordination compounds notably the six-co-ordinate D3 metal complexes 56 Y.Saito Coordination Chem. Rev. 1974 13,305. 5’ H. P. Jensen and F. Galsb~l,Inorg. Chem. 1977 16 in press. 58 R. Kuroda and Y. Saito Bull. Chem. SOC.Japan 1976,49,433. 59 H. J. Hofrichter and J. A. Schellman ‘Jerusalem Symposia on Quantum Chemistry and Biochemistry (V)’,Israel Academyof Sciences and Humanities Jerusalem 1973;J. Opt. SOC.Amer. 1977,67,in press. 60 H. P. Jensen Actu Chem. Scund. 1976 A30 137. 61 B. V. Bokut F. A. Lopashin and A. N. Serdyokov Optics and Spectroscopy 1976 40 184 400. 62 J. Jerphagnon and D. S. Chemia J. Chem. Phys. 1976,65 1522. Chiral Systems 63 containing saturated ligands were based mainly upon the crystal field In the basic model it is assumed contrary to the indications of Fajans rules that the significant perturbations are those of the electronic states of the meta1,cation by the static ground-state charge distribution of the ligands which are either anions or neutral species with generally a substantial polarizability.The problems of the model early became acute.64 The simplest ligand field potential of pseudo-scalar A lu symmetry in Oh,required to confer a non-vanishing first-order rotational strength upon a d + d transition of an octahedral metal ion is ninth-order with respect to the electronic co-ordinates and is negligible as an effective perturbation. In the second-order simultaneous T2uand T2,crystal field potentials generate d-electron optical activity but a finite T2gpotential breaks the degeneracy of Tl and T2octahedral d-electron states so that crystal field optical activity is precluded to second-order in chiral metal complexes of 0 symmetry and in chiral complexes of lower symmetry where the component d-electron states with a common Tl or T2 octahedral parentage are accidentally degenerate e.g.the D complex A-( + )-[Co(en),13+ where the components of the octahedral d-electron transition in the visible region 'A,,+ 'Tlg,are known to have a common band origin from the single-crystal spectrum. Finally on carrying the treatment of the T2uand T2,crystal field potentials to all orders of perturbation theory it is found for a wide range of parameter sets that the computed rotational strengths conflict qualitatively with the experimental data.6' In particular it is shown6' that the rotational strengths of the two 0,components of the transition to the octahedral T, cobalt(lI1) d-electron state 'Al -N 'A and 'Al + 'El polarized respectively parallel and perpendicular to the C,axis of the complex ion have the theoretical ratio IR(E)I/IR(A2)( < 1 whereas experimentally this ratio is generally greater than unity for the tris-1,2-diamine and tris-oxalato complexes of cobalt(m) rhodium(III) and chromium(rI1).Hitherto the experimen- tal ratio has been obtained from direct measurement of R(E),from the axial single-crystal c.d. spectrum and the determination of the sum R(T,)= [R(E)+R(A2)], from c.d. measurements of randomly oriented microcrystals in a matrix or from solution The validity of this procedure is now supported by the direct measurement of R(E)and R(A,) from the single-crystal axial and ortho-axial c.d.spectrum of A-( +)-[Co(en),l3' in a host lattice." An alternative ligand-polarization model complementary to crystal field theory allows for the perturbation of the ligand atoms or groups by the potential originating from the charge distribution of the d-electr~n,~~ transition in the or f-electr~n,~' central metal ion of a co-ordination compound. An electronic transition of the 1 41 type at a particular atomic centre in a polyatomic molecule while devoid of an electric dipole moment possesses an electric multipole moment and may have a magnetic dipole moment dependent upon the rn values of the 1-orbitals connected.The allowed electric multipole moments are the even 2"-poles in the range 2 < n < 21 Q,, where rn refers to a particular member of the (2n + 1) components of the multipole. The transition multipole of a metal ion in a co-ordination compound correlates coulombically the transient electric dipole moments induced in the 63 G. Hilmes and F. S. Richardson Inorg. Chem. 1976,15,2582. 64 S.F. Mason and R. H. Seal J.C.S. Chem. Comm. 1975,331;Mol. Phys. 1976,31 755. 65 S.F.Mason R. D. Peacock and B. Stewart Mol. Phys. 1975 30 1829. S. F. Mason individual ligand atoms or groups during the transition. Each of these dipoles is proportional to the electric-dipole polarizability a(L) of the ligand atom or group (L) at the frequency of the metal-ion transition.Subject to constraints imposed by the particular stereochemistry of the complex the coulombic correlation gives the d-electron or f-electron metal-ion transition Mo-+ Ma a net resultant electric dipole moment coawhich is located wholly in the ligands. The z-component of the first-order moment is given by the ligand polariza- tion expression [equation (6)],64,65 where the geometric tensor Gk,,= represents the radial and angular factors governing the Coulombic potential between the z- component of an electric dipole located in the ligand group L and the rn-component of the 2"-pole transition moment Q,, of the metal ion. The general selection rule for a non-vanishing electric-dipole transition moment [equation (6)] is that the mul- tipole component Q, and the dipole component pa(a= x y or z)transform under the same irreducible representation or the same row of a degenerate representation in the point group to which the complex belongs.65 This condition is generally less restrictive than the corresponding crystal field criterion and its application disposes of a number of anomalies encountered in the development of the latter In the application of the ligand-polarization model to the d-electron optical activity of chiral complexes containing the octahedral chromophore [Co"'N6] a non-vanishing rotational strength emerges in the first-order for complexes of as high a symmetry as 0.The principal d-electron transition of this chromophore consi- de~ed~~ is the 'A + T1octahedral excitation near 465 nm consisting of the three single-orbital promotions d, -+ d,2-,2 and the analogues obtained by cyclic permu- tations of the electronic co-ordinates.The leading moments of the transition dxy are the z-component of a magnetic dipole nz:o (242 Bohr magneton) -+dX2-,2 and the [xy (x2-y2)] component of an electric hexadecapole. The potential of the hexadecapole component orders coulombically the transient induced dipole of each ligand group which does not lie in an octahedral symmetry plane of the [Corr1N6] chromophore. The resultant electric dipole moment has a z -component [equation(6)] collinear with the intrinsic magnetic dipole moment of the d, -+ d,2-,2 transition affording the rotational strength Ria= -ip&p~:~. The other two compo- nents of the octahedral 'Al +IT1transition give analogous contributions R:a and Rga,and the sum over all three components provides a non-vanishing net first-order rotational strength for chiral complexes of 0 symmetry.The calculated rotational strengths of the 'A,+'T transition in chiral mono- or truns-bis-1,2-diamine complexes containing the [Cor1'N6] chromophore have the correct sign and order of magnitude,64 although the symmetry of these complexes is lower than 0. The tris-ethylenediamine complex [Co(en),13' and its analogues have strict D3 symmetry and both the oriented single-crystal and the randomly oriented solution c.d. spectra of these complexes over the frequency region of the octahedral 'A + TItransition are accounted for quantitatively to within a few percent in the most-studied case of [Co(en>,l3' by extending the ligand-polarization model to 66 R.Gale R.E. Godfrey and S. F. Mason Chem. Phys. Letters 1976 38 441,446. Chiral Systems second ~rder.~~,~~ The second-order treatment is dependent upon the single-crystal and vacuum-ultraviolet absorption and c.d. spectra of [Co(en),]" which charac- terize two strong electric-dipole allowed transitions in the 160-230 nm region,64 one to a 'Estate and the other to a higher-energy 'A2state from the 'A ground state of the 0,complex. These two U.V. transitions serve as the primary source from which electric dipole strength is borrowed within the [Co"'N,] chromophore by d-electron transitions in the visible region. In the second-order augmentation of the ligand-polarization model the transient electric dipoles in the individual ligand groups themselves ordered by the potential originating from the electric hexadecapole moment of a 0 component of the *Al+'TI d-electron transition in the visible region coulombically correlate in turn the electric dipole moment of the corresponding D component of the intense U.V.transition in the [Co"'N,] chromophore. Computations based on this model employ empirical quantities the isotropic polarizabilities di(L) of the ligand groups and the heavy-atom co-ordinates of those groups determined by X-ray ~rystallography,~~ and the calculations have little latitude. The main adjustable parameter obtained from double-exponent 3d-functions is the radial extension of the hexadecapole moment which gives rotational strengths varying by a factor of four between the limiting assumptions of a neutral or a tripositively charged cobalt ion in the complex.Satisfactory agreement with experiment is found generally for a hexadecapole radial extension corresponding to a cobalt ion with a +1.3 effective charge.64 In addition to the general ~rystal-field~ treatments a and ligand-p~larization~~ semi-empirical MO calculation of the d-electron optical activity of [C~(en)~],' has been reported for both the lel and ob conformation of the ethylenediamine chelate rings.67 In the case of the lel isomer satisfactory agreement with experiment is obtained using the dipole-length method for calculating the electric transition moments but the overall rotational strength of the randomly oriented complex ion R(TI) has the incorrect sign when the alternative dipole-velocity procedure is empl~yed.~' For the corresponding 0b3 complex A(Ahh)-[Co(en),13' which has not been experimentally characterized a relatively small and negative value is calcu- lated67 for R(Tl),whereas in the cases of the 0b3 complexes which have been characterized A(hhA)-[Co(R -pn),I3+ and A(hhh)-[Co(R,R -chxn),I3+ R (Tl) is found to be relatively large and The optical activity of the square-planar complexes of copper(I1) with the L-amino-acids the dipeptides and their amides and with tripeptides has been extensively investigated by semi-empirical MO and other method~.~'-'' Sector rules relating the position of a ligand group to the sign of the d-electron optical activity induced are disc~ssed,~~*~' and the change in the sign of that activity observed on replacing S-proline by its N-methyl derivative in the [Cu(S-Pro),] complex is rationali~ed.~' For the S-alanine complexes it is predicted that the cis and trans isomers of [Cu(S-Ala),] have an overall d-electron rotational strength with opposite signs and that for each isomer the net charge transfer and d-electron rotational 67 R.S. Evans A. F. Schreiner and P. J. Hauser Inorg. Chem. 1974 13 2185. 68 A. Decinti and G. Larrazabal Inorg. Chim. Actu 1976 18 121. 69 R. W. Strickland and F. S. Richardson J. Phys. Chem. 1976 80 164. 70 G. Hilmes C. Y. Yeh and F. S. Richardson J. Phys. Chem. 1976 80 1798.71 C. Y. Yeh and F. S. Richardson Inorg. Chem. 1976 15 682. S.F. Mason strengths have the same sign.71 The axial single-crystal d-electron optical activity of [Cu(H,O),]*' doped into the lattice of [Zn(H,O),]SeO, which crystallizes into the enantiomorphous tetragonal space group P4,2,2 or P43212,has been calculated by the crystal-field procedure which accounts qualitatively for the observed temperature-dependence of the net rotational strength.72 6 Organic Chromophores While the octant rule continues to provide the general framework for the interpreta- tion of the n +T*Cotton effect of chiral carbonyl compounds elaborations of the rule have been indicated by both empirical and theoretical studies. The detailed analysis of the c.d. increments (SAE)due to the annellation or to the alkyl substitu- tion of cyclohexanones has been extended to the corresponding cyclopentanones and bicyclo-deri~atives.~~*~~ These studies emphasize the significance of a 'primary zig-zag' of C-C bonds which in the customary XY projection of the octant rule lie along or close to the diagonals of the diagram.That is a bond or group lying on the primary zig-zag has an optimum value of its octant-rule co-ordinate function XYZ for a given distance R between the group and the carbonyl chromophore. Alkyl substituents which extend the array of the primary zig-zag give a consignate contribution to the n -+ r*Cotton effect whereas others notably a @-axial methyl group may afford a dissignate (antioctant) c~ntribution.~~'~~ Theoretical of the rotational strength Rn,*of di-n-alkyl ketones over a range of chiral conformations based on the CNDO/S procedure show that R,,*is optimized when the C-C chains are arrayed in a region within *30° from the primary zig-zag conformation.The mapping of the R,,*contribution due to a methyl group as a function of its position in octant-rule space shows that the third nodal surface additional to the symmetry-determined XZ and YZ planes of the C, chromophore is concave from the viewpoint of the carbonyl oxygen atom.75 The three nodal surfaces intersect at a point some 2 A behind the carbon atom of the carbonyl group so that the dissignate contribution of a @-axial methyl group may be reinterpreted as consignate front-octant beha~iour.~' Two island pockets corres- ponding to dissignate contributions appear in each rear octant of the revised octant diagram and they accommodate other observed cases of anti-octant beha~iour.~~ The importance of a W-shaped array of C-C bonds linking the carbonyl group to a substituent first became apparent from studies of the long-range effect of a heterosubstituent upon the R,,* value of a chiral ketone.76 These effects and those arising from alkyl substituents over a range of conformations have been investigated by the CND0/2 method.77 The effects are ascribed to electron delocalization mainly in the lower-energy n-orbital and to only a minor degree in the r*-orbital.The predominant role of ground-state delocalization rationalizes the analogy drawn between long-range n.m.r.coupling through a W-shaped bond array and the 72 F. S. Richardson and G. Hilmes Mol. Phys. 1975 30 237. 73 D. N. Kirk and W. Klyne J.C.S. Perkin I 1976 762. 74 D. N. Kirk J.C.S. Perkin Z,1976 2171. 75 T. D. Bouman and D. A. Lightner J. Amer. Chem. SOC.,1976.98 3145. '6 J. Hudec J.C.S. Perkin Z,1975 1020; G. P. Powell R. N. Totty and J. Hudec ibid. p. 1015. 77 E. E. Ernstbrunner M. R. Giddings and J. Hudec J.C.S. Chem. Comm. 1976 953 954 956. Chiral Systems 67 corresponding effect upon the R,,* value.77 General rules for the identification of effective coupling paths based upon the analogy have been The MO treatments of the rotational strengths of chiral ketones follow and rationalize the related experimental studies in the main and hitherto they have yielded expectations of a general nature such as the form of the third nodal surface in the octant rule diagram.Firmer and more specific expectations emerge from the independent-systems methods the static-field and the substituent-polarization mod-els in both of which the symmetric carbonyl chromophore is coupled coulombically through space rather than through bonds with a dissymmetrically positioned substituent or substituents. The octant rule for chiral ketones is generally based in the static-field model upon the mixing of the n +T,*transition of the carbonyl chromophore with the Rydberg n -+ 3dy transition7’ under the pseudo-scalar component of the potential originat- ing from the sub~tituents.’~ The mechanism requires that the rotational strengths of the two transitions in a given ketone are of equal magnitude and of opposite sign.79 A standard compound for test runs on v.u.c.d.instruments is S-(+)-3-methylcyclopentanone,80*81 and such runs show that the rotational strength of the Rydberg n -+ 3d transitions2 at 165 nm is positive like that of the n +n* transition at 300nm. Thus the static-field mixing of these two transitions is not a tenable mechanism for the primary origin of the n +T* Cotton effect at least in the case of the ketone in~estigated.~~ In the dynamic-coupling or substituent-polarization model the octant rule for dissymmetric ketones emerges as a consequence of the Coulombic coupling between the leading electric multipole of the carbonyl n -+ n,*transition the quadrupole component Ox, and the component p of the transient-induced dipole in a chirally disposed substituent with an effectively isotropic p~larizability.~~~’~ There is a fixed phase relationship between the magnetic dipole in and the electric quadrupole moment Ox of the carbonyl n +n* transition and the particular location of the substituent in octant-rule space determines whether the induced electric dipole component p lies parallel or antiparallel to m,.Anti-octant effects are accommo- dated by taking into account the anisotropy of the substituent’s polarizability represented by (a,,-(Y L) on the assumption of cylindrical symmetry about the bond between the substituent and the residual symmetric The contributions from the anisotropy of the substituent’s polarizability necessarily vanish in chiral ketones of C2symmetry by the selection rule connected with equation (6) as only the component p of a dipole transforms under the same representation as the quadrupole component Ox in the C2group.Thus it is a firm expectation of the substituent-polarization model that all ketones with C symmetry show consignate octant-rule behaviour if the mean polarizability of the substituent is greater than that of the hydrogen atom it replaces.83 In particular a dissignate monosubstituted 7x T. D. Bouman and A. Moscowitz J. Chem. Phys. 1968 48 3115. ’9 J. A. Schellman Accounts Chem. Res. 1968 1 144. 80 0.Schnepp S. Allen and E. F. Pearson Rev. Sci. Znstr. 1970 41 1136. 8’ W. C. Johnson jun.Rev. Sci. Instr.. 1971 42 1283. 82 M. B. Robin ‘Higher Excited States of Polyatomic Molecules’ Academic Press New York Vol. 11,1975. 81 S. F. Mason ‘Handbook of Stereochemistry’ ed. H. Kagan G.Thieme Verlag Stuttgart Vol. 2a 1977. x4 E. G. Hohn and 0.E. Weigang J. Chern.Phys. 1968,48. 1127. 85 M. P. Kruchek Optics and Spectroscopy 1976 41 56. 68 S.F. Mason ketone is expected to become consignate in the corresponding disubstituted deriva- tive with C ~ymmetry,'~ e.g. a diaxial 2,6-disubstituted adamantan-4-one. A general method of obtaining sector rules for optical activity based on the substituent-polarization model has been pr~posed,'~ following the corresponding and well-established procedure based on the static field Again the method employs the basis-functions of the pseudo-scalar representation in the point group of the symmetric chromophore the appropriate functions being identified by the characteristics of the electronic transition inv01ved.~' The simplest sector rule function for a given transition is always one power higher in the substituent's co-ordinates for the polarization model than the static field procedure e.g.an octant XYZ and a quadrant XY rule respectively for the carbonyl n -+7r* transition as a substituent dipole and an effective charge are respectively inv~lved.~~.~~ Vibronic effects in the carbonyl n +V* optical activity have been employed to account for the temperature-variation ofthe c.d. absorption of (+)-camphor and its analogues,86 and for the non-vanishing R,,*of two cy -diones owing their chirality to isotopic substit~tion,~~ (lR)-[1D]-and (1R)-[2180]-cy-fenchocamphoronequinone.In the latter cases it is shown that the observed sign and order of magnitude of the long wavelength R,,* are explained by the polarizability model if R,,*varies linearly with the normal vibrational co-ordinates principally those of the electronic ground state and the anharmonicities of the vibrational modes are explicitly c~nsidered.~~ The treatment is extended to the larger R,,* values observed in the case of (1R)-camphorquinone and its analog~es.'~ The c.d. absorption of chiral olefins over the quartz U.V. region 185-230 nm has been analysed empirically by the method of pairwise comparisons in order to relate structural features to the substituent SAE contributions.88 The analysis covering 228 compounds divides chiral olefins into four types on a chiroptical basis using the octant rule with the carbonyl n +7r* signs as a general reference frame.The substituents of the class of exocyclic methylene derivatives are generally consignate in octant-rule space the contribution of a p-axial methyl group being particularly large. In the class of substituted cyclohexenes including the 1-methyl analogues an allylic axial C-H group is generally consignate. The (Z)-or (E)-stereochemistry is dominant in the third class of alkylidene cyclohexane derivatives the sign of the c.d. being determined by the chirality of the ethylidenecyclohexane unit. Rather weak c.d. absorption has been reported for the class of tetra-substituted ethylenes where axial allylic methyl groups give rise to dissignate contributions.88 These generaliza- tions apply to the lowest energy c.d.absorption which is often followed by a c.d. band of opposite sign." The lowest energy c.d. absorption of chiral olefins does not always refer to the 7r +V* transition of the chromophore. Comparisons between the gas-phase and the solution c.d. spectra and variable-temperature studies indicate that the lowest frequency c.d. band arises from the Rydberg 7r +3s transition in a number of chiral 01efins.'~ The V.U. c.d. spectra of a range of chiral ~lefins'~.~~ show two major c.d. *6 H. P. Gervais and X. Desalbres Compt. rend. 1976 282 C 1101. 87 R. F. R. Dezentje and H.P. J. M. Dekkers Chem. Phys. 1976 18 189. 88 J. Hudec and D. N. Kirk. Tetrahedron 1976 32 2475. 89 A. F. Drake J.C.S. Chem. Comm. 1976 515; A. F. Drake and S. F. Mason Tetrahedron 1977 33 in press. 90 K. P. Gross and 0.Schnepp Chem. Phys. Letters 1975 36 531. Chiral Systems bands of comparable area and with opposite signs due to the mixing of the electric dipole 7r +T* excitation with a valence-state magnetic dipole excitation in the 160-210 nm region and a minor Rydberg c.d. absorption is detectable at longer wavelengths if it has a sign opposite to that of the lower energy member of the major couplet. The mixing mechanisms of the two valence-state excitations based on the n-bond-torsion the substituent-polarizability and the static-field models have been discussed in connection with the octant rule for chiral~lefins.~~ A comparison of the available MO methods ranging from the Hiickel to the ab initio for calculating the rotational strengths of twisted ethylene and other chromophores has been reported empIoying both the dipole-length and the dipole- velocity procedure^.^' The ratio of the rotational strength obtained by the two procedures affords a measure of the quality of the wavefunctions used being unity for exact functions.In the twisted-ethylene case the ratio varies from 9.73 for the CNDO method with configuration interaction to 1.49 for a non-empirical INDO method with improved virtual orbitals (IVO).91The expectation from RHF-IVO calculations that (R)-2-methylcyclohexane has a positive R,,* value91 is not how- ever supported e~perimentally.~~ The c.d.spectra of a series of chiral cyclopropanes have been measuredg3 to 185 nm and that94 of 1S72S-( +)-trans-dimethylcyclopropane to 150 nm. The c.d. absorption in the 185 nm region of the latter isomer has a sign opposite to that of the corresponding c.d. band given by the trans-1,2,2,3-tetramethyl analogue with the same absolute stereochemistry suggesting that the c.d. arises from the pairwise coupling of excitation moments directed along the exocyclic C-C Calculations of the rotational strengths of penta-2,3-diene and other chiral allenes at the CNDO/S and of non-planar buta-1,3-diene at levels up to the ab initio,” have been discussed. Experimentally it has been found that the 260 nm c.d.band of conformationally rigid 5a -steroidal 1,3-dienes changes sign when the allylic axial bonds are changed from C-H to C-CH3 the contribution of the twist in the diene chromophore to the optical activity being less than that of a single allylic axial methyl group.96 q1 A. Rauk J. 0.Jarvie H. Ichimura and J. M. Barriel J. Amer. Chem. Soc. 1975,97 5656. 92 C. J. Cheer and C. Djerassi Tetrahedron Letters 1976 3877. 93 L. Crombie D. A. R. Findiay R. W. King I. M. Shirley D. A. Whiting P. M. Scopes and B. M. Tracey J.C.S. Chem. Comm. 1976 474. q4 A. Gedanken and 0.Schnepp Chem. Phys. 1976,12 341. q5 H. Dickerson S. Farber and F. S. Richardson Theor. Chim. Acta 1976 42 333. 96 A. W. Burgstahler L. 0.Weigel and J. Gawronski J. Amer. Chem. SOC.,1976,98 3015.

ISSN:0308-6003    

DOI:10.1039/PR9767300053

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Electrochemistry -Simple Electron Transfer Reactions By D. PLETCHER Department of Chemistry The University Southampton SO95NH The last review of electrochemistry to appear in Annual Reports was published in 1964’” and it is interesting to note the changes which have occurred during the intervening period. Firstly it was during the mid-sixties that modern instrumenta- tion for the study of electrode reactions became widely available. More recently one has seen the development of a range of powerful spectroelectrochemical methods which give a simultaneous spectral and electrochemical readout and the introduction of computers and microprocessors both for the control of experiments and the treatment of data. Hence while many of the techniques and fundamental concepts of electrochemistry were already well developed at the time of the last review it is now much easier to obtain reliable data and to carry out complex analysis of experimental data.In consequence the outlook of electrochemists has changed and we are much more able to examine complex systems and to question established theories. Certainly there has been a considerable increase in the number of publications and in consequence the scope of this current review will be much more limited than that of its predecessors. Its aim will be to discuss the literature published during 1975 and 1976 concerning simple heterogeneous electron transfer reactions. Many interesting topics such as nucleation and phase growth corrosion electrocatalysis synthesis and analysis will not be mentioned while others such as the double layer and adsorption will only be covered where they directly impinge on the main topic.1 Theory Most experimental investigators are happy to analyse their data for a simple electron transfer reaction O+ne-R (1) using the classical rate equation to relate the measured current density I to the overpotential q ;a is the transfer coefficient and I. the exchange current density. It should be noted that this classical equation predicts that at sufficiently high q values the ‘Tafel plot’ (log I us. q)will be linear and that the rate of the electron transfer reaction will increase indefinitely with 1 R. Parsons Ann. Reports 1964,61,80. 2 Note however ‘Electrochemistry’ (Specialist Periodical Reports) The Chemical Society London Vols.1-5 1970-1975. 7 1 72 D. Pletcher overpotential. Generally the kinetics of the reaction are characterized by quoting values for I. and a or a and kt the standard rate constant (the rate constant at the standard electrode potential) which may be calculated from the exchange current density using the equation where Co and C are the surface concentrations of 0 and R respectively. For interpretation the resulting data are commonly subjected to a ‘double layer correc- tion’ to allow for the potential drop across the inner double layer and the difference in concentration of electroactive species between the bulk solution and the plane of closest approach to the electrode where electron transfer is assumed to occur i.e.the plane. The ‘corrected’ equation is where zo is the charge on the electroactive species and the potential at the O2plane is calculated from double layer theory (see standard texts). Although this classical theory shows good agreement with most experimental data it is unsatisfactory bwause it adds little to our understanding of the intimate nature of the electron transfer reaction. Marcus3 was the first to produce a statistical mechani- cal approach to electron transfer reactions and this in particular predicted that Tafel plots should be non-linear or in other words that the transfer coefficient should be a function of potential. These effects should however be most marked at high overpotentials and for fast reactions circumstances where experimental data are most difficult to obtain.The theory also predicts that a limiting rate will be reached at very high overpotentials. The last fifteen years have seen other attempts to produce statistical and quantum mechanical descriptions of electron transfer reactions and these have recently been ~eviewed.~.~ Schmidt4 has considered both homogeneous and heterogeneous electron transfer while Dogonadze and KuznetsovS have con- centrated on electrode reactions. Several recent papers have continued to emphasise the role of solvent and co-ordination shell rearrangements in determining the energy of activation of an electrode process. Thus Dogonadze and Kuznetsov6” have described methods for calculating the transition probability for electron transfer taking into account the reorganization of the ionic atmosphere and solvent shell to the transition state the density matrix of all ions in the system and image forces thus including in a unified manner the dynamic behaviour of all the degrees of freedom.The transition state is shown to have an ionic atmosphere and charge intermediate between the initial and final states and the current is dependent on the concentration of reactant with an intermediate charge. Krishtalik’ has commented on the reason for electron transfer apparently occurring only to and from species in the dense part of the double layer R. A. Marcus Ann. Rev. Phys. Chem. 1965,15,155. P.P.Schmidt ‘Electrochemistry’ (Special Periodical Reports) The Chemical Society London 1975 Vol.5 p. 21. 5 R. R. Dogonadze and A. M. Kuznetsov Progr. Surface Sci. 1975,6,1. R. R. Dogonadze and A. M. Kuznetsov Soviet Electrochem. 1975,11,1. R. R. Dogonadze and A. M. Kuznetsov J. Electroanalyt. Chem. 1975,65 545. R L. I. Krishtalik Soviet Electrochem. 1975 11 174. Electrochemistry -Simple Electron Transfer Reactions when electron tunnelling might be expected to occur at long range; he suggests this is because the species in the inner double layer is partially desolvated which causes a decrease in the activation energy required to reorganize the medium around the reacting species so as to create the necessary conditions for electron transfer equality of energy levels between the initial and final states. Schmickler' has examined the approximations which have been used in the Levich and Dogonadze model of electron transfer and their effect on the predicted I-E relationship.Firstly he has considered the approximations which have been used for the energy level involved on the electrode side of the interface. He shows that the two assumptions that the electron jumps to or from (a) the Fermi level or (b) the Fermi distribution approximated by the low temperature limit lead to different I-E characteristics. Close to the equilibrium potential the former seems to be the better approximation but the latter is to be preferred at high overpotentials. Both models lead to a considerable dependence of the transfer coefficient on potential and a limiting or falling rate at high overpotentials. Since these effects are not usually observed he also examined the effect of variation of the model for solvation of the electroactive species and its changes to the transition state.In a second paper" he uses quantum mechanics to consider the effects of vibrations of the inner co- ordination shell on the energy of activation transfer coefficient and the Tafel plots and compares the results with the classical model. The results are independent of the model for the outer co-ordination shell and suggest that the transfer coefficient is a function of temperature that the curvature of Tafel plots should be most marked at low temperatures and that at high overpotentials a limiting current is to be expected owing to activationless transitions. A different approach using the iterative extended Hiickel molecular orbital method has been suggested for examining interfacial problems." As a first step the method has been used in the calculation of the structure of the inner layer of the water/Pt(lll) surface giving a picture of the adsorption of water in which the water molecule lies above three Pt atoms with the oxygen closest to the surface.A hydrogen atom should adsorb at a position in the centre of three surface Pt atoms. Several papers have sought to develop the theory for the complex situation where an electron transfer reaction is occurring at an electrode surface partially or fully covered by an electroinactive adsorbate. Two Russian paper^'^.'^ describe the derivation of equations when the electroinactive adsorbate is a neutral molecule inhibiting the electron transfer process; these theories take into account the effect of the adsorbate on the electronic levels in the electrode the position of the Q2 plane the effective electrode area the dielectric constant of the inner double layer and the effect of adsorbate depolarizer interactions.Lipkowski and Galus14 have taken a more experimental approach to the same problem. They have compared a number of the theoretical equations which have been derived in the earlier literature pointing out that each may be considered to arise by treating the situation at the electrode solution interface as one of competitive adsorption between the solvent W. Schmickler Electrochim. Actu 1975 20,137. lo W.Schmickler Electrochim.Actu 1976 21,161.l1 M.A. Leban and A. T. Hubbard J. Electrounafyt. Chem. 1976 74 253. F. I. Danilov and M. A. Loshkarev Soviet Electrochem. 1975 11,1434. l3 B.N. Afanesev and B. B. Damaskin SovietElectrochem. 1975 11,1451. l4 J. Lipkowski and Z. Galus J. Electrounafyt. Chem. 1975 61,11. 74 D.Pletcher adsorbate and the 'activated complex for electron transfer' where the coverage by the activated complex is described by various isotherms. They have also carried out a statistical analysis of the considerable volume of data for the Cd2"/Cd(Hg) and Zn*'/Zn(Hg) reactions in the presence of various adsorbates and conclude that the best correlations are with the Flory-Huggins Frumkin and Blomgren-Bockris is0 therms. Fawcett and Levinel' have considered the converse but related effect that of acceleration of the electron transfer process by adsorbed non-electroactive ions of opposite charge to the reactant.They have considered the effect as due to ion pairing and treated the situation by estimating the interaction between discrete electroactive ions and the adsorbate represented by a two dimensional distribution function. 2 Techniques Methods for the study of simple electron transfer reactions should be capable of allowing recognition of and discrimination against the effects of other processes such as adsorption coupled chemical reactions and competing non-Faradaic reac- tions. In particular the I-E characteristics must be measured either under conditions where there is no interference from the effects of mass transport or more usually in circumstances where the rate of mass transport may be varied in a controlled manner so that the effects of mass transport and electron transfer may be separated by an extrapolation procedure (to the hypothetical situation where the rate of mass transport is infinite).Commonly we shall be interested in the study of rapid electron transfer reactions (kz> cm s-') and this in turn requires the measurements to be made under conditions of very fast mass transport generally either forced convection or non-steady state diffusion. The most widely used techniques remain cyclic voltammetry chronocoulometry the rotating disc and a.c. methods. It is the purpose of this section to review the important innovations in these methods and with the above criteria in mind to discuss a number of novel methods described during the last two years.Opekar and Beran" have published an extensive review of the theory practice and applications of rotating electrodes. Two modifications of the normal rotating disc electrode the rotating cone electrode" and the rotating patch electrode,18 have been described and it has been shown that there is good agreement between the equations describing the mass transport conditions and experimental data. The equivalent of the rotating ring-disc electrode the rotating patch-patch electrode was also described and this electrode structure certainly has the advantage of ease of construction. Bruckenstein and Miller continue to describe the advantages of modulating the rotation rate of disc electrodes and have considered sinusoidal speed mod~lation.'~ Other possible ways of obtaining high steady-state rates of mass transport arise by using microelectrodes or thin layer cells with a very narrow gap.The steady-state rates of diffusion to a sphere radius r and across a thin layer gap L are proportional lS W. R. Fawcett and S. Levine J. Electroanalyt. Chem. 1975,65 505. 16 F. Opekar and P. Beran J. Electroanalyt. Chem. 1976,69,1. 17 E. Korowa-Eisner and E. Gileadi J. Electrochem. SOC. 1975,123,22. A. R. Despic M. V. Mitrovic B. Z. Nikolic and S. D. Cvijovic J. Electroanal. Chem. 1975,60,141. K.Tokuda S.Bruckenstein and B. Miller J. Electrochem. SOC. 1975 122 1316. Electrochemistry -Simple Electron Transfer Reactions 75 to D/r and D/L respectively (D is the diffusion coefficient of the electroactive species) and hence by making r and L sufficiently small high rates of diffusion become possible.While these methods are in principle both simple and attractive the construction of the microelectrodes and thin-layer cells is a difficult problem since to measure a rate constant of 1cm s-' the key dimension is 0.1 pm. Attempts to design such a thin-layer cell by plunging a carbon rod electrode into a mercury pool did however lead to a new pseudo-steady method for the determination of the kinetics of fast electron transfer reactions. The theory for the growth of mercury droplets on the carbon in such a cell has been discussed20 and it has been shown that the shape of the growth transients may be used to calculate the rate constant for the Hgz2+/Hg couple.The method is possible in fact owing to the high rate of mass transport to the small mercury centres rather than to the dimensions of the thin layer and is suitable for the study of the kinetics over a wide potential range. It may be noted that the solution in the thin layer is unchanged since the reaction at the mercury anode is the reverse of the deposition process. The technique might also be applied to metal ion/amalgam couples. Losev et u1." have pointed out the additional information to be obtained from a steady state I-E study at low overpotentials if the data are presented as a derivative plot dI/dE us. E as well as a direct I us. E plot.The technique is advantageous where there is the possibility of consecutive electron transfers. Several papers have reported innovations in the relaxation techniques. Kojima and Bardz2 have described a simple and reliable apparatus using only commercially available instrumentation for a.c. measurements; the method is based on phase sensitive detection using a lock-in amplifier and a frequency range of 425-4250 Hz and has been used to study the rates of electron transfer to aromatic hydrocarbons (0.5 <kz <10cm s-'). This simple procedure had a good precision and gave values comparable with those already in the literature. An experimental set-up for square-wave faradaic rectification at radio frequencies has been described23 but the study of three couples at Pt or Au electrodes consis- tently gave standard rate constants a factor 10' larger than those reported in the literature.Because of the experimental difficulties associated with this method Sluyters et al.24 have developed a faradaic rectification method based on a sinusoidal modulation. The same authorsz5 have emphasised the increased reliability which may be obtained by the simultaneous use of first and second order techniques for example a.c. impedance and faradaic rectification respectively and the correlation of the data over a wide range of potential and concentration of the reactant. This technique has been used to study the Zn*+/Zn(Hg) and the Cd2+/Cd(Hg) reactions the former process is shown to occur in two consecutive one electron steps but the cadmium reaction has some additional complication.Christie Jackson and Osteryoungz6 have proposed a method alternate drop pulse polarography which has the advantage over normal pulse polarography that 20 P. Bindra A. P. Brown M. Fleischmann and D. Pletcher J. Electroanalyt. Chem. 1975 58 31. 21 V. V. Losev V. V. Gorodetskii K. A. Mishenina and I. P:Slutskii SovietElectrochem. 1975,11,24. 22 H. Kojima and A. J. Bard J. Electroanalyt. Chem. 1975 63 117. 23 M.A. V. Devanathan and S. Abeyagunawardena J. Electroanalyt. Chem. 1975,62 195. Z4 F.Van der Pol M. Sluyters-Rehbach and J. H. Sluyters J. Electroanalyt. Chem. 1975 62 281. 2s F.Van der Pol M. Sluyters-Rehbach and J. H. Sluyters J. Electroanalyt. Chem. 1975 58 177. z6 J. H.Christie L. L.Jackson and R. A. Osteryoung Analyt. Chem. 1976 48 242. 76 D.Pletcher correction is made for the capacitance current due to the expanding mercury drop; alternate drops are used for the measurement of the charging current and the faradaic current so that the former may be subtracted. The same procedure may be used for differential pulse polarography. These authors also point out the improved signal/noise ratio obtained by employing a short drop time down to 50 ms and this has been confirmed by other worker^.^' Rangarajan et aLZ8have applied the decreasing current ramp method to the study of the Fe(CN)64-/Fe(CN)63- couple with excellent results. In this method a linearly decreasing I-t profile is applied to the working electrode and the resulting E-t response recorded.The particular beauty of this method is the ease with which the kinetic data may be extracted from experimental data. Several groups have considered the possibility of using a white noise input to perturb the electrode reaction. RangarajanZ9 has presented a theoretical discussion of the response of the interface to a random current or potential input while Blanc et aL3’ have described a method for rapidly obtaining the impedance diagram over a wide frequency range using a white noise irput technique. The response of the system to the input is deduced by a real time correlation and the impedance is then determined through a Fourier transform. The authors believe that measurements may be made at a sufficient rate to allow the study of time variant systems.Ichise et aL31have reported an essentially similar method. The techniques described above rely heavily on the availability of microprocessors or on-line computational facilities to process data rapidly. This is also the case for the reasonable implementation of the closely related methods of convolution linear sweep voltammetry and neopolarography which are methods of applying semi- integration to the analysis of data from potential sweep experiments. Saveant and Tessier3’ have described the use of convolution linear sweep voltammetry for the study of the kinetics of electron transfer reactions. Their analysis does not require the assumption of a particular form for the potential dependence of the rate constant but requires knowledge of the formal electrode potential; it was shown that this may be obtained from experimental data even for an irreversible process if use is made of both the current-potential and the convoluted current-potential data.The method was applied to the study of the rate of reduction of t-nitrobutane in two solvents (for results see later). Goto and Oldham33 have discussed the shape of neopolarograms for a totally irreversible electron transfer reaction (ktsmall) and the influence of the potential scan rate and the initial potential on the form of the curve. The latter has also applied the semi-integration technique to the analysis of steady- state as opposed to first-sweep cyclic voltammograms. He asserts that the steady- state cyclic voltammogram is easier to obtain experimentally and contains all the 27 H.Blutstein and A. M. Bond Analyt. Chem. 1976 48 248; ibid. J. Electroanalyt. Chem. 1976 68 257. 28 G. Prabhakara Rao S. Lakshmanan and S. K. Rangarajan J. Electroanalyt. Chem. 1975,62 273. 29 S. K. Rangarajan J. Electroanalyt. Chem. 1975,62 43. 30 B. Blanc I. Epelboin C. Gabrielli and M. Keddam Electrochim. Acta 1975 20 599; ibid. J. Electroanalyt. Chem. 1975 62 59. 31 M. Ichise Y. Nagayanagi and T. Kojima J. Electroanalyt. Chem. 1976,70 245. 32 J. M. Saveant and D. Tessier J. Electroanalyt. Chem. 1975 65 57. 33 M. Goto and K. B. Oldham Analyt. Chem. 1976,48 1671. 34 K. B. Oldham J. Elecrroanalyt. Chem. 1976 72 371. Electrochemistry -Simple Electron Transfer Reactions 77 required information.The theory is compared with experimental data for the ferrocyanide/ferricyanidecouple. Semi-integration has also been applied to the analysis of I-t transients from chron~amperometry.~~ Rodgers has shown that a plot of the current versus the semi-integral of the current is linear and the rate constants for the forward and reverse electron transfer reactions may be obtained from the slope and intercept of this graph. It is suggested that this procedure is suitable for on-line digital analysis of chronoamperometric data and that correction for the double layer charging current is possible using a square-wave current pulse. Two other digital procedures for the analysis of I-t transients have been outlined. The is based on a rearrangement of the analytical solution for the I-t transient under conditions of mixed diffusion/electron transfer control showing that a plot of (dI/dt).t4 us. It' is linear and that the slope contains the rate constant for electron transfer. The second is basically a simulation and curve-fitting procedure and the authors3' have also considered the effect of an irreversible following chemical reaction on the I-t transients. Harima and Aoyagui3' have developed a relaxation technique based on temperature-jump. The potential-time response following a rapid increase in the temperature has been shown to be a function of the kinetics of the redox couple in solution and the equation observed has been tested again using the ferrocyanide/ferricyanidecouple. A pressure bomb has been modified to allow electrochemical studies in aprotic solvents at pressures up to 2000 atm.39 Cyclic voltammetry has been used to obtain the reversible potentials for the oxidation and reduction of a series of aromatic hydrocarbons at several pressures and the shift in these potentials with increasing pressure has been explained in terms of solvation and ion pairing effects.One of the most sophisticated on-line computer systems is that described by Mohilner et aL40 for the high precision measurement of differential capacitance curves; the system both controls the experiment and analyses the data. The results are compared with those from an earlier indirect determination of capacitance via drop time measurements (also computer controlled and analysed) and the differen- tial capacitance curves at the dropping mercury electrode obtained by the two methods show systematic differences.It is argued that the drop-time method is to be preferred for the measurement of electrosorption. Finally readers interested in the development of electrochemical methods apd instrumentation are reminded of the biannual reviews which appear in Analytical Chemistry. ' 3 Experimental Investigations The Effects of the Solution Environment.-In several papers the effects of the solvent and the base electrolyte on the thermodynamics and kinetics of the 35 R. S. Rodgers Analyt. Chem. 1975 47 281. 36 P. Kruse Electrochim. Acta 1976 21 85. 3' T. E. Cummings and J. A. Cox J. Electroanalyt. Chem. 1975 60 245. 3R Y. Harima and S.Aoyagui J. Electroanalyt. Chem. 1976,69 419. 39 M. Fleischmann W. B. Gara and G. J. Hills J. Electroanalyt. Chem. 1975,60 313. 4o D. M. Mohilner J. C. Kreuser H. Nakadomari and P. R. Mohilner J. Electrochem.Soc. 1976,123,359. dl D. K. Roe and P. Eggimann Analyt. Chem. 1976,48,9R. 78 D.Pletcher ferrocyanide/ferricyanide couple have been discussed. Gritzner Danksagmiiller and G~tmann~~ have studied this couple in twelve solvents including water acetic acid alcohols and several aprotic media. In all but acetic acid the couple was found to be reversible and hence by assuming that the potential for the oxidation of bisphenylchromium was independent of the solvent it is possible to compare the formal potentials for the ferrocyanide/ferricyanide couple in these solvents.These potentials varied substantially ranging between -0.63 and +1.27 V and the authors found that the formal potentials correlated well with various solvent parameters which describe the ability of the solvents to act as electron acceptors on the assumption that the ferrocyanide is more strongly solvated than the oxidized half of the couple. This is in accord with the known electronic structure of the complexes. The same authors have compared the formal potentials in the twelve solvents when the base electrolyte is a tetraethylammonium or a tetrabutylammonium salt. In some solvents the change in the electrolyte produced a 300 mV shift in Ez whereas in others the shift was much smaller. Since the shift was largest with the solvents of low accepting ability i.e.the weakest solvators this result was taken to indicate competi- tion between the solvent and tetra-alkylammonium ion for sites in the outer co-ordination sphere.Peter et aZ.43have determined both the formal electrode potential and the standard rate constant for the same couple in a series of aqueous electrolytes. The formal electrode potential depends on the nature and the concentration of the cation of the base electrolyte; it becomes more positive with increasing concentration and increases along the series Li' <Na' <K' <Cs' (for concentrations < 1.O moll-') and these trends indicate ion pairing of the ferrocyanide ion to be an important factor. The kinetics were determined using a current impulse technique and a small gold sphere electrode.It was found that the standard rate constant increased along the series Li' <Na' <K' and depended linearly on the concentration of the cations (0.1-10.0 moll-'); the rate constant varied between 5 X and 1.0 cm s-'. Measurements were also reported at a series of temperatures for two electrolytes KF and LiNO,; the enthalpies of activation were independent of the electrolyte and its concentration but the pre-exponential factors both depended on the cation and increased linearly with its concentration. These data were taken to indicate that the formation of the activated complex for electron transfer involved a further associa- tion of a cation of the base electrolyte with the electroactive species which may already be ion-paired.Two earlier papers employing rotating disc methods to determine the kinetic parameters essentially confirm this work. In the in which gold was used as the electrode material a marked effect of the cation of the base electrolyte on the standard rate constant was found. For 0.1M-solutions the rate constant increased along the series Li' <Na' <K' <Cs' and Mg2+ <Sr2' <Ba2' <La3+ the values varying by more than an order of magnitude. In the in which a graphite rotating disc was used a similar dependence on the nature of the cation was found 42 G. Gritzner K. Danksagmiiller and V. Gutmann Inorg. Chem. Acta 1975 17; ibid. J. Electroanalyt. Chem. 1975.72 177. 43 L. M. Peter W. Diirr P. Bindra and H. Gerischer J. Electroanalyt.Chem. 1976.71 31. 44 J. Kuta and E. Yeager J. Electroanalyt. Chem. 1975 59 110. 45 R. Sohr and L. Miiller Electrochim. Acta 1975 20 451. Electrochemistry -Simple Electron Transfer Reactions 79 and it was also shown that the rate constant increased with electrolyte concentration although the dependence found was more complex than that described above and non-linear. These authors also found the mass transport controlled current to depend on the cation ofthe base electrolyte another indication of ion-pairing in bulk solution. Jensen Ronlan and Parker46 have used cyclic voltammetry to study the rate of reduction of cyclo-octatetraene and benzocyclo-octatetraene as a function of the aprotic solvent employed and the size of the tetra-alkylammonium ion of the base electrolyte.The rate constant for this reaction is known to be unusually low and the generally accepted explanation has been the large activation energy associated with the change in molecular geometry from the tub-shaped neutral species to the near planar anion radical. The rate of addition of an electron to benzocyclo-octatetraene and cyclo-octatetraene and the importance of coupled chemical reactions are observed to vary with the solvent. More importantly however in dimethylfor- mamide the heterogeneous rate constant is found to decrease substantially with size of the tetra-alkylammonium cation and also to depend on the concentration of the electrolyte. The authors feel that these observations are compatible with variation of the double layer structure with the solvent the electrolyte and its concentration and that such factors are most important in determining the low rate constant.On the other hand there seems little doubt that the standard rate constant for this couple is low compared with those for other aromatic hydrocarbons. In another paper47 the same reaction in dimethylsulphoxide has been studied by d.c. and phase sensitive a.c. polarography. Again the standard rate constant for the reduction of cyclo-octatetraene is found to be abnormally low and to depend on the size of the tetra-alkylammonium ion of the electrolyte. A further interesting solvent effect has been noted;48 in the aprotic solvent sulpholane cyclic voltammetric studies show the standard rate constants for the addition of an electron to nitrobenzene and the removal of an electron from ferrocene are very low compared with other aprotic media.For ferrocene the effects of the electrode metal and its preparation and of the base electrolyte on the standard rate constant are small and the authors suggest that unusual long-range second-order structuring of the medium (which is very viscous) may be responsible. The variation in the rate of electron transfer reactions with the composition of various alcohol/water mixtures has attracted some attention. Lipkowski and Gal~s~~ have reported an extensive study of five couples [V3+/V2+,Cd2+/Cd(Hg) HPbO,-/Pb(Hg) Mn(NH,X*+/Mn(Hg) and C6H,N02/C,H,N0,-'] in various mix- tures of water with n-propanol i-propanol and t-butanol; the couples were chosen to cover a variety of mechanisms and to examine reactions both close to and away from the point of zero charge.First the equilibrium potentials were measured as a function of solvent composition to determine the changes in the free energy of solvation of the solution-free species. Then the standard rate constants and transfer coefficients were measured using a classical steady-state method. The transfer 46 B. S. Jensen A. Ronlan and V. D. Parker Acta Chem. Scand. 1975 B29 394. 47 A. J. Fry C. S. Hutchins and L. L. Chung J. Amer. Chem. SOC. 1975 97 591. 48 N. R. Armstrong R. K. Quinn and N. E. Vanderburgh J. Electrochem. SOC.,1976 123 646. 49 J. Lipkowski and Z. Galus J. Electroanalyt. Chem. 1975 58 51. 80 D.Pletcher coefficient was found to be independent of solvent composition but the standard rate constant was found to show a dramatic fall on addition of small quantities of the alcohol.A plot of standard rate constant versus solvent composition generally showed a minimum at a few percent added alcohol and then a slow rise with further added alcohol; the minimum occurred at a value of kz several orders of magnitude below that for pure water. The exact position of the minimum depended on the alcohol and the reaction investigated. The results were also typical of those found by other investigators. Tanaka et aL50found a similar dependence for the standard rate constant of Cr'r'(CyDTA),/Cr"(CyDTA) in various CH30H/H20 C2HsOH/ H20 n-C3H70H/H20 and n-C4H90H/H20 mixtures (CyDTA =1,2-cyclo-hexane-diaminotetra-acetate) as did Behr and coworkers5' for the reduction of Zn2' in acetone/water and methanol/water mixtures.All these authors agree that the cause of this fall in the rate constant with small changes in solvent composition is adsorption of the organic solvent at the electrode surface. The details of their explanations of the data differ. Galus et al.49believe the major factor to be a change in the energy of activation and define three possible situations (a) wherc there is no specific solvation of the electroactive species (b) where the electrode and the depolarizer are solvated by the same component of the mixed solvent and (c) where the electrode and the depolarizer are solvated by different components of the mixed solvent.Situations (a) and (b) were likely to be uncommon in the systems studied but would lead only to small changes in kz with solution composition whereas (c) would lead to the observed results owing to the increased energy of activation of reorganiz- ing the solvent shell of the electroactive species in an 'alien medium'. On the other hand Behr Taraszewska and StrokaS1 discuss the effect in terms of changes in the equilibrium concentration of the electroactive species in the surface phase the presence of organic solvent in the interphase lowering the concentration of the charged depolarizer. 'Solvent effects on mechanisms and characteristics of electrode reactions' was the title of one of the plenary lectures at the 1975 ISE meeting in'Vienna.52 In this published lecture Tanaka reviewed the effect of solvent on mass transfer and coupled chemical reactions as well as the electron transfer step itself.Electrode Material Effects.-In the absence of specific interactions between the electroactive species and the electrode the standard rate constant corrected for double layer effects should be independent of the electrode material when metals only are considered. With this thesis in mind Rosanske and Evanss3 have reinvesti- gated the rate constant for the reduction of benzoquinone at Pt Au and Hg electrodes in dimethylformamide; using cyclic voltammetry they obtained values between 0.1 and 1.2 cm s-' the rate constant increasing in the order Pt <Au <Hg. The data necessary to make a double layer correction for these systems is not available but although this correction would reduce the difference (the p.2.c.became more positive in the order Hg <Au <Pt) it is unlikely to explain the large difference in values observed. It may be that oxides or impurities adsorbed at the surface reduce the values at the solid electrodes. These authors also report standard rate N. Tanaka K. Kanno and A. Yamada J. Electroanalyt. Chem. 1975,65 703. 51 B. Behr J. Taraszewska and J. Stroka J. Electroanalyt. Chem. 1975 58 71. 52 N. Tanaka Electrochim. Actu 1976 21 701. 53 T. W. Rosanske and D. H. Evans J. Electroanalyt. Chem. 1976,72 277. Electrochemistry -Simple Electron Transfer Reactions 81 constants for four quinones at Hg and when approximate double layer corrections are made the values are similar ca.1cm s-’. There is increasing interest in non-metal electrodes. A study of the kinetics of two couples at tungsten bronze electrodes has been rep~rted.’~ A series of tungsten bronzes Na WO (x = 0.4 -0.9) were prepared and the rate constants for the Fe(CN)64-/Fe(CN)63- and Fe(Ox),4-/Fe(Ox),’- couples in aqueous solutions were determined by cyclic voltammetry. While differences in rate constant with structure of the bronze were observed they were less than expected perhaps because of the depletion of sodium ions from the surface which results in a tendency to leave a WO surface in each case. The tungsten bronzes were however shown to be good electrode materials in aprotic solvents and the oxidation and reduction of aromatic hydrocarbons was shown to give reversible cyclic voltammograms.In two papers electron transfer reactions at semiconductor electrodes have been considered.s5.’6 Gleria and Memming” have compared several electron transfer reactions at n- and p-Sic and used the results to deduce the energy levels of the conduction and valence bands at the surface of the electrode materials. These energy levels are compared ‘with those of other common semiconductor electrodes. In the second papers6 similar arguments were used to deduce the solid-state properties of the iron oxide layer produced by passivating iron in alkali from studies of the rate parameters for the Fe(CN)6“-/Fe(CN)63- couple at such materials. Good Tafel behaviour was found and the rate constant was found to be less than at a Pt electrode.The oxidation of aromatic amines at a calomel electrode has been reported.” The layer of calomel was formed in situ using a hanging mercury drop electrode and a chloride electrolyte. The concentration of chloride ion and the potential scan rate affect the thickness and properties of the surface layer of the calomel ana in cyclic voltammetric studies the positive limit affected the form of the reverse scan probably because of a decrease in the conductivity of the calomel layer when its potential is made more positive than ca. 0.7 V. Under suitable conditions good reversible cyclic voltammograms were obtained for benzidine and for all amines investigated the oxidation peak current was proportional to their concentration.Other forms of chemical modification of the surfaces of electrodes have also been investigated. Moses Wier and Murray’’ initiated the study of simple electron transfer reactions e.g. Fe(CN)64-/Fe(CN)63- at a tin oxide electrode to which organic bases had been chemically bonded. These modifications are expected to have particular importance in directing the selectivity and controlling the stereochemistry of electrode reactions. For example Watkins et ~1.’~ have described a procedure for covalently bonding an optically active amino-acid ester to graphite and the use of this electrode in chiral synthesis; this type of synthesis is an extension of more classical procedures where the optically active species directing the stereochemistry of the reduction is adsorbed on to the electrode.60 Very recently two papers have reported the chemical attachment of an electroactive group to the 54 M.Amjad and D. Pletcher J. Electroanalyt. Chew. 1975 59 61. 55 M. Gleria and R. Memming J. Electroanalyt. Chew. 1975 65 163. 56 A. M. T. Olmedo R. Pereiro and D. J. Schiffrin J. Electroanalyt. Chew. 1976 74 19. 5’ W. Kernula B. Behr and J. Taraszewska J. Electroanalyt. Chem. 1975 65 651. 58 P. R. Moses L. Wier and R. W. Murray Analyt. Chem. 1975,47 1882. 59 B. F. Watkins J. R. Behling E. Kariv and L. L. Miller J. Amer. Chew. Soc. 1975 97 3549. J. Hermolin J. Kopilov and E. Gileadi J. Electroanalyt. Chew. 1976 71,245. 82 D.Pletcher electrode surface; in one the electroactive group is the methylpyridinium cation61 and in the other an iron-sulphur cluster.62 These modified surfaces may also prove to be of theoretical interest since it should be possible to study the effects on the kinetics of electron transfer reactions of varying the structure and length of the chain attaching the electroactive group to the surface.Structural Effects.-Kojima and Bard,63 using the a.c. method described above,” have determined standard rate constants for the reduction of 16aromatic hydrocar- bons in dimethylformamide and at a Hg electrode. After correction of the data for double layer effects the free energies of activation were calculated. The Marcus theory predicts that these free energies of activation should be the same as those for the corresponding homogeneous electron transfer reactions and with a few excep- tions this appeared to be the case.Furthermore there was a reasonable correlation between the free energies of activation and the reciprocal of the molecular radii although the slope of this plot did not agree with that estimated by the Marcus theory. It is clear however that the reduction of most aromatic hydrocarbons is an essentially simple outer-sphere reaction where the major factor in determining the energy of activation is rearrangement of the solvent shell. The slow rate of reduction of cyclo-octatetraene has been mentioned ea~lier.~~.~’ A further paper64 has described experiments to confirm the importance of changes in molecular geometry during electron transfer in increasing the energy of activation for electron transfer.Following the synthesis of a series of polynuclear hydrocarbons with an eight carbon atom central ring some with a planar structure and some with a tub shape their electrochemical reduction in dimethylformamide was studied. Although in one case there was a complication from the proximity of a second one-electron reduction leading to the dianion it was possible using simulation and curve fitting procedures to obtain from the experimental cyclic voltammograms the standard potentials and standard rate constants for the R/R-and R’-/R-couples. It was clear that where there was a change in molecular geometry on going from the neutral hydrocarbon to the anion radical i.e. tub to planar the standard rate constant was an order of magnitude lower than when both neutral molecule and anion radical were planar.The R-/R-couples were all fast since no changes in molecular geometries were involved. It was also suggested that the deviations from a linear relationship between the half-wave potential for the R/R-process and the energy of the lowest unfilled molecular orbital estimated by Huckel calculations were mea- sures of the energy required to bring about the change in molecular structure. Saji and coworkers have published several describing the elec- trochemistry of metal ion/2,2-bipyridine complexes in aprotic solvents particularly emphasizing the relationship between electrochemical parameters and structural factors. Using the galvanostatic double pulse technique they have measured the standard rate constants for the reduction of a series of iron(II1) dipyridyl complexes65 and showed that the values decreased as the dipyridyl ligands were displaced by cyanide ion.This correlation between the standard rate constant and the number of 61 P. R. Moses and R. W. Murray J. Amer. Chem. SOC.,1976 98 7436. 62 R. J. Burt G. J. Leigh and C. J. Pickett Chem. Comrn. 1976 940. 63 H. Kojima and A. J. Bard J. Amer. Chem. SOC.,1975 97 6317. 64 H. Kojima A J. Bard H. N. C. Wong and F. Sondheimer J. Amer. Chem. SOC.,1976,98,5560. 6s T. Saji T. Yamada and S. Aoyagui J. Electroanalyt. Chem. 1975,61 147. 66 T. Saji and S. Aoyagui J. Electroanalyt. Chem. 1975,63 31. 6’ T. Saji and S. Aoyagui J. Electroanalyt. Chem. 1975 58 401; ibid.1975 60 1. Electrochemistry -Simple Electron Transfer Reactions 83 dipyridyl ligands was thought to be due to the delocalization of the added electron to a large ligand 7r orbital when there were several aromatic bidentate ligands. The same technique was employed to obtain standard rate constants for the reduction of the trisdipyridyl complexes of Fe Ru Os Cr Ti V and Mo66 and it could be shown that the values fell into two groups depending on whether the added electron went into a ligand r*-orbital or a metal t2g orbital. The difference probably lies in the activation energy required to reorganize the inner sphere co-ordination shell in the two cases. In an earlier paper67 the relationship between the formal electrode potentials for the electron transfer couples of such complexes and their electronic structure was studied (it should be noted that these dipyridyl ligands stabilize several oxidation states of many transition metals and hence polarograms show up to four reversible reduction waves).Constant and Davi~~**~' have reported similar studies of the biologically important iron(II1) porphyrin complexes in aprotic solvents. A relationship between the pKA of the axial ligands and both the formal electrode potential of the Fe"'/Fe" couple and the standard rate constant for these processes was observed. The electrochemical studies are complicated by a number of factors particularly electron transfer reactions associated with the porphyrin ring competition for the axial co-ordination sites between the organic bases and the solvents and ion pairing phenomena.There is no doubt however that the need for ligand exchange or a change in spin state of the metal nucleus during electron transfer causes the value of the standard rate constant to drop. In water-rich media the rate of these reactions increases substan- ti all^.^' Vijh and Randin71 have pointed out that there is a good linear correlation between the exchange currents for the couples M2'/M and M2+/M(Hg) where M is one of a series of transition metals and the rates of substitution of the aquo-metal complexes by water in homogeneous solution. This may again be taken as an indication of the importance of reorganization of the solvent shell in determining the energy of activation of the electron transfer process and perhaps that partial dehydration is the first step in the overall reaction sequence.The Mechanism of Two-electron Processes.-Many electrode reactions involve the overall transfer of two electrons and in most cases there remains doubt as to whether the electrons are exchanged simultaneously or consecutively (or in other words the degree to which the one-electron intermediate has a discrete role in the reactions). Thus several investigations of this problem have been made. A Norwegian group have continued their studies of a series of M"/M and M"/M(Hg) reactions and have published an impressive sequence of In 68 L. A. Constant and D. G. Davis Analyt. Chem. 1975,47 2253. 69 L. A. Constant and D. G. Davis J. Electroanalyt.Chem. 1976 74 85. 70 L. Bynum and D. G. Davis Bioelectrochem.and Bioenergetics,1975 2 184. A. K. Vijh and J. P. Randin J. Phys. Chem. 1975,79 1252. 72 T. Hurlen and H. A. Dasnes Acta Chem. Scand. 1975 A29 21. 73 T. Hurlen Electrochim. Acta 1975 20 499. 74 E. Eriksrud J. Electroanalyt. Chem. 1975 60 41. 75 E. Eriksrud J. Electroanalyt. Chem. 1975 60 53. 76 T. Hurlen and K. P. Fischer J. Electroanalyt. Chem. 1975,61 165. 77 T. Hurlen and E. Eriksrud J. Electroanalyt. Chem. 1975,63 157 78 E. Eriksrud J. Electroanalyt. Chem. 1976 67 69. 79 T. Jurlen and R. Smaaberg J. Electroanalyt. Chem. 1976 71 157. 8o E. Eriksrud J. Electroanalyt. Chem. 1976 71 169. 81 T. Hurlen J. Electroanalyt. Chem. 1976,73 285. 84 D.Pletcher general the investigators set out to characterize the mechanism and kinetics of the processes in non-complexing aqueous solutions and then study the changes which occur on addition of complexing agents.The experimental procedures involve equilibrium measurements to determine the forms of the metal ions in solution and to evaluate activity coefficients followed by steady-state potential step and chronopotentiometric experiments to elucidate the nature of the electroactive species and the mechanism and kinetics of the electron transfer process. At a nickel metal cathode the Ni(H20)62+ ion is shown to reduce in two one- electron steps the Ni'/Ni reaction occurring at kink sites but the Ni"/Ni' reaction over the whole In high concentrations of chloride the mechanism is modified only to the extent that there is parallel reduction of Ni(H20)62+ and the monochloro-complex NiC1(H20)s'.Studies of the Ni"/Ni(Hg) couple showed that in non-complexing media both the direct two-electron transfer and the two-step mechanism with a discrete Ni' intermediate can be important in different potential regions. In solutions containing ammonia it is the ammonia complex which is reduced and only the symmetrical direct two-electron transfer (i.e. n =2 CY =i)is obser~ed.'~ Similar conclusions were drawn from the experiments with the Co/Co(Hg) couple in ammonia ~olutions.~~ The Zn2'/Zn couple in aqueous chloride was also shown to involve a solution-free zinc(1) intermediate.76v77 The Zn'/Zn couple was very rapid but the Zn"/Zn' complex was complicated by some slow equilibria between zinc@) species in solution; above l.0M-chloride ion it was mainly the hydrated ZnC1 species which was reduced.On addition of ammonia to chloride media the characteristics for the Zn"/Zn(Hg) couple changed from those for a mechanism involving two consecutive one-electron transfers with zinc(1) as an intermediate to those for an almost symmetrical two-electron transfer (n=2 CY =i).The conclusions drawn concerning this couple in non-complexing media are in accord with those of Sl~yters~~ discussed above. The studies of the Mn"/Mn(Hg) couple were carried out in a range of aqueous chloride The mechanism and kinetics were independent of the cation of the electrolyte and the reaction was shown to take place by two consecutive one-electron steps with Mn' as a low-concentration intermediate.It is the present overall conclusion of these authors that the metal(1) species is a discrete intermediate in the reduction of bivalent ions in non-complexing media when the additional electron goes into a c+-antibonding orbital (Mn Ni Cu Zn) but not when it is a c+-nonbonding orbital which is involved (Fe Co). In the field of organic chemistry direct two-electron transfers are very unusual and indeed although many examples have been claimed few have stood the test of time. Phelps and Bards2 have reported a thorough study using a wide range of elec- troanalytical techniques of the oxidation of tetra-p-anisylethylene and a series of dimethylamino-substituted tetraphenylethylenes.They were able to demonstrate examples where (a) the potentials for the two one-electron oxidations were well separated and two distinct processes were observed (b) the potentials were close together and hence overlapping waves or peaks were obtained on I-E curves and (c) direct two-electron transfer appeared to occur. Even with this last class it was 82 J. Phelps and A. J. Bard J. Electroanalyt. Chem. 1976,68 313. Electrochemistry -Simple Electron Transfer Reactions 85 however possible to obtain e.s.r. spectra for the cation radical intermediate during a controlled potential oxidation and therefore it must be concluded that the oxidation occurs in two consecutive one-electron steps but the potential for the cation radical/dication couple is less positive than the hydrocarbon/cation radical couple.Solvation ion pairing and structural factors are shown to determine the relative potentials of the two couples; it is suggested that an important factor reducing the difference in potentials between the R/R+ and R*+/R++couples is relief of steric strain because of conformational changes during oxidation. The oxidation of carotenes has been reported to be a direct two-electron process in aprotic solvents.83 The I-E curves for these molecules are independent of electrode potential and solvent and conform closely to those expected for a two-electron reversible process. It is proposed that this observation was due to the effect of paired correlation in extended .rr-electronic systems. Whether the cation radical is a discrete but readily oxidized intermediate is uncertain until the mechanism has been more closely investigated.The Potential Dependence of the Transfer Coefficient.-As pointed out in an earlier section most modern theories of electron transfer would indicate that the transfer coefficient should be a function of potential i.e. plots of log I uersus E should be non-linear. The magnitude of this effect is however relatively small and in order to test this postulate it is necessary to carry out accurate measurements of the rate of the electrode process over a wide potential range and to be able to make precise double layer corrections. In addition the theories only apply to simple one-electron transfers and the variation of the transfer coefficient with potential is greatest with reactions with a low activation energy.Hence few experimental techniques are suitable and the experimental studies necessary to investigate this facet of the theory remain at the limits of our capabilities. Therefore while three papers have described such studies it is not surprising that their conclusions are dissimilar. Saveant and Tessier3* have applied convolution cyclic voltammetry to the study of the reduction of t-nitrobutane in acetonitrile and dimethylformamide; as a result they obtained Tafel slopes which were non-linear. They considered that this apparent variation of the transfer coefficient was not due to double layer effects since there are experimental data to show that the (D2potential varies linearly with potential in the region studied.Analysis of the data showed that the transfer coefficient was a linear function of potential and that the slope of this plot was of the order predicted by Marcus theory. Similar conclusions were drawn by Bindra Brown Fleischmann and Pletcher who used the thin layer method described above2' to investigate the mercurous ion/mercury rea~tion.'~ They were able to carry out studies over a 500 mV range; these indicated that not only was the transfer coefficient a function of potential but that the rate constant/potential plots went through maxima at high overpotentials the rate of electron transfer actually decreasing. The results were analysed using the equations derived by Marcus and were shown to be both entirely self-consistent and in good agreement with his theory i.e.plots of transfer coefficient versus corrected 83 V. G. Mairanovsky A. A. Engovatov N. T. Ioffe and G. A. Samokhvalov Soviet Electrochem. 1975 11 174; ibid.,J. Electroanalyt. Chem. 1975 66 123. 84 P. Bindra A. P. Brown M. Fleischrnann and D. Pletcher Electroanalyt. Chem. 1975 58 39. 86 D.Pletcher overpotential were linear with reasonable slopes and intercepts. The major doubt about this study however must lie in the nature of the couple investigated. Overall it is not a simple electron transfer reaction since it involves the transfer of two electrons per mercurous ion and the formation of a new phase. The opposite viewpoint is represented by the paper by Weaver and An~on,~' They studied the reduction of three chromium(Ii1) species Cr(H,O),SO,' Cr(H20)5F2+ and CX-(H,O)~~' chosen because of their different charges and hence different double-layer corrections.Using polarography and chronocoulometry they were able to obtain data for the Cr"'/Cr" couples over a wide potential range and after double layer corrections they were unable to find any evidence for variation of the transfer coefficient with potential for these couples. The authors however point out that their conclusions are not necessarily at variance with the essential notions of Marcus theory because of the relatively high energy of activation for these CrlI1/CrlI couples; the best evidence in homogeneous solution is for reactions of very low activation energy. The Influence of the Double Layer and Adsorbed Species.-The presence of the supporting electrolyte and added adsorbates are known to have a marked effect on the rate of electrode reactions owing to both electrostatic and chemical (e.g.complexation ion pairing ligand bridging) factors. Normally the contribution to the change in rate due to electrostatic interactions is calculated by using the equations which relate the 42potential to the surface charge and the concentration and type of the supporting electrolyte and which result from the Gouy-Chapman-Stern model of the electrode/solution interface and substituting the value of the 42potential into the Frumkin equation [for example see equation (4)]. Discrepancies between the rate-potential relations for different electrolyte solutions or different concentrations of the electrolyte after this double layer correction has been made are then attributed to chemical factors.Weaver and Ansons6 have sought to test this approach by examining the kinetics of the Cr"'/Cr" and Eu"'/Eu" couples in a series of electrolytes which do not specifically adsorb. Using polarography and chronocoulometry to determine the rates of the reactions and a potential step method to obtain the surface charge-potential curves they conclude that the Gouy- Chapman-Stern model almost always overestimates the variation of the 4 potential with applied potential. Various other factors which could account for this apparent discrepancy are considered and ruled out. The statistical theory of Krylov and Levich is considered better but not perfect.In the following papers the same authors consider the effect of the addition of specifically adsorbing anions on the same couple^.^'*^^ It is suggested that the addition of specifically adsorbed anions to solutions containing cationic reactants may produce changes in the reaction rate due to (i) changes in the double layer structure particularly to the potential across the double layer (ii) formation of ion pairs or complexes in solution and (iii) specific chemical interactions in the transition state e.g. ligand bridging. It is concluded from the data obtained for the solutions 85 M. J. Weaver and F. C. Anson J. Phys. Chem. 1976,80 1861. 86 M. J. Weaver and F. C. Anson J. Electroanalyt. Chem. 1975 65 71 1.8' M. J. Weaver and F. C. Anson J. Electroanalyt. Chem. 1975 65 737. 88 M. J. Weaver and F. C. Anson J. Electroanalyt. Chem. 1975,65 759. Electrochemistry -Simple Electron Transfer Reactions containing iodide and bromide ions that the rate enhancement observed is in good agreement with the Frumkin equation when experimentally determined 42values were employed but not when the values calculated from Gouy-Chapman-Stern model were used (this is taken as further evidence that this model overestimates the variation of 42with E). This agreement with the Frumkin equation indicates the absence of specific interactions and that the rate enhancement is due to (i) above. The behaviour of chromium(II1) in solutions of thiocyanate was similar to that in iodide and bromide but the data for europium(II1) showed the presence of an additional specific chemical interaction.Analysis of the potential dependence of the rate of the Eu"'/Eu" reaction in the presence of thiocyanate indicated that this additional factor is ligand bridging by the adsorbed thiocyanate ion. This is essen- tially confirmed by the observation of a decrease in rate on addition to the solution of iodide ion the major effect of iodide in this system being to compete with thiocyanate for adsorption sites on the electrode surface. The general approach outlined by Weaver and Anson in these three papers86-88 is complex but seems to offer hope for a more detailed understanding of electron transfer at electrode/electrolyte solution interfaces.Similar studies of the V1ll/Vrr and Eu"'/Eu" complex in sulphuric perchloric hydrochloric and hydrobromic acid solutions were undertaken by Niki and Mi~ota.~~ In each case the 42potential was estimated from electrocapillary curves and it was found that when the Frumkin correction had been applied the data in sulphuric perchloric and hydrochloric acid were the same. Indeed only for the V1xl/Vxr couple in hydrobromic acid was a substantial enhancement in rate observed; this was again attributed to ligand bridging by bromide ion. Two papers have suggested the investigation of the effect of the addition of a strongly adsorbed but chemically inactive species on the kinetics of a couple as a method of distinguishing inner- and outer-sphere electron transfer reactions at electrode s~rfaces.~~~~~ In the first Weaver and Anson9' studied the kinetics of reduction of six Cr(H20)5X2+ complexes Cr(H,O),SO,' and Cr(H20)63+ and noted that in three respects the complexes fell into two groups.The results for the first group showed an increase in the rate on addition of iodide a specifically adsorbed but chemically inactive anion a transfer coefficient greater than 0.5 and a relatively high standard rate constant. On the other hand the data for the second group showed a decrease in the rate on addition of iodide a transfer coefficient less than 0.5 and a relatively low standard rate constant. The authors consider on theoretical grounds that the behaviour exhibited by the first group is that to be expected for complexes reduced by an outer sphere mechanism; conversely the data obtained for the second group is that predicted for complexes reduced by an inner-sphere mechanism.Kravtsovgl has suggested a related but different set of measurements for making this distinction (i) a study of the kinetics of the couple as a function of the double layer structure; (ii) the effect on the kinetics of the addition of an adsorbed species of opposite charge; (iii) variation of the electrode material -an outer sphere reaction will show only a small change in rate when corrected for the c#~ potential on 89 K. Niki and H. Mizota J. Electroanalyt. Chem. 1976 72 307. 90 M. J. Weaver and F. C. Anson Inorg. Chem. 1976,15 1871. 91 V. I. Kravtsov J. Electroanalyt. Chem. 1976,69 125.88 D.Pletcher variation of the electrode material; (iv) comparison of the rate of the electrode process with that for homogeneous ligand substitution reactions -the latter must be faster for inner sphere reactions; and (v) determination of the energy of activation -EAfor an inner sphere reaction is larger than for an outer sphere reaction. It is clear however that these rules should be applied with extreme caution since the pos- sibilities for misinterpretation of the data are many; in addition to the complexities discussed above there are also the possibilities that the complex itself will adsorb9' or that anions adsorbed on the surface will induce adsorption of the complex.93 Hence mechanistic assignment should be based only on a thorough and broad investigation.Fronaeus and Johans~on~~ have studied the Cu"/Cu(Hg) couple in aqueous solutions containing acetate glycollate glyoxylate and pyruvate using an a.c. technique. In all systems they conclude that it is the Cu"/Cu' step which is rate determining and that the enhancement in the rate of this process by the carboxylate anions is far in excess of that predicted by a simple double-layer correction. This acceleration of the electron transfer is accounted for by ligand bridging similar to that observed with these anions in homogeneous solution. As discussed in Section I the presence of an adsorbate layer on the electrode does not necessarily cause rate enhancement; inhibition is often observed. The latter is for example found when the Fe3'/Fe2' couple is studied at a gold electrode in the presence of phosphonium and arsonium ions and dibenzyls~~phoxide.~~ These species are strong inhibitors particularly in the Tafel regions and cause changes in the Tafel slope.The mechanism of inhibition is considered to be largely 'reactive' i.e. the Fe3'/Fe2' interconversion occurs on top of the adsorbate layer which serves to increase the energy of activation of the electron transfer process. In the anodic limiting current region the mechanism may change to 'indifferent inhibition' i.e. the reaction occurs only at free sites on the surface since the inhibitor blocks the electron transfer completely. In this potential region the inhibitor may partly be surface oxide. The study of the reduction of anions is a traditional testing ground for the effect of the double layer on electrode kinetics because of the low values of the transfer coefficient which allow studies over a wide potential range.Moreover the minima observed in the limiting current plateaux are striking and unusual features and agreement between theory and experiment are therefore convincing. De Levie and Nemesg6 have studied the reduction of perbromate in dilute solutions of sodium halides using both d.c. and a.c. polarography. In the very weakly adsorbing electrolyte sodium fluoride they find a low and potential-dependent value for the transfer coefficient. They further conclude that the marked effect of the other halides on the kinetics of the reduction can be accounted for quantitatively by a classical double-layer correction and that there are no specific chemical interactions between the anions.This latter conclusion has been criticised by Guidelli and Fore~ti,~' 92 M. J. Weaver and F. C. Anson J. Electroanalyt. Chem. 1975,60 19. 93 E. A. Neves and F. C. Anson J. Electroanalyt. Chem. 1976,71 181. 94 S. Fronaeus and C. L. Johansson J. Electroanalyt. Chem. 1975,60 29. 95 M. S. Abdelaal A. A. El Miligy G. Reiners and W. J. Lorenz Electrochim. Acta 1975 20 507. 96 R. de Levie and M. Nemes J. Electroanalyt. Chem. 1975,58 123. 97 R. Guidelli and M. L. Foresti J. Electroanalyt. Chem. 1975 67 231. Electrochemistry -Simple Electron Transfer Reactions 89 whose data show specific effects due to halides and thiocyanate in addition to those predicted by the Frumkin equation.They point out however that some of the differences observed may be due to differences in the electrolyte concentrations. Chauan Fawcett and McCarrick9* have sought to study the effect of the double layer on the energy of activation of electrode processes. Using periodate as well as proton as the electroreducible species they measured 'corrected' Tafel plots as a function of temperature (15-35 "C) for different supporting electrolytes. For periodate they found that the energy of activation and the transfer coefficient depended on the cation of the electrolyte; the transfer coefficient also depended on temperature. The data for proton reduction were different the energy of activation was independent of the cation and the transfer coefficient did not change with temperature.The absolute rate (or indeed the frequency factor) depended markedly on the cation of the electrolyte for the hydrogen evolution reaction. The authors conclude that both reactions occur at the (P2 plane whose distance from the surface depends on the cation of the electrolyte. The periodate reduction is additionally affected by ion pair formation. Further studies of the reduction of persulphate have also been reported. Frumkin .~~ et ~ 1have studied the reaction at a series of electrodes (copper amalgam bismuth tin lead cadmium and indium) and in a range of electrolytes. The Tafel plots when corrected for double-layer effects are independent of the electrode metal but show variations with the cation of the electrolyte.These results are interpreted as indicating that the site of electron transfer is further from the electrode surface than the (P2 plane. Slow penetration of the anion through the double layer to the negatively charged electrode is rejected as an explanation. loo Other Studies.-Simakin'o' has reported probably the first electrode kinetic data for the transuranium element neptunium; steady-state measurements were made at a Pt electrode in several aqueous electrolytes for the couple NpO2'+/NpO2'. The standard rate constant cm s-l and transfer coefficient 0.4 were almost the same in acidic and basic solutions. Ogura et a1.'02 have reported a study of the oxidation of the iron(I1) tris-o- phenanthroline complex in aqueous media and have determined the standard rate constant as 0.054 cm s-' at room temperature using a potential step method.The reaction was also investigated at a series of temperatures in order to determine the energy and entropy of activation; the values obtained were 7.12 kJ mol-' and -0.24 J K-' mol-'. The value for the entropy of activation for this oxidation in homogeneous solution is -0.17 J K-' mol-'. This difference may be due to the high degree of order of the solvent molecules around the activated complex at the electrode surface or a highly symmetrical ion species as the activated complex although this would require cleavage of Fe-N bonds. This review has largely been a discussion of the factors affecting the kinetics of simple electrode reactions and hence relatively little mention has been made of 98 B.G. Chauan W. R. Fawcett and T. A. McCarrick J. Electroanalyt. Chem. 1975 58 275. 99 A. N. Frumkin M. V. Nikolaeva-Fedorovich N. P. Berezina and K.H. E. Keis J. Electroanalyt. Chem. 1975 58 189. 100 V. S. Krylov W. R. Fawcett and V. A. Kir'yanov Soviet Electrochem. 1975 12 416 521. 101 G. A. Simakin Soviet Electrochem. 1975 11 947. 102 K. Ogura K. Nahara and M. Ueda Electrochim. Acta 1976 21 807. D.Pletcher reversible one-electron processes. Before finishing however it is appropriate to emphasize that to the many chemists who use electroanalytical techniques to investigate synthesis homogeneous chemical reactions or as a tool for probing molecular structure it is usually highly advantageous to find conditions where the electrode reaction is reversible.Firstly it allows the definite identification of the product of the electrode process at least on the timescale of the experiment. Thus for example cyclic voltammetry has been used to prove the stability of the dianions of aromatic hydrocarbon^,"^ the ferrocene anion,lo4 and the chromium hexacar- bony1 cation radi~a1.l’~ Secondly it allows the rapid determination of the formal electrode potential for the couple; this potential gives information on the redox behaviour of the couple and the energy levels and/or solvation of the two halves of the couple. For example the reversible oxidation potentials of a series of metal carbonyls [M(CO),-,L,]” may be directly related to the energy of their highest filled molecular orbital and shown to depend in a simple manner on the nature of the ligand L the number of substituent ligands and the charge on the complex.’o6 103 B.S. Jensen and V. D. Parker J. Amer. Chem. Soc. 1975,97 5024. 104 N. El Mur and E. Laviron Tetrahedron Letters 1975 875. 105 C. J. Pickett and D. Pletcher J.C.S. Dalton 1976 636. 106 C. J. Pickett and D. Pletcher J. Organometallic Chem. 1975 102 327.

ISSN:0308-6003    

DOI:10.1039/PR9767300071

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

6 Spectroscopic Studies of Solvation BY M. C. R. SYMONS Departmentof Chemistry University of Leicester Leicester LEI 7RH 1 Introduction This is a large field which has received only glancing attention in recent Annual Reports. Since the Reporter is limited to some 100references justice cannot be done and he has therefore allowed some of his own bias to influence the choice of topics. Thus only n.m.r. e.s.r. i.r. Raman and U.V. spectroscopic studies are considered. Biological systems are ignored despite the many exciting advances in this area and transition-metal ions are also ignored. Also acid-base studies are omitted. Solvents and ‘neutral solutes are considered relatively briefly the accent being on ionic solvation. Structural aspects are discussed in greater detail than kinetic phenomena.Although references over the past two years are called upon when possible earlier key references are also quoted. Developments in technique and in theory are not explicitly considered. Various aspects of the subject have been recently reviewed. Gordon’s interesting book entitled ‘The Organic Chemistry of Electrolyte Solutions’’ includes frequent references to spectroscopic studies; a two-volume work on ion-pairing includes chapters on the application of spectroscopic techniques especially e.s.r. spectros- copy;2 and the treatise on ‘Water’ edited by Franks contains chapters on various forms of ~pectroscopy.~ The huge upsurge of papers on the use of Fourier Transform n.m.r. techniques includes many that are concerned with solvation and there have been several books and reviews on this topic.Dynamic aspects of n.m.r. studies have been reviewed extensively by Jackman and C~tton.~ The Specialist Periodical Reports of the Chemical Society on n.m.r. contain in particular excellent chapters on ‘Medium Effects’ by Foreman.’ The application of spectroscopy to anion solvation has been reviewed in a book primarily concerned with solvated electrons,6 and a forthcoming review deals with n.m.r. studies of electrolyte solutions.’ J. E. Gordon ‘The Organic Chemistry of Electrolyte Solutions’ Wiley-Interscience New York 1975. ‘Ions and Ion Pairs in Organic Reactions’ ed. M. Szwarc Wiley-Interscience New York 1972 Vols. 1 and 2. ‘Water -A Comprehensive Treatise’ ed. F. Franks Plenum Press New York 1972.‘Dynamic Nuclear Magnetic Resonance Spectroscopy’ ed. L. M. Jackman and F. A. Cotton Academic Press New York 1975. ‘Nuclear Magnetic Resonance’ ed. R. K. Harris (Specialist Periodical Reports) The Chemical Society London 1972-1976 Vols. 1-5. M. C. R. Symons in ‘Electron-Solvent and Anion-Solvent Interactions’ Ed. L. Kevan and B. Webster Elsevier Amsterdam 1976. ’ A. K. Covington and K. E. Newman in ‘Modern Aspects of Electro-chemistry’ ed. J. O’M. Bockris and B. E. Conway Plenum Press N.Y. 1977 Vol. 12 pp. 41-127. (The Reporter thanks Dr. A. K. Covington for allowing him to see this review prior to publication.) 91 M.C.R.Symons 2 N.M.R. Spectroscopy Solvents.-We are only concerned with structurally significant shifts but care must be taken in attributing all shifts to structural effects such as hydrogen bonding since there are a variety of non-specific effects that may be significant.Thus the general equation' for the shielding u of a nucleus in some medium is u=ug+u~+u,+ow+uE+uc (1) where only ucis of real chemical significance. The term upis the gas-phase shielding and (Tb is the bulk susceptibility shift which can be ignored if an internal reference is used. The term u,arises from any non-zero averaging of magnetic anisotropies of the solvent molecules and is frequently significant. The van der Waals term u,,, is always present in the liquid-phase and uE,the so-called reaction field term may sometimes be considered together with uc.Foreman (Ref.5 Vol. 3) has recently considered these non-specific effects in depth and it is clearly extremely difficult to differentiate between them. One vital factor is the use of a suitable reference. Internal references are often misleading especially if shifts are small since they may also be subject to the factors that are shifting the resonance of interest. An example is the use of TMS as a reference for studying aromatic solvent-induced shifts (ASIS). It seems that there is a relatively large ASIS effect for TMS protons' and hence absolute ASIS shifts must be re-calculated. Fortunately the empirical use of ASIS effects is not altered provided TMS is always used as a reference. Nevertheless this underlines the dangers and it must always be wise to check with an external marker despite the loss of precision that this introduces.For hydrogen-bonding systems it is customary to link the magnitude of the acidic proton shift with the energy of formation of the bond but this can be a dangerous procedure as has been stressed for example by Slejko and Drag0.l' Using AH values obtained calorimetrically they showed that linear relationships between AH and the shift Aw were not always obeyed. They explained the shifts in terms of an electric field model which utilises the polarizability of the X-H bond and the field from the lone-pair of electrons from the base. Another study that seems to illustrate the complexity of the underlying physical causes of shifts centres around the 19Fshifts for a variety of aromatic fluorides.Thus effects are intra- rather than inter-molecular but the controversy over their origin can be carried through to medium effects. Thus for the systems (1)and (2) Adcock and Gupta" consider that the polar field effect is most important in controlling 19F shifts whereas Fukunaga and Taft'* consider that this contribution is minor. It may well be that for medium shift studies it is wiser not Me Me (1) (2) A. D. Buckingham T. Schaefer and W. G. Schneider J. Chem. Phys. 1960 32 1227. F. H. A. Rummens and R. H. Krystynak J. Amer. Chem. SOC.,1972,94 6914. F. L. Slejko and R. S. Drago J. Amer. Chem. SOC.,1973,45 6935. W. Adcock and B. D. Gupta J. Amer. Chem. SOC.,1975,97,6871. j2 J. Fukunaga and R. W. Taft J. Amer. Chem. SOC.,1975,97 1612. Spectroscopic Studies of Solvation 93 to attempt a detailed explanation of the physical sources of the shift but simply to utilise it to provide empirical information about the system.Water and aqueous solutions still dominate solvent studies. Temparature studies for pure water have been extended to -38 “C using narrow capillary tubes or by using water emulsion^.'^ The results tie in well with those previously published and confirm that the shift is non-linear (Figure la). Also in an important technical advance Linowski et aZ.14have succeeded in measuring the pressure dependence of the proton shift for liquid water. In accord with the results from a number of other studies plots of shift against density were non-linear initially for low temperatures but linear for temperatures greater than ca.50 “C. This initial low-temperature trend is upfield indicative of hydrogen-bond breakage (Figure 1b). The subsequent downfield shift has the same sign as that predicted recently by O’Reilly,” but is very much smaller. The initial upfield shift accords with relaxation studies16 which show that at low temperatures rotation speeds up as the density increases. These changes accord with expectation since in order to preserve good hydrogen bonds liquid water like ice tends to form a rather open structure which is clearly opposed by high pressures. Aggregation of water in chloroform has been studied by n.m.r. spectr~scopy.~’ The results were interpreted in terms of the formation of dimers only which were thought to be a mixture of linear and cyclic species.This conclusion can be compared with those considered on p. 101. The enthalpy of dimerization of -1.8 kcal mol-’ (-7.5 kJ mol-’) is surprisingly small. The authors consider that this low value arises because the solvent tends to form hydrogen bonds to oxygen electrons thus competing with dimer formation. Aqueous alcohols have been a continuing subject of interest.18-21 Most organic compounds cause an upfield shift in the hydroxyl proton resonance but alcohols cause an initial downfield shift. Various explanations have been offered but as stressed by Covington and Newman,’ the shift is a combined one since exchange between water and alcohol is fast in the water-rich region. They have extrapolated the resolved shifts into this region and consider that the water shift is entirely upfield.However Harvey et aZ. have recently found that separate 0-H proton resonances for various sugars and for t-butyl alcohol in water can be resolved at low tempera- tures,22 and this has enabled to confirm the occurrence of initial downfield shifts for the water protons. These are thought to have at least two underlying causes but for t-butyl alcohol which induces by far the greatest initial shift the dominating effect is thought to be the scavenging effect of cage formation by water around the t-butyl group since such ‘enclathration’ should be extremely temperature sensitive and the initial downfield shift was found to vanish at high temperatures.18 l3 C. A. Agnell J. Shuppert and J.C. Tucker J. Phys. Chem. 1973,77 3092. l4 J. W. Linowski N. Liu and J. Jones J. Chem. Phys. 1976 65 3383. D. E. O’Reilly J. Chem. Phys. 1974 61 1592. Ih J. Jones T. DeFries and D. J. Wilbur J. Chem. Phys. 1976 65 582. Y. H. L. Shaw S. M. Wang and N. C. Li J. Phys. Chem. 1973,77,236. l8 B. Kingston and M. C. R. Symons J.C.S. Faraday II 1973,69 978. l9 W. Y. Wen and H. G. Hertz J. Solution Chem. 1972,1 17. 2o J. Oakes J.C.S. Faruday ZZ 1972,68 1464. 21 M. Marciacq-Rousselot and M. Lucas J. Phys. Chem. 1973 77 1056. 22 J. M. Harvey M. C. R. Symons and R. J. Naftalin Nature 1976 261 435. 23 J. M. Harvey S. E. Jackson and M. C. R. Symons Chem. Phys. Letters to be published. M. C.R.Symons -80 -60 -40 -20 0 20 40 60 1 1 I I I I -20 0 20 40 60 80 4.0 -(b) >0°C 3.5 -\-s-=-z-s-20°C € i50"c 2 '.c1 3.0 -3loo"c I I I I Spectroscopic Studies of Solvation 95 Ammonia and amines and their solutions especially in water have been studied extensively using 'H 15N and 13Cresonance shifts.24 From a comparison between the "N shifts for I5NH3and I5NMe3 in a range of solvents Alei et aZ.25concluded that the shifts are controlled largely by hydrogen-bonding to the nitrogen lone-pairs.This is not surprising since the ammoniagrotons form very weak hydrogen bonds. Aqueous solutions of amides have also been widely studied an example being the work of Hinton and his co-workers.26 Using 'H and 13Cresonances they observed very complex concentration shifts for which no clear explanation has yet been offered.Solvent Shifts for ElectrolyteSolutions.-There are many advantages in the fact that solvent resonances are usually in the fast-exchange regime thus giving narrow average signals from components which for solvents such as water probably span a wide field-range. However it is unfortunate that most solutions of electrolytes are still in this regime and single averaged features are still observed the shift from the pure solvent value comprising a weighted mean of the shifts for solvent molecules associated with cations and anions together with those from a potential range of more distant solvent molecules that differ from those in the 'bulk' solvent. Fortu- nately for certain bi- and ter-valent cations separate resonances can be detected especially at low temperatures from those solvent molecules that exchange slowly namely those directly bonded to the cations.Thus cation solvation can be studied in isolation and in particular solvation numbers can be obtained. For example a solvation number of 6 for gallium and aluminium ions in methanol and ethanol was estimated using the perchlorates although at low temperatures that for Ga3' in methanol increased to 7.27However when aluminium nitrate or chloride were used the solvation number was reduced because of anion co-ordination. Enthalpies and entropies of activation for solvent exchange were measured and discussed for these solutions. Solvent competition can also be conveniently studied by this technique.For example Green and Sheppardz8 and Covington and Co~ington~~ studied competi- tion between water and acetone for magnesium cations separate signals being obtained in the OH proton and methyl proton regions from the various solvates Mg2+(Hz0) (MezC0)6-,.29 Extreme preference for water was observed but a statistical distribution of the intermediate solvates was obtained in the acetone-rich region. Competition between water and methyl cyanide for the aluminium ion has also been studied in this way.3o Again a range of different peaks was obtained both from water and from methyl cyanide but in this case some evidence for co-ordination of perchlorate ions was obtained. Schneider studied competition between dirnethylfor- 24 See for example J. E.Sarneski H. L. Surpenant F. K. Molen and C. N. Reilley Anufyt. Chern. 1975 47 21 16; W. M. Litchman M. Alei and A. E.Florin J. Arner. Chern. Soc. 1969,91 6574. 25 M. Alei A. E. Florin and W. M. Litchman J. Arner. Chern. Soc. 1970,92,4828. 26 J. F. Hinton and C. E. Westerman Spechochirn. Actu 1970 %A 1387; J. F. Hinton and K. H. Ladner ibid. 1972,28A 1731; J. F. Hinton K. H. Ladner and W. E. Stewart,J. Mugn. Resonance 1973,12,90. 27 D. Richardson and T. D. Alger J. Phys. Chern. 1975,79 1733. 28 R. D. Green and N. Sheppard J.C.S. Furuduy 11 1972 68,821. 29 A. D. Covington and A. K. Covington J.C.S. Furuduy I 1975 71 831. 30 Y. Ruben and J. Reuben J. Phys. Chern. 1976,80,2394. M. C.R. Syrnons mamide and dimethyl sulphoxide for aluminium ions using nitromethane as an inert bulk The solvation number was always 6 and surprisingly no preference between the two co-ordinating solvents was observed.This was also true for 27Al resonance studies. Curiously this was not the case in the absence of an inert diluent. When the resonance from 27Al was used preferential solvation by dimethyl sul- phoxide was quite marked. No explanation of this change was offered. It was suggested some time that systems showing resolved resonances from the cation solvates can provide information from which individual ion shifts can be obtained. Since previous attempts to divide salt-shifts of solvent resonances have been based upon arbitrary assumptions this procedure is useful even though it may not be strictly accurate. Thus for example secondary cation solvation will influence the residual solvent peak since these solvent molecules exchange rapidly.Neverthe- less some confidence in the method stems from the result that calculated shifts for large tetra-alkylammonium ions in methanol tended towards the shifts for compara- ble neutral molecules. This was not the case for aqueous solutions because of the specific effects that these large cations have on water ~tructure.~~ Several others have used this method of obtaining cation and anion shifts but the results have been explained in various ways. For example Akitt34 viewed the cation shifts in terms of the electric field effect and obtained good correlations between measured and calculated shifts. However this assumption failed for the anions.We to accent the role of hydrogen-bonding since the ion shifts from the gas-phase values for the hydroxyl proton resonances of solvents such as methanol and water are all comparable with that for the bulk solvent. Thus we consider that it is better to incorporate the field effect into that caused by hydrogen bonding since they have a comparable origin rather than to ignore hydrogen bonding. In this way the trends depicted in Figure 2 are readily understood. The bonds formed by the protons of solvates such as Mg(ROH)62+ are stronger than those formed by bulk solvent whereas those formed by K(ROH),+ are weaker. The very large cations are not solvated and hence the shift swings back towards zero. Similarly for the anions the shift is primarily governed by their basicities the major exceptions being ions such as CN-that have strongly anisotropic shift components.Although the trends shown in Figure 2 are comparable for the hydroxyl solvents those for ammonia differ in that the anions that normally give upfield shifts all give downfield shifts in ammonia. This is particularly striking since ammonia is a weak hydrogen-bond donor and hence a poor anion solvator. This result was explained35 in terms of the presence of a huge excess of non-bonded N-H groups (NH)f,,,. For water (OH)f,, groups are rare and for most alcohols almost non-existent so there is a gain and loss balance when the anions form hydrogen bonds. However for ammonia there is no loss and hence the downfield shift represents just the direct effect of the anions.3' H. Schneider Electrochim. Acta 1976 21 711. 32 J. Davies S. Ormondroyd and M. C. R. Symons Trans. Faraday Soc. 1971,67,3465;R. N. Butler and M. C. R. Symons Trans. Faraday Soc. 1969 65 945 2559. 33 J. Davies S. Ormondroyd and M. C. R. Symons J.C.S. Faruday II 1972 68 686. 34 J. W. Akitt J.C.S. Dalton 1973 42. 35 M. C. R. Symons and J. Davies J.C.S. Faraday II 1975 71 1037. 97 Spectroscopic Studies of Solvation C Rb' Me,N+Ca+K+ Na' Ca+ + tttt t t 1, 1 I 1 0 0.8 1.6 2.4 3.2 4.0 -16 -I-Br-CI-1 1 I I s t y\ \;:2+ 98 M. C.R. Symons the hydrogen bonding certainly will not be. As might be expected the cation-solvent peak is relatively insensitive to temperature for AI3+ and only mildly sensitive for Mg2+,37 but it is expected to be somewhat more sensitive than that of bulk solvent for the larger univalent cations and anions.If this is so then there is no basis for Malinowski's procedure and it should be abandoned. Another view of the relative insensitivity of the cation solvent shell resonances to changes in temperature and in solvent composition is that secondary solvation is strong because of the large S + charge on the hydroxyl This augments the relatively sparse evidence for secondary solvation but it weakens the case that the deduced 'anion' shifts are entirely caused by the anions. Using a modification of this method Akitt3' has recently estimated that the solvation number for Ag' is ca 0.6. He also found that for its size this ion has an unusual downfield shift in water and this was explained in terms of the postulated asymmetric solvent shell.Brown and Symons on the other hand found that other d" ions also exhibited extra downfield shifts both in water and in methanol including Zn" which is known to have a solvation number of 6 in methanol. The abnormal shifts were interpreted in terns of slight covalency and the solvation number for Ag' was thought to be in the normal 4-6 region.39 Two papers on selective solvation of ions by water are especially ~ignificant.~~~~' In the former propylene carbonate was used as the major solvent and the 'H resonance of water was studied as a function of various addedsalts. In the latter methyl cyanide was the major solvent and other hydroxylic solvents were studied in addition to water.Association constants and shifts for 1:1complexes were determined. In the latter study an interesting attempt was made to link the cation shifts (Ac)with those estimated for cations in the bulk solvents (Am).41 The large difference A,, was described as a desolvation shift characteristic of the solvent and interpreted in terms of structure-making by small cations and structure-breaking by large anions. How- ever it must be borne in mind that shifts are a function of the number of solvent molecules bonded to each cation and also that the remaining solvent plays an important role in determining the final proton shifts. When more inert media are used with tetra-alkylammonium salts added protic solvents bond only to the anions and shifts can be assigned directly to the anion mono-s~Ivates.~~ Such systems are well studied by i.r.spectroscopy (see p. 102) which confirms this contention and provides comparable thermodynamic data. These shifts turn out to be relatively close to anion shifts estimated from bulk solvent shifts,42 which suggests that an increase in solvation number does not have a major effect on the shifts. Some mention should be made of the extensive use of 'shift reagents' especially lanthanide ions in solvation studies. In the main these are used to study the solution conformations of large bio-polymers with remarkable success. Critical reviews of their application have been given by Foreman.' 38 J. W. Akitt J.C.S. Dalton 1974 175.39 R. D. Brown and M. C. R. Symons J.C.S. Dalton 1976,426. 40 D. R. agley J. N. Butler and E. Grunwald J. Phys. Chem. 1971,75 1477. 41 G. W. Stockton and J. S. Martin J. Amer. Chem. SOC.,1972 94 6921. 4* S. Ormondroyd E. A. Phillpott and M. C. R. Symons Trans. Faraday Soc. 1971,67 1253. Spectroscopic Studies of Solvation 99 Cation Resonances.-Various studies using 23Na+ have appeared perhaps the most notable being that of Popov et al. who found a reasonably linear correlation between the shift and Gutmann's donor number for a range of donor Less satisfactory correlations have been found for 'Li+ and 133Cs+. However these studies are plagued by lack of sensitivity and hence extrapolation to 'zero' concentration is sometimes hazardous.Hinton and Brigg~~~" have shown that using the very sensitive '05T1 nucleus combined with FT methods 5 X mol I-' solutions of T1' are readily studied. They also observed a good correlation between shift and Gutmann's donor numbers. Provided no special effects arise because of the dlos2configuration for this ion Tl' promises to be by far the best n.m.r. probe for univalent cations being far more suitable than lo9Ag+ which has also received some attention as has the 'I3Cd2+ ion. . In addition to metal cations organic cations have been widely studied but it is mainly the formation of ion-pairs and clusters that seems to generate useful shifts. This is true for trimethylsulphonium cations in water and methyl cyanide,446 and of symmetrical tetra-alkylammonium ions in a range of In the latter study unusual changes were found for aqueous solutions that were interpreted in terms of cation-cation interactions.It is particularly noteworthy that the monitored parameter a0= (aCH2 -8CH3)C-0 was much larger for aqueous solutions than for those in methyl cyanide. This presumably reflects the special mode of solvation of these ions in water. This is supported by the fall in So towards the methyl cyanide value with increase in temperature. Other studies of organic cations have used a variety of shift reagents to give geometrical differentiation between the different protons. Thus Hill et al. have used conventional lanthanides to study R4N+ion-pairs in methyl cyanide,46 and Lim and Drago have used Ph,PCoBr,- anions as a shi% reagent in several In the former study strong evidence for ionic clusters was obtained in agreement with other studies on such systems whereas in the latter association constants were estimated over a range of concentrations and dielectric constants.The results were used to challenge the procedure of making activity corrections to spectroscopic data. In an interesting series of papers Schiemenz has shown that the tetraphenylborate anion can be used as an effective shift reagent for a range of organic cations. This work has interesting implications regarding the degree of interpenetration of contact ion pairs and completely belies the concept that ions such as R4Nf can be properly treated with a spherical Anion Resonances.-Of a variety of studies of halide ion resonances attention is called to the work of Langford and co-w~rkers.~~ They measured 35Cl 7yBr and 1271 resonances for these ions in a range of pure and mixed solvents and found that there was good agreement between our early studies of CTTS absorption for I-and Br- 43 R.H. Erlich and A. 1. Popov J. Amer. Chem. SOC. 1971 93 5620. 44a J. F. Hinton and R. W. Briggs J. Magn. Resonance 1975 19 393; and unpublished data. 44b A. K. Covington M. L. Hassall and I. R. Lantzke J.C.S. Faraday 11 1972 68 1352. 45 G. Kabisch Ber. Bunsengesellschaft phys. Chem. 1976 80 602. 46 H. A. 0.Hill R. G. Roberts D. Williams and N. Zarb-Adams J.C.S. Faraday I 1976 72 1267. 47 Y. Y. Lim and R. S. Drago J. Amer. Chem. SOC.,1972,94 84. 4x G.P. Schiemenz J. Organometallic Chem. 1973,52,349; Tetrahedron 1973,29,741;J. Mol. Structure 1973,16,99. 4y J. W. Akitt J.C.S. Faraday I 1975 71 1557. 100 M. C.R.Symons and the n.m.r. shifts despite the fact that relatively large concentrations were needed for the n.m.r. work. This illustrates in a rather satisfactory way the control exerted by the paramagnetic shift term with its AE-’ dependence. There have been various 19Fstudies of the BF,- anion. In a recent study Akitt has been able to use relatively low concentrations by employing the FT technique both for 19Fand “B He studied aqueous solutions as a function of added cations and anions the former having a dominating effect on the shift as expected. These cation shifts together with changes in IJ(BF) were interpreted using an electric field model.Various possible modes of cation-anion interaction are discussed. Day and co-workersS0 have continued their studies of tetra-alkylaluminate anions using conductance and *’A] ‘H and 13Cn.m.r. techniques. With dimethyl sulphox- ide as solvent well-resolved 27Al coupling with a-carbon 13Cspectra was observed whereas in benzene only extremely broad singlets were detected. This confirms the presence of long-lived ion-pairs or aggregates in the latter solvent. 3 infrared and Raman Spectroscopy Despite the ready availability of instruments it is only in recent years that these techniques have been widely applied to the study of solvation phenomena. These methods are complementary to n.m.r.spectroscopy in that averaging processes are generally “slow” on the infrared time-scale. This leads to the appearance of relatively broad lines which are frequently too broad to be very informative since the shifts are often small. Solvents.-These techniques are very good for studying hydrogen bonding between proton-donor (A-H) and acceptor (B) molecules in the gas phase or in ‘inert’ media. Monomeric A-H molecules are characterized by intense narrow A-H stretching components and A-H -B adducts generally give broader features shifted to lower frequencies. Hence equilibrium constants enthalpies and entropies of forma-tion have been obtained for a wide range of proton donors and acceptors. Results from gas-phase studies5’ are found to differ to a significant extent from data for the same donor-acceptor pair in ‘inert’ media.Hence the role of the medium is less passive than many suppose. However since the information derived from these studies is usually required for application to condensed phases it may still be wiser to utilise the results from condensed-phase studies. An area that is less clear-cut is that of self association for proton-donor solvents in inert media. Almost all proton donors are also proton acceptors and hence it might be supposed that dimers HA --HA could be studied conveniently by these techniques. There are two complications however. One is that this ‘linear’ dimer may H not always be a correct structure since the cyclic species A/ ’*.A may be ..H/ energetically preferable.The other is that hydrogen-bond strengths are strongly dependent upon the extent of bonding. Thus the dimer bond is weaker than the 50 T. D. Westmoreland N. S. Bhacca J. D. Wander and M. C. Day,J. Amer. Chem. SOC.,1973,95,2019. s1 See for example A. J. Barnes H. E. Hallam and D. Jones J.C.S.Furuday ZI 1974 70 422; E. E. Tucker and S. D. Christian J. Amer. Chem. SOC., 1976,98 6109. Spectroscopic Studies of Solvation 101 trimer bond a H-A -H-A -6 H-A because of the polarizing effect of bond p and also p is stronger because of the effect of a. This reinforcing effect reaches a maximum in extended ‘linear’ polymers and in unstrained cyclic structures. This means that the [dimer] may remain small because of its ability to scavenge mono- mers.The situation is still more complicated for water and it must be remembered that the single bond in B -. -HOH will be stronger than either of the bonds in B * -HOH * * B. This aspect of water structure has been Experimentally these problems remain unresolved. Thus for example Luck considers that alcohols form cyclic dimer~.’~ His case rests heavily on the dipole minimum obtained as the [ROH] increases and upon the fact that a band inter- mediate between those for monomer and ‘polymer’ falls in the region (ca. 3510 cm-’) predicted from data for cyclic structures formed intramolecularly. These arguments are not compelling especially if [dimer] is always small since cyclic polymers can then account for the dipole-moment minima. Also on the arguments given above the dimer bond should indeed be relatively weak.The case for linear dimers comes mainly from matrix isolation If inert gas matrices and very low temperatures are used features are relatively narrow and detailed analysis is in far better accord with the linear structure for a variety of alcohols. Furthermore good theoretical calculations strongly support linear struc- tures. In the particular case of water in carbon tetrachloride a case in favour of a cyclic structures5 has been discussed in terms of a very rapid internal rotation (1).In order to give an averaged spectrum which would resemble that of the cyclic dimer a jump correlation time of ca. s would be required but this could well be collision- induced.56 In view of these factors it is likely that many attempts to obtain dimerization constants from i.r.and n.m.r. data are in error. An example of a thorough study using vapour pressure measurements as well as n.m.r. and i.r. techniques is that of Tucker and Becker on dilute solutions of t-butyl alcohol in hexadecane.” They concluded that a ‘linear’ trimer and cyclic higher polymers are formed and derived two constants which accommodate all the data. Another example that supports the concept of co-operativity is the methanol + tri-n-octylamine system in n-hexadecane. ’* 52 M. C. R. Symons Phil. Trans. Roy. Soc. 1975 B272 13. s3 W. A. P. Luck in ‘The Hydrogen Bond’ ed. P. Schuster G. Zundel and C. Sandorfy North-Holland Publishing Co. Amsterdam 1976 Vol. 2 p. 527. 54 See for example A.J. Barnes and H. E. Hallam Trans. Faraday SOC.,1970,66 1920 1932; also A. J. Barnes H. E. Hallam and D. Jones Proc. Roy. Soc. 1973 A335,97. ss L. B. Magnusson J. Phys. Chem. 1970,74 422. s6 P. W. Atkins and M. C. R. Symons Mol. Phys. 1972 23 831. s7 E. E. Tucker and E. D. Becker J. Phys. Chem. 1973,77 1783. s8 E. E. Tucker and S. D. Christian J. Amer. Chem. Soc. 1975,97 1269. 102 M. C.R.Symons Dilute solutions of protic solvents in basic aprotic media are again relatively simple an example being that of water in propylene ~arbonate.~' Aggregation of water is strongly suppressed because B --HOH --B units are formed. However evidence for dimerization was obtained. Bulk protic solvents however are far less tractable. Their vibrational spectra in the X-H stretching region are usually extremely broad and this reflects at least in part the presence of a wide range of different species in rapid equilibrium.The most useful alternative spectral region is the i.r. overtone region especially the 2v(OH) region for water and the alcohols. However great care must be exercised because of the appearance of other overtones or combination bands." These can frequently be eliminated by suitable deuteriation. One great advantage of this region is that intensity relationships are reversed the 2v (XH),, band being relatively stronger than the ~v(XH)~,,""~ band compared with their intensities in the fundamental region or in the Raman scattering. This is particularly important for water and aqueous solutions since [OHlf,, is quite high and the effect of solutes can be monitored.In contrast methanol gives no evidence for any (OH)freegroups although higher homologues may do. This has been explained in terms of the presence of a large excess of lone pairs of electrons for alcohols relative to Thus an (OH),, group is readily scavenged to give units such as (2) which contain two hydrogen bonds of intermediate strength. Me Me Me Ill ...OH. ..OH. ..OH. . . H Me-O... (2) Gentric et al. have shown that the bending band v2 is useful for studying 1:1 water-base complexes,61 and Bonner and Choi recommend the use of the vT2+v3 combination band for the study of aqueous solutions.62 One great advantage of both these regions is that alcohols have no corresponding absorption and hence water in alcohol-water mixtures can be more readily studied.The latter authors have analysed their spectra by a computer fit of three Gaussian components and many of their conclusions are novel. Unfortunately one of these bands is usually present in very small amounts and despite the computer fit the results must be treated with considerable reserve. Electrolyte Solutions Solvent Spectra.-Again use of inert media provides a fairly safe method for studying solvation by single solvent molecules. For example R,N'X--.HA complexes can be readily detected and accurately m~nitored.~~ However it is difficult to use these results to make inferences about solutions in bulk protic solvents because of the co-operative effect and because of multiple solvation.59 D. R. Cogley M. Falk J. N. Butler and E. Grunwald J. Phys. Chern. 1972 76 855. 6o See for example A. Burneau and J. Corset Cunud.J. Chern. 1973 51 2059. 61 E. Gentric A. le Narror and P. Saumagne J.C.S. Furuduy I 1974 70 1191. 62 0.D. Bonner and Y. S. Choi J. Phys. Chern. 1974,78 1723 1727. 63 See for example A. Allerhand and P. von R. Schleyer J. Amer. Chem. SOC.,1963,85 1233. Spectroscopic Studies of Solvation 103 This is unfortunate since most studies of electrolytes in media such as water or alcohols are relatively uninformative. Important exceptions are solutions of perchlorates fluoroborates and other large weakly solvated These show a resolved 0-H stretching component on the high-frequency side of the main i.r.or Raman band. This may be due to (OH),, groups,64 to OH groups weakly bonded to. the anions,65 or possibly to both.66 The contrast with nitrate ions which do not give rise to such a high frequency band is discussed on p. 104. Whatever is the correct interpretation use can be made of this resolution to separate out the effect of the anion component from the main absorption (or scattering) band. The effect of cations seems to be generally less than that of anions but characteristic shifts have allowed us to get some idea of the spectral modifications caused by cations.67 Unfortunately relatively concentrated solutions need to be used before significant changes can be detected and care has to be taken to avoid the effect of the formation of ion pairs especially those involving solvent sharing.Preliminary studies suggest that some of the difficulties involved in the use of fundamental bands for bulk protic solvents can be overcome by using low tempera- tures.66 For aqueous solutions this has to mean using glasses and great care needs to be taken to avoid phase separation effects. In an important paper Kuntz and Cheng68 have shown that both cation and anion solvation can be studied using dilute solutions of protic solvents in basic aprotic media (methyl cyanide propylene carbonate 1,1,3,3-tetramethylurea and dimethylformamide). In addition to detecting features for solvent bonded to cations and anions features from solvent-shared ion-pairs were clearly obtained. Very approximate values for individual ion association constants are reported.Again the overtone i.r. region is useful. Jolicoeur et aZ.69have used a differential method for studying salts containing large organic ions in the second OH stretch overtone region. They found that Bu,N'Br- caused a loss in the (OH)free band whilst Na'BPh,-caused a marked gain. Using the concept of structural temperature first suggested by Bernal and Fowler and very frequently used for such solutions they concluded that Bu4N' ions 'lower the temperature' by reinforcing water structure whilst BPh4- ions act as structure breakers. Another view7' is that these large organic ions are to a fair approximation unsolvated. In that case loss of (OH),,, is simply due to solvation of the bromide and gain in (OH)freearises indirectly from solvation of sodium ions.For most salts these two effects approximately cancel and hence changes are small. In the light of n.m.r. results we would expect to detect an extra effect from R4N' ions and the temperature effect observed by Phillip and Jolicoeur may indicate that the structural effects of these ions play some part in the spectral changes.71 64 G. E. Walrafen J. Chem. Phys. 1970 52 4176. 6s D. M. Adams M. J. Blandamer M. C. R. Symons and D. Waddington Trans. Faraday SOC.,1971,67 611; L. J. Bellamy M. J. Blandamer M. C. R. Symons and D. Waddington ibid. p. 3435. 66 I. M. Strauss and M. C. R. Symons Chem. Phys. Letters 1976,39 471. 67 M. C. R. Symons and D. Waddington Chem. Phys. Letters 1975,32 133. 68 I. D. Kuntz and C.J. Cheng J. Amer. Chem. SOC.,1975,97,,4852. 69 C. Jolicoeur N. D. The and A. Cabana Canad.J. Chem. 1971,49,2008. 70 S. E. Jackson and M. C. R. Symons Chem. Phys. Letters 1976,37 551. 71 P. R. Phillip and C. Jolicoeur J. Phys. Chem. 1973 77 3071. 104 M. C.R. Syrnons Bonner and Jumper have used an overtone band at 1.15pm (probably v1+v2+ v3),together with a differential absorption technique to study water (H,O) and a wide range of aqueous salt Their conclusion that all cations are 'structure makers' and all anions 'structure breakers' is far from chemical expecta- tion and from our own results.70 Mention should also be made of measurements in the far i.r. and the low- frequency scattering region of Raman spectra. One example must suffice Bulmer et al.have used a computer storage and averaging system to study the weak v1mode for the hexahydrates Mg(H20)6,+ and ZII(H~O)~*+.~~ The results are curious in that the zinc band at 390 cm-' was almost temperature-independent whereas the mag- nesium band at ca. 362 cm-' shifted to low frequencies with increase in temperature. This may possibly be linked with the more covalent character of the zinc-water bonds. Spectra of Ions.-By far the most studied ion is nitrate which has been investigated in great depth by Irish and his co-w~rkers.~~ One important aspect of their results is that the v3band is readily split into two components when the local symmetry falls below D3h.This can of course be caused by ion-pair formation which may produce large splittings but surprisingly it is also caused by protic solvents.As might be expected tetra-alkylammonium nitrates in inert media exhibit a singlet and addition of one methanol molecule splits this into two. The surprising result is that the splitting is the same as that found in bulk metha1-101.~~ This and other results led us to the novel conclusion that the distortion arises because nitrate forms one or possibly two strong hydrogen bonds to protic solvents rather than three. The difference in solvent absorption for nitrate and perchlorate ions is then explained since perchlorate ions are thought to form four very weak bonds on a~erage.'~ This remarkable difference is ascribed to the relatively high polarizability of nitrate and very low polarizability of ions like C10,- and BF4-.75 Thus nitrate forms one or two strong hydrogen bonds which pull the negative charge away from the remaining oxygen atom($ thereby inhibiting them from forming strong bonds.Bonding to perchlorate causes little if any charge distortion and hence all four oxygen ligands can solvate independently. The chlorate ion has also been widely studied. A recent Raman study is that of Sprowles and Plane,77 who postulated the formation of solvent separated ion-pairs with Zn2' but not with Na' salts in water. Ca2' ions gave rise to a third species thought to be the contact pair. MtC103- ion-pairs have also been studied in inert gas matrices and in water and ammonia matrices.78 Both v3 and v4 were split into doublets but this splitting was small compared with that found for nitrate ions under comparable conditions.Also this splitting was independent of the nature of M'. This may reflect the smaller polarizability of C103- ions. In ammonia and to a less extent 72 0.D. Bonner and C. F. Jumper &frured Physics 1973 13 233. 73 J. T. Bulmer D. E. Irish and L. Odberg Cunud.J. Chem. 1975 53 3806. 74 T. G. ChangandD. E. Irish,J. Phys. Chern. 1973,77,52;3.SolutionChem. 1974,3,175; D. E. Irish,in 'Structure of Water and Aqueous Solutions' ed. W. A. P. Luck Verlag Chemie 1974 p. 333. 75 T. J. V. Findlay and M. C. R. Symons J.C.S.Furuduy ZZ 1976,72,820;J. T. Bulmer T. G.Chang P. J. Gleeson and D. E. Irish J. Solution Chem. 1975 12 969. 76 M. C. R. Symons and D. Waddington Chem. Phys. Letters 1975,32 133.77 J. C. Sprowles and R. A. Plane J. Phys. Chem. 1975 79 1711. 78 N. Smyrl and J. P. Devlin J. Chem. Phys. 1974,60 2540; 61 1596. Spectroscopic Studies of Solvation 105 water matrices this splitting was reduced presumably because of solvation of the cations. Perchlorates have also been studied as MCIO pairs in inert gas Most interestingly the relatively large splittings of v3into three components show that the anion is using two oxygen ligands to bind to the cation presumably because they are relatively close together. These splittings were again greatly reduced when water and ammonia matrices were used. The sulphate Raman spectrum for aqueous magnesium sulphate has been studied over a range of temperatures and pressures.The results indicating ion-pair forma- tion were used to give the volume changes associated with the formation of contact ion-pairs.80 The special problems associated with hydroxide and hydronium ions in water have been reviewed by Zundel.81 Strong general absorption in the 3200-2000 cm-' region is accompanied by the appearance of an extra band near 1100cm-' for H30+ solutions and near 2800 cm-' for OH- solutions.** Various extra peaks for the trifluoroacetate ion in aprotic solvents have been interpreted in terms of ion-pairing to lithium gegen-i~ns.'~ Marked aggregation was deduced for dilute solutions in methyl cyanide. Solutions of cyanides in liquid ammonia also give multicomponent Raman features in the CN stretching region indicative of the formation of a range of different types of i~n-pairs.~~ There have been many studies of NH stretching frequencies for R3NH' ions since these form strong hydrogen bonds.However it seems that Me," ions can also form weak hydrogen Harmon et al. studied the i.r. spectra of a range of salts containing this ion in the CH stretching region and detected characteristic shifts for the different anions. This result should be borne in mind when these ions are used as n.m.r. internal markers. Some studies of cation-anion stretching frequencies in the far i.r. have been reported for ion-pairs and clusters. An interesting example is the study of Ault and Pimentel who used the matrix isolation method to study a range of lithium ion-pairs and their interactions with various bases.86 They have used their results to produce a 'vibrational correlation diagram' and draw attention to the relationship between these 'lithium bonds' and normal hydrogen bonds.4 Ultraviolet Spectroscopy Although early applications of spectroscopy to solvation studies were mainly in this area it has proved to be less widely applicable. One difficulty that does not significantly affect the other forms of spectroscopy is the inability to decide if a given 79 G. Ritzhaupt and J. P. Devlin J. Chem. Phys. 1975 62 1982. 80 R. M. Chatterjese W. A. Adams and A. R. Davis J. Phys. Chem. 1974 78 246. 81 G. Zundel in 'The Hydrogen Bond' ed. P. Schuster G. Zundel and C. Sandorfy North-Holland Publishing Co. 1976 VO~. 2 p. 683. 82 P. Rhine D. Williams G.M. Hale and M. R. Querry J. Phys. Chem. 1974 78 1405. 8' A. Regis and J. Corset Chem. Phys. Letters 1975 32 462. 84 P. Gans J. B. Gill and M. Griffin,J. Arner. Chem. SOC.,1976,98 4661. 85 K. M. Harmon I. Gennick and S. L. Madeira J. Phys. Chem. 1974 78 2585. 86 B. S. Ault and G. C. Pimentel J. Phys. Chem. 1975,79 621. 106 M. C.R.Symons solvent effect has been on the ground or the excited state or both. Also because of the generally large line-widths shifts need to be large to be detected. Solvents.-One of the most studied solvents is acetone because its so-called n + v* absorption band is well resolved conveniently situated and weak enough to permit studieson the pure solvent. Fox studied the shift in v,, as a function of concentration for aqueous This was plotted as an ‘excess’ shift which proved to change in an irregular fashion with the mole fraction of solute.This method of display is perhaps unfortunate since the spectral changes must occur in a stepwise fashion. This is because they are not actually small shifts but rather the gain and loss of a set of closely spaced overlapping features. An initial high-frequency shift detected only at low temperatures was interpreted in terms of hydrophobic hydration. Del Bene has extended her extensive ab initio MO studiesof hydrogen bonding to include formaldehyde and acetone interacting with one or two water The favoured structure for the monosolvate is (3),which nicely supports the concept of bonding via lone-pairs of electrons. The calculated n +T* transition energy for acetone is very close to experiment for pure acetone and the monosolvate value is close to that for aqueous acetone.This leads her to suggest that acetone forms only one hydrogen bond to water. It would in my view be dangerous to accept this argument. This is partly because the theory does not allow the 0-C bond length to change on forming hydrogen bonds but mainly because it utilises monomeric water molecules. As stressed throughout this review bulk water forms quite different bonds from those formed by the monomer. H \ / Me Electrolyte Solutions Solvent Spectra.-The only recent study in this area that this Reporter has noticed is that of Rao et al. in which carbonyl n +v* bonds for solvents such as acetone in dilute (lO~l-lO~zmoll~l) solution in water were monitored as a function of the concentration of added ele~trolyte.~~ The growth of peaks shifted to high energy with surprisingly well-defined isobestic points was interpreted in terms of stepwise replacement of water by the carbonyl solvent (L) as in equation (2).However in the light of the n.m.r. results for Mg2+ discussed above,28729this seems to be a very surprising result. The n.m.r. data show quite unambiguously that for Mg2+ acetone only replaces water when it is in large excess. Nevertheless the shifts do demonstrate an increase in the strength of the interaction and it seems probable that this is partly caused by the formation of units such as (4) 8’ M. F. Fox J.C.S. Faraday I 1972 68 1294.88 J. E. Del Bene J. Amer. Chem. Soc. 1974,96 5643. 89 C. N. R. Rao K. G. Rao and N. V. R.Reddy J. Amer. Chem. SOC.,1975,97,2918. Spectroscopic Studies of Solvation which resemble the solvent-shared ion-pairs also present in concentrated aqueous solutions. Taft and his co-workers have used a variety of aromatic molecules as probes of solvation as has been done by several others in the past. However they have analysed their data in an extremely thorough manner so as to average out errors and inconsistencies and have thus produced two solvent scales described as the a-scale and the @-scale.90 They also selected probe molecules that would respond to the hydrogen-bond donor ability of the solvent (a)and its hydrogen-bond acceptor ability (p),since these are clearly the overriding cause of such shifts.They have made an interesting attempt to include solvents such as water and alcohols in these scales but their ‘amphoteric’ character may still give rise to misleading behaviour. There is fairly good agreement between these scales and those of others but nevertheless there are some serious discrepancies which need to be resolved. Nevertheless the Reporter expects that the Q-and @-scales will become widely used in solvation studies. Spectra of Ions.-The iodide ion remains the most studied anion probably because of the intensity and accessibility of its CTTS absorption band. This band is in fact a doublet the splitting being associated with the 2P1/2 states of the iodine atom. Fox and Hayon91 have made a careful computer analysis of many spectra of iodide in a range of solvents and concluded that several other bands are also present.Although in some solvents ion-pairing is expected to give rise to other features concentration studies eliminated this possibility and hence they concluded that other transitions are involved. One trouble with this work is that these bands are generally not directly discernible and computer fitting requires an accurate knowledge of the shapes of the major components. Nevertheless such bands are discernible in the well-resolved low-temperature spectra of alkali-halide crystals so their presence in solution is to be expected. Griffiths and Wijayanayake9’ have extended our earlier work on the effects of pressure temperature and solvent on the first CTTS band of iodide ions.In 90 T.Yokoyama R.W. Taft and M..J. Kamlet and R. W. Taft J. Amer. Chem. Soc. 1976,98,377,2336; M. J. Kamlet ibid. p. 3233. 91 B. E. Barker M. F. Fox A. Walton and E. Hayon J.C.S. Faraday I 1976,721,344. 92 T.R. Griffithsand R. H. Wijayanayake Trans.Faraday Soc. 1970,66,1563;J.C.S.Faraday I 1973.69 1899. 108 M. C.R. Symons particular they have made a systematic study of ion-pair formation. Interaction with tetra-alkylammonium ions causes a large shift to low energy comparable with that caused by inert solvents whilst alkali-metal cations cause a small high-energy shift. Clearly the former shift is a result of direct displacement of solvent from iodide whilst the latter may well be due to solvent-shared ion-pair formation.Solvated electrons have been widely studied by optical methods since they display an intense allowed transition in the visible or near i.r. regions. The clear link between the band maxima for these transitions and those for I-in the same has been extended by Fox and Hay~n.’~ This common behaviour seems to reinforce the concept that the excited state for I-in such solvents is structurally comparable with the ground state of solvated electrons. Plots of band maxima of iodide versus mole fraction for binary solvent mixtures often display quite complicated trends and qualitative interpretation in terms of preferential solvation is not always clear. Covington and his co-worker~~~ have presented a mathematical treatment for such plots which appears to accommodate many of the contradictions that an intuitive analysis might reveal.This treatment however contains a variety of approximations said to be needed to make the system tractable. Also some of the conclusions are not chemically attractive. For example from an analysis of results for iodide in aqueous methyl cyanide preferential solvation by water was inferred whereas for aqueous dimethyl sulphoxide preferen- tial solvation by dimethyl sulphoxide was required. Since water forms strong hydrogen bonds to anions including iodide and since C-H hydrogen bonding is very weak and probably comparable for MeCN and Me2S0 this conclusion is puzzling. The trouble with such treatments inevitably is that they have to be kept simple in order to be tractable but Nature is not simple.In this particular case it is necessary to include the way in which a given water molecule changes as its environment moves from water to an aprotic medium. Also the competition between a basic medium and the anions for OH groups must be considered. Thus the stronger base dimethyl sulphoxide will dehydrate iodide more rapidly than methyl cyanide. To describe this effect as a preferential solvation by dimethyl sulphoxide is misleading. Fluorescence.-This is a very large field which is outside the scope of the present review. It should not however be omitted without passing reference because it is an extremely powerful method for probing environment and fast processes therein. It is used very widely by biochemists and others interested in large polymers and in micellar systems since different fluorescing probes will choose different parts of such systems as preferential ~ites.’~ 5 E.S.R.Spectroscopy Although limited to the study of paramagnetic solutes the technique of e.s.r. spectroscopy has been established as a powerful tool for studying solvation and 93 M. J. Blandamer R. Catterall L. Shields and M. C. R. Symons J. Chem. Soc. 1964,4357. 94 M. F. Fox and E. Hayon J.C.S. Faraday I 1975,71 1990. 95 A. K. Covington T. H. Lilley K. E. Newman and G. A. Porthouse J.C.S. Faraday I 1973,69,963; A. K. Covington K. E. Newman and T. H. Lilley ibid. p. 973; A. K. Covington I. R. Lantzke and J. M. Thain ibid. 1974,70 1869; A. K. Covington and J.M. Thain ibid. 1974 70 1879. 96 See for example M. R. Eftink and C. A. Chiron J. Phys. Chem. 1976 80 486 and M. Gratzel K. Kalyanusundaram and J. K. Thomas J. Amer. Chem. SOC.,1974,96 7869. Spectroscopic Studies of Solvation particularly so for studying ion-pairs and aggregates. It is also very useful for probing dynamic processes in which the components have lifetimes in the region of s which is a range not readily accessible by other techniques. It is for this reason in particular that dialkyl nitroxides are souseful as ‘spin-labels’ in biological studies. Solvation of Neutral Radicals.-In addition to their use in biological studies nitroxide radicals have been used to probe solvent The former study centred on linewidth effects which were interpreted in terms of spin-rotation relaxation (T,) causing a uniform broadening of the MI= 0,f1 14N hyperfine components and rotational motion (T,)causing an asymmetric broadening through modulation of the g and A tensor component^.^' In our studies attention was primarily focused upon changes in A (14N),98 which were ignored in the former work.In fact linewidth studies in the fast averaging region are extremely difficult especially when the widths are controlled to a major extent by unresolved proton hyperfine coupling. We found that the widths and the I4N hyperfine coupling changed in a parallel manner and probably had a similar origin. The changes for aqueous-aprotic solvent systems were largely interpreted in terms of the competitive reaction (3)?the coupling being a maximum for the fully hydrogen-bonded nitroxide.It was concluded that such bonding was essentially complete in cold water but occurred for only about half the molecules in methanol. This was interpreted in terms of competition from the non-bonded lone-pairs of methanol. The trend with added t-butyl alcohol was complex. At low temperatures an initial plateau in A (14N)was found but this was lost with increase in temperature. This was followed by an extremely rapid fall to the limiting value. This was interpreted in terms of clathrate cage formation which was also invoked to explain a marked increase in asymmetric linebroadening in the 0 to 0.04 M.F. region. Organic Radical Ions.-Attention has been almost completely confined to organic anions although evidence for ion-pair formation with halide gegen-ions has been forthcoming for the cation of 1,2,4,5-tetrametho~ybenzene.~~ Whilst most work has centred on ion-pair formation semiquinones and aromatic nitro-anions have been studied widely in various good solvating media.As with the nitroxides the most significant changes occur when the anions form hydrogen bonds to solvent molecules via specific groups (=C=O and -NO2). Exchange is always rapid so that fast averaging is observed. For semiquinones and dinitro-compounds two extremes can be envisaged. In one solvent molecules form hydrogen bonds to both groups and in the other one group is more strongly solvated at the expense of the other (cf. C104-and NO discussed on p. 104).The former method appears to hold for semi- quinones but most interestingly it is the latter that is found for rn-dinitrobenzene 97 C.Jolicoeur and H. L. Friedman Ber. BunsengesellschaftPhys. Chem. 1971,75,248; J. Solution Chem. 1974,3,15. 98 Y. Y. Lim E. A. Smith and M. C. R. Syrnons J.C.S. Faraday I 1976 70 2876. 99 G. Goez-Morales and P. Sullivan,J. Amer. Chem. SOC.,1974 96 7232. M. C.R. Syrnons anions.'oo Indeed in aqueous solution exchange of strong solvation between the two nitro-groups is slow on the e.s.r. time-scale. Stevenson and Echegoyen have made extensive equilibrium studies to derive the enthalpy and entropy of hydrogen-bond formation between p-dinitrobenzene anions and methylacetylene using hexamethylphosphoramide as solvent.lo' This is apparently an ideal medium for such studies provided allowance is made for hydrogen bonding between the donor and solvent molecules. This type of study has been extended to methanol and a range or para -substituted nitrobenzene anions. lo' A linear correlation between In K and the (T+ values of these substituents was observed. Ion-pairs.-A wealth of information has been obtained about ion-pairs using e.s.r. spectroscopy. This is because alkali-metal gegen-ions in ion-pairs often give rise to extra hyperfine coupling as well as modifying the couplings exhibited by the anion nuclei. If there are two binding sites asymmetric adducts are formed at low temperatures and the rates of migration of the cations between sites can be estimated both in the slow and the fast exchange region.Excess cations give rise to cation exchange but again if there are two binding sites the intermediate triple ions may be detected [equation (4)]lo3 Stevenson and his co-workers have studied a range of ion-pair equilibria again using hexame thylphosphoramide as solvent. lo4 This is a relatively good ionizing medium and hence excess electrolyte sometimes had to be added. They obtained values for AGO AH" and ASofor the ion-pair process for p-benzosemiquinone and compare their results with those obtained using dimethoxyethane. lo' Hirota and his co-workers have made an intensive study of cation migration between the two oxygen atoms in the anthraquinone anion radical.lM Values for AGO* AHo*,and ASoswere obtained for both Na' and K' using tetrahydrofuran solvent and a wide range of temperatures.The effect of adding the good solvent dimethylformamide was also investigated. Activation energies were small (34 Kcal mol-') but ASo' values were relatively large and negative with that for Na' greater in magnitude than that for K'. Added dimethylformamide greatly reduced the magnitude of ASo*.The key is the large negative entropy which arises because the solvent which binds strongly to the cations binds more strongly in the transition state. That is to say extra solvent is needed to move the cation from its binding site. The role of dimethylformamide is preferential binding to the cations in the ion-pairs thus weakening the anion binding and making extra solvation less necessary.loo D. Jones and M. C. R. Symons Trans. Faraday Soc. 1971,67,961. Io1 G. R. Stevenson and L. Echegoyen,J. Amer. Chem. Soc. 1974,96,3381. Io2 G. R. Stevenson L. Echegoyen and H. Hidalgo J. Phys. Chern.,1975,79 152. Io3 T. E. Gough and D. R. Hindle Canad.J. Chem. 1969,47,1698; 3393; Trans. Faraday Soc. 1970,66 2420. Io4 G. R. Stevenson and A. E. Alegria J. Phys. Chem. 1973,77,3100;G. R. Stevenson and L. Echegoyen ibid.,p. 2339; A. E. Alegria R. Concepcion and G. R. Stevenson,ibid. 1975 79 361. lo5 R.D. Allendoerfer and R. J. Papez J. Phys. Chem. 1972,76 1012. Io6 K. S. Chem T. Takeshita K. Nakamura and N. Hirota J. Phys. Chem. 1973,77,708. Spectroscopic Studies of Solvation 111 As well as changing the nature of ion-pairs in a quantized manner for example from a contact to a solvent-separated pair solvation can modify the magnetic properties of ion-pairs without there being any clear-cut change.Early work of Oakes and Symons in this area'" has been extended by Nakamura et al.,using the alkali-metal salts of fluorenone in mixed protic-aprotic media. lo' Except for the lithium ion-pair A ("C) for the carbonyl carbon atoms increased rapidly when alcohol was added to ethereal solutions. The added solvent molecule surely binds to the carbonyl oxygen to achieve this change but it does not completely displace the cation. However the hyperfine coupling to the cation nuclei increases which can be understood nicely in terms of an out-of-plane displacement by the solvent since this moves the cation into a region of favourable orbital overlap thereby facilitating electron transfer.In a rather similar study Chen et al. added dimethylformamide to a range of alkali-metal aromatic ketyls in ether^.''^ Again A (M') increased as one molecule was added. Further solvation resulted in dissociation probably in a one-step process. That solvent-shared ion-pairs were not formed is to be expected for such aprotic basic solvents since they only bind to the cations. It is amphoteric solvents such as water or alcohols that encourage the formation of solvent shared ion-pairs. To explain the increase in A(M') when solvent is bonded to the cation one can postulate a loosening of the anion-cation bond with a consequent increase in the thermal motion of the solvated cation out of the nodal plane of the unpaired electron.This fits in nicely with the effect of dimethylformamide on the migration rates discussed above.lo6 Information from Radiation Studies.-Attention should be called to the way in which high-energy radiation can be harnessed to give information pertinent to solvation studies. If a radical is formed by radiation in a crystal there may be a direct interaction with neighbouring molecules or ions. When neutral radicals are formed this may be very weak but when ions are formed such environmental effects can be large. Particularly interesting examples involve charge-transfer to or from cations with d Ios configuration such as Tl+or Pb2+.' lo Another aspect relates to gain or loss of solvation on gain or loss of charge.For example when electrons are trapped in solvent cavities at 4K,no orientational 'solvation' is detected but on annealing to 77 K this grows in as evidenced both by e.s.r."l and optical'" studies. Recent work in our laboratories shows that this is also true for 02-anions formed from unsolvated dioxygen. In contrast loss of charge need not lead to loss of solvation. For example solvated silver cations capture electrons to form Ago centres but these have e.s.r. spectra that often differ markedly from those for the normal atoms. Hence solvation is retained and the observation that a variety of such species can be formed suggests that there is a comparable variety present in the fluid solution prior to irradiation.l13 Io7 J. Oakes and M.C. R. Symons Trans. Faraday SOC.,1970,66 1. Io8 K. Nakamura and N. Hirota J. Amer. Chem. SOC.,1973 6919. 109 K. S. Chen. S. W. Mao K. Nakamura and N. Hirota J. Amer. Chem. SOC.,1971,93 6004. ll0 M. C. R. Symons D. X. West and J. G. Wilkinson J.C.S. Dalton 1974,2247; 1975 553. D. R. Smith and J. J. Pieroni Canad. J. Chem. 1967,45 2723. H. Yoshida and T. Higashimura Canad. J. Chem. 1970,48 504. 113 B. L. Bales and L. Kevan Chem. Phys. Letters 1969,3,484; J. Phys. Chem. 1970,74 1098. M. C.R. Symons 6 Conclusions Much of the discussion above may seem to the reader to be too qualitative. Certainly for some precisely defined systems such as those involving the use of relatively inert solvents it is possible to extract meaningful and quite precise thermodynamic data.However for the far more complex bulk systems generally under consideration the time for this is not yet ripe in this Reporter’s opinion. Certainly attempts are made to reproduce complex spectroscopic data quantitatively and some appear to be quite successful. However it is surely necessary to get the chemistry right before indulging in such numerical exercises if these are to have any real meaning and unfortunately the chemistry is demonstrably or at least intuitively wrong in most if not all such cases. Hence the reader will have to be satisfied with more qualitative considerations for the time being. It seems likely however that machine calculations along the lines of molecular dynamics may hold some of the answers if they don’t prove to be too costly to extract.

ISSN:0308-6003    

DOI:10.1039/PR9767300091

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

PART II INORGANIC CHEMISTRY 7 Introduction By M. F. LAPPERT School ofMolecular Sciences University ofSussex Brighton BN 1 9QJ The general form of the 1976 Annual Reports (Vol. 73) on 1norgani.c Chemistry follows the pattern set last year. Thus our main aim is to provide a broad overview of many of the advances in the subject published in 1976. Inevitably there is a considerable degree of selection of topics in order to have the space briefly to put the latest publications into the context of the prior art. It is hoped that within a three year cycle (Vols. 72-74) such selection will not be regarded as unduly subjective or arbitrary. The treatment is intended to be complementary to that adopted in the Specialist Periodical Reports which provide agonvenient secondary source of literature for the researcher.We on the other hand wish to address ourselves primarily to the scientist as the informed generalist whether teacher student or industrial chemist in order to draw attention to current developments and therefore limit ourselves severely as to the number of references cited; inevitably much excellent work is omitted. The main change from Volume 72 is the inclusion of a section on ‘Scandium yttrium the lanthanides and the actinides’ by Professor K. W. Bagnall. In this a rather denser coverage of the literature was necessary than elsewhere in order to make up for the earlier neglect and to set the scene for next year’s Report. We have tried to list numerical results in SI units and to adopt stricter standards than hitherto on the presentation of formulae and in systematic nomenclature.It is hoped that next year’s Report will take this process still further. On the whole we have been guided in these matters by the editorial house rules of the Chemical Society. During 1976 three books were published which will be of interest to under- graduates and their In the preface to one of these the distinguished authors’ claim to have adopted a ‘Baconian’ view of inorganic chemistry; i.e. grounded firmly on factual material an approach also adopted elsewhere,* and one with which this writer is very much in sympathy. The publishers of the Journal of Organometalfic Chemistry have (for the second time in 12 years) hived off their reviews sections as separate’monographs of which F.A. Cotton and G. Wilkinson ‘Basic Inorganic Chemistry’ John Wiley New York 1976. * R. B. Heslop and K. Jones ‘Inorganic Chemistry. A Guide to Advanced Study’ Elsevier 1976 (a revised and expanded edition of R. B. Heslop and P. L. Robinson’s well-known textbook). W. L. Jolly ‘Principles of Inorganic Chemistry’ McGraw-Hill New York 1976. 115 116 M. F. Lappert three hard-back volumes have already appeared.4d We also note the publication of a number of specialist J. Organometallic Chem. Library Vol. 1 1976 ‘New Applications of Organometallic Compounds in Organic Synthesis’ (proceedings of a symposium). J. Organornetallic Chem. Library Vol. 2 1976 ‘Organometallic Chemistry Reviews Organosilicon reviews’ (specialist reviews).J. Organometallic Chem. Library Vol. 3 1977 ‘Organometallic Chemistry Reviews’ (annual subject reviews). Adv. Chem. Ser. (Amer. Chem. SOC.) ed. R. B. King Vol. 150 1976 ‘Inorganic Compounds with Unusual Properties’. Adv. Chem. Ser. (Amer. Chem. SOC.) ed. J. J. Zuckerman Vol. 157,1976 ‘Organotin Compounds New Chemistry and Applications’. C. H. Bamford and C. F. H. Tipper eds. ‘Comprehensive Chemical Kinetics’ Vol. 18 1976 ‘Selected Elementary Reactions’. lo D. Benson ‘Mechanism of Oxidation by Metal Ions’ Elsevier Amsterdam 1976. D. Delmon P. A. Jacobs and G. Poucelet eds. ‘Preparations of Catalysts. Scientific Basis for the Preparation of Heterogeneous Catalysts’ Elsevier Amsterdam 1976. 12 J. Emsley and D. Hall ‘The Chemistry of Phosphorus’ Harper and Row London 1976. l3 N. N. Greenwood and E. J. F. Ross ‘Index of Infrared Spectra of Inorganic and Organometallic Compounds’ Vol. 2 1979. l4 C. T. Horovitz ed. ‘Scandium. Its Occurrence Chemistry Physics Metallurgy Biology and Technol- ogy’ Academic Press New York 1,975. 15 A. D. McIntyre and C. F. Mills eds. ‘Ecological Toxicology Research Effects of Heavy Metal and Organohalogen Compounds’ Plenum New York 1976. l6 A. G. Sharpe ‘Chemistry of Cyano Complexes of the Transition Metals’ Academic Press New York 1976.

ISSN:0308-6003    

DOI:10.1039/PR9767300113

出版商:RSC    

年代:1976

数据来源: RSC

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The Typical Elements ByA. J. CARTY Guelph- Waterloo Centre for Graduate Work in Chemistry Department of Chemistry University of Waterloo Waterloo Ontario Canada N2L 3G1 R. H. CRAGG Department of Chemistry University of Kent Canterbury CT2 7NH J. D. SMITH School of Molecular Sciences University of Sussex Brighton BN 1 9QJ G. E. TOOGOOD Department of Chemistry University of Waterloo Waterloo Ontario Canada N2L 3GI PART I Groups I and I1 By R. H. Cragg 1 Group1 The main area of interest in Group I Chemistry during 1976 has been the application of physical techniques mainly n.m.r. to the elucidation of structures. An optical and 13C n.m.r. study of the dilithium and disodium salts of the tetraphenylethylene dianion supports the structure Li'Ph2c-CPh,Li' for the former compound in which the two CPh groups are lying in mutually perpendicular planes with one Li' cation near the negatively charged framework and the other solvated by THF further away.' The two cations show equivalence in the n.m.r.but not in the electronic spectra hence they are suggested to be rapidly exchanging [equation (l)]. tight Li++ solvated Li+ $ solvated Li'+ tight Li+ (1) In a recent study of the complexes formed between sodium ions and sugars it was observed that the 23Na n.m.r. linewidth increases when small amounts of sugars such as sorbose fructose galactose or glucose are codissolved with the sodium salt in pyridine; the stability constants (Table 1)complexes were determined. Pol yether 18-crown-6 or monobenzo-2,2,2-cryptandcomplexes of CsI in non- aqueous solvents such as Me2C0 MeCN Me2S0 or pyridine show a change in the 133 Cs n.m.r.chemical shift as a function of the I-/Cs' mole ratio which suggests that the solvent plays a part in the complexation proces~.~ G. Levin B. Lundgren M. Mohammad and M. Szwarc J. Amer. Chem. Soc.,1976,98 1461. * C. Detellier J. Grandjean and P. Laszlo J. Amer. Gem. Soc. 1976 98 3375. 3 E. Mei J. L. Dye and A. 1. Popov J. Amer. Chem. SOC.,1976,98 1619. 117 A.J. Carty,R. H. Cragg,J. D.Smith and G.E. Toogood Table 1 Temp./K 250 Sugar Sorbose t Linewidth in :omplex vi/Hz 2700f800 Stability constant K/I mol-' 12.5 *3.75 260 Sorbose 1890f570 8.2 f2.5 270 Sorbose 1640f500 7.4 f2.5 280 Sorbose 1040f3 10 -8.4f2.5 290 300 Sorbose Glucose 800 f240 845 *250 7.2 f2.2 2.6* 0.8 300 Galactose 850* 250 5f 1.5 300 Fructose 830f 250 6.2* 1.8 The syntheses of KO2 and K202 from potassium hydroxide using an electric discharge sustained in oxygen have been rep~rted.~ The degree of oxidation depends upon the operating conditions of the discharge and the particle size of the potassium hydroxide.The presence of unco-ordinated Rb' has been observed in an Rb' exchange zeolite.' The interaction of RbOH and a single crystal of sodium zeolite 4A during 8 days resulted in the formation of a cation of composition RbllNa,. A least-squares refinement showed the presence of an unco-ordinated Rb' in the cation and that the ion is zero-co-ordinated with the interionic contacts longer than expected by more than 150pm.2 Group11 The results of two X-ray studies are singled out for comment. The crystal structure (Figure 1) of bis(di-t-butylmethy1eneamino)beryllium dimer prepared from the interaction of Bu',C=NH and P*,Be shows the presence of both bridging and @Be OC Figure 1 Skeleton of [Be(N=CBu',),],. Interatomic distances (pm) Be-N 168; Be-N 150; C=N 128; C=N 127; Be-..Be 223. Bond angles (O) N,-Be-NL 97; Be'm-aBe-N 161; Be-N,=C 161; Ni-Be-N Be-Nu-Be' 83; 129; Be-N,=C 138. P. Sadhukhan and A. T. Bell J. Inorg. Nuclear Chem. 1976,38 1943. 5 R. L. Firor and K. Seff,J. Amer. Chem. Soc. 1976,98 5031. The Typical Elements terminal methyleneamino-groups the latter attached to the three-co-ordinate metal atoms by Be-N bonds of only 150 pm.6 Reaction of PhMgBr with PhCN in excess THF gives a THF adduct of diphenyl-methyleneamidomagnesium br~mide.~ An X-ray structure determination showed the compound to contain bridging THF molecules attached to the magnesium atoms by unusually long bonds (Figure 2).The crystals are monoclinic with a = 1781.9 nC Figure 2 Molecular structure of Mg2Br2(THF)2 (P-N=CP~~)~ (p-THF). Interatomic distances (pm); Mg-N 207,8(4); Mg-Br 247.4(2); Mg-0 206.6(5); Mg-Ob 245.3(5); (O): C=N 125.9(9); Mg-Mg 288.6(3). Bond angles Mg-N-Mg 88.0(2); N-Mg-N 89.0(2); Mg-ob-Mg 72.1(1); Br-Mg-0 96.6(2); Br-Mg-0 87.4(1);O,-Mg-ob 173.1(2). b=1064.7 c=2205.1 pm /3=112.86" space group C2/c and Z=4. In the molecule two MgBr (THF) units are joined not only by two N=CPhz units but also by one THF molecule which symmetrically links both metal atoms by unusually long bonds (245 pm).It has been observed that under pressure one of the THFmolecules possibly the bridging one can be removed resulting in the isolation of a compound formulated as in (1). Br Ph \ / C Ph \ JTHF /Mg\N N=CI/Mi2 Ph Ph Br 2THF J. B. Farmer H. M. M. Shearer J. D. Sowerby and K. Wade J.C.S. Chem. Comrn. 1976 160. ? K. Manning E. A. Petch H. M. M. Shearer K. Wade and G. Whitehead J.C.S. Chem. Cornm. 1976 107. A.J. Carty,R. H. Cragg,J. D.Smith,and G.E. Toogood Magnesium strontium and barium dissolve in the mixed non-aqueous solvent system DMSO-SO, although they are insoluble in either solvent.* Magnesium reacts to form the pyrosulphate in contrast to strontium and barium which both form the sulphate.Phase studies indicate that DMSO and SO form a 1:1 adduct (m.p. -38 "C) and this may account for the dissolution of the metals (Scheme 1). In the case of magnesium the reaction is complete after two days but with strontium or barium the reaction is slower because a coating of insoluble sulphate renders the metal impassive. Me2SO-SO2+M +MS03 2Me SO MS207 t-f-MS,O Scheme 1 The application of the pressure jump technique to a study of chemical relaxation effects in aqueous solutions of beryllium formate has enabled the rate and equilib- rium constants for the formation of [Be(O,CH)]' at 25 "C to be determined.' A redetermination of the sodium-strontium phase diagram," up to 37.9 mol% (439"C) indicates that the solubility of strontium is less than previously reported. Strontium is quite soluble in sodium but not to the same extent as barium. In contrast beryllium magnesium and calcium are almost insoluble.

ISSN:0308-6003    

DOI:10.1039/PR9767300117

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

A.J. Carty,R.H. Cragg,J. D.Smith and G.E. Toogood PART 11 Group I11 By A.J. Carty and G.E. Toogood 1 Boron Boranes Substituted Boranes and Borane Anions.-Theoretical Studies of Bonding and Structure. The bonding electronic structure and properties of borine carbonyl BH,CO have been studied by three different groups this year.'"- Use of two Gaussian-type basis sets containing polarization functions'" gave a best energy of -365.391 x lo3kJ mol-' for BH,CO which compares with -365.115 x lo3kJ mol-' for the best previous calculation. The estimated Hartree-Fock energy AE for the reaction BH,CO +BH3+CO differs greatly from that found in earlier calculations probably because the latter used smaller basis sets and different geometries. Interaction of the 5u MO of CO with the vacant 3a MO of BH and a smaller interaction (back-bonding) between the le BH orbital and a vacant CO 27~MO are primarily responsible for bonding in BH,CO.The inclusion of polarization functions appears to enhance the importance of hyperconjugation. 8 W. D. Harrison J. B. Gill and D. C. Goodall J.C.S. Chem. Comm.,1976 540. 9 B. Gruenwald W. Knoche and N. H. Rees J.C.S.Dalton 1976 2338. lo P. R. Bussey P. Hubberstey and R. J. Pulham J.C.S. Dalton 1976 2327. The Typical Elements There is however an apparent disagreement over the effects of basis sets and polarization functions on contributions to bonding in BH3CO.la4 A suggested la analysis of BH3C0 bonding in terms of the energy decomposition scheme of Iwata and Morokumald has now been carried out .lb The analysis decomposes the interaction energy into component terms uiz.electrostatic polari- zation charge-transfer and exchange interactions. This approach is conceptually attractive. Calculations were of the ab initio LCAO SCF-MO type using the 4-3 1G basis set. lb For BH,CO electrostatic polarization and charge-transfer terms contribute almost equally to the stabilization. At the near-equilibrium B -C distance of 160pm back-bonding is very important (CT,,,,, :CT,, -+ CO = 2 1)(CT = charge transfer) (cf.la). Moreover OC-BH bonding is preferred over CO-BH owing to more favourable charge transfer in the former. Electrostatic interactions are chiefly responsible for strong N-B bonding in H3N-BH3 and H,N-BF,; electrostatic stabilization is greater in the latter.The barrier to internal rotation in H3N-BH (the difference in stabilization energy between eclipsed and staggered forms) results from diff erences in exchange repulsion. In the eclipsed form proximity of B-H and N-H bonds gives rise to a large overlap repulsion. Mention should also be made of calculations on B2H4(C0)2 B3H7C0 B2H4 and B3H7.1e A staggered form of bis(carbonyl)diborane(4) is more stable than the eclipsed isomer by 74 kJ mol-' as observed experimentally. The structure of the unstable molecule B2H4 is predicted to contain a strong B-B bond with staggered BH units and no bridging hydrogens." In last year's Report the utility of inner-shell eigenvalues and group charges calculated in the PRDDO approximation for predict- ing favoured reactivity sequences for smaller boron hydrides was pointed out.Lipscomb and co-workers" have now presented details of calculations for Bl3Hl9 B14H20 B16H20 n-Bl8H22 B20H16 [BZOHl8I2- and phofo-[B20H18]2- These molecules consist of fused fragments from smaller hydrides. Reactivity patterns might therefore reflect those of the fragments as well as the structural and electronic effects of fusion. An example is provided by B14H20 which can be considered as two moieties fused at B-4 and B-5. From the predicted order of electrophilic attack 2 >4 > 1> 3 > 7 in B14H20 which is identical to that in [B8H13]- it appears that replacement of the B-4-H-B-5 bridge hydrogen in by two terminal hydrogens to give [B8H13]- has a very similar effect on the reactivity of B-4 as the addition of a six-boron fragment of across B-4 and B-5to generate B14H20.The neutral molecule BH5 (an adduct of BH and H2) has been implicated as a reaction intermediate in the hydrolysis of BH,-. By analogy with the isoelectronic five-co-ordinate cation CH5+ which has an experimental binding energy of 158.6 kJ mol-' a transitory existence for BH5 might be expected. The structure bonding and stability of BH5 have now been probed by three independent MO studies.lg-' The conclusions of these investigations are gratifyingly similar i.e. a C,-symmetry BH5 molecule is unstable with respect to BH and HZ subunits unless (a)W. C. Ermler F. D. Glasser and C. W. Kern J. Amer. Chem. SOC.,1976,98,3799 (b)H. Urneyarna and K.Morokurna ibid. p. 7208; (c) T. K. Ha J. Mol. Srrucr 1976 30 103; (d) S. Iwata and K. Morokuma J. Arner. Chem. SOC.,1973,95,7563;(e)D.R. Armstrong Znorg. Chim.Acru 1976,18 13; (f) D. A. Dixon D. A. Kleier T. A. Halgren and W. N. Lipscomb J. Amer. Chem. Soc. 1976,98,2086; (g) C. Hoheisel and W. Kutzelnigg ibid. 1975 97 6970; (h) J. B. Collins P. von R. Schleyer J. S. Binkley J. A. Pople and L. Radom ibid. 1976,98,3436; (i) I. M. Pepperberg T. A. Halgren and W. N. Lipscomb ibid. 1976 98 3442. 122 A. J. Carty,R.H. Cragg,J. D. Smith and G.E. Toogood polarization functions and electron correlation are incorporated in the calculations. The most refiaed calculafionslh (UMP2/6-3 1G"")indicate a binding energy of only 8.4 kJ mol-'.Thus BH is more likely to be a transition state for hydrogen atom exchange rather than a reaction intermediate. Synthesis and Structure of Boranes and Derivatives. The principle of combining two small or medium sized boranes to generate a larger molecule has been utilized to advantage in synthetic boron hydride chemistry. A new synthesis of B13H19 is based on this concept [equation (l)]. The structure of B13H19 is that of a n-B9H15 cage sharing two borons with a B6H1 cage.2" KB6H8Br+qB2H6 + KB7H11Br%BI3Hl9+H2+KBr (1) The three hydrides B6H12 B8Hl4 and i-B9Hl have resisted attempts to obtain suitable crystals for X-ray analysis. In this situation structural proof rests heavily on 11 B and 'H n.m.r. spectroscopy. Line-narrowing of "B spectra has proved For B8H14 n.m.r.data are inconsistent with static 4412 structures; hydrogen tautomerism might explain equilibration of B-4,B-5 B-7 and B-8 resonances in 4412-type structures; however no evidence suggesting tautomerism was evident in 'H spectra at -100 "C.Structure (1) therefore seems most reasonable. For i-B9Hl a structure similar to the C3 model proposed earlier2' but with slightly asymmetric bridging hydrogens is consistent with n.m.r. data. (2) 2 (a) J. C. Huffman D. C. Moody and R. Schaeffer Inorg. Chem. 1976,15,227; (6) D. C. Moody and R. Schaeffer ibid. p. 233; (c) P. C. Keller ibid.,1970,9,75; (d)M. Mangion R. K. Hertz M. L. Denniston J. R. Long W. R. Clayton and S. G. Shore J. Arnef. Chem. Soc. 1976,98,449; (e)E. J. Stampf A. R. Garber J.D. Odom and P. D. Ellis ibid. p. 6550. The Typical Elements I23 In last year's Report we mentioned anions belonging to the hypho-class of boranes with 2n +8 skeletal electrons. Further details have now been published on the adduct B,H,,(PMe,), which is isoelectronic with the dianion [B6Hl2I2- and the neutral hydride B6H14.2d The structure (2) has a boron framework resembling the equatorial belt of an icosahedron. As a continuation of the more open frameworks from closo to nido to arachno as the number of skeletal electrons increases B6Hlo(PMe3)2 can be related to the nine-vertex system [B,H9I2- with 20 skeletal electrons but three vertices removed. The molecule is stereochemically non-rigid in solution; inter- change of bridging and terminal roles for hydrogens by BH2 group rotation bridge cleavage and reformation may be a mechanism for fluxionality.A very significant paper describing an indirect method of obtaining boron-boron coupling constants has appeared.2e Previously values for JBB which may provide useful bonding information have been measured with only limited success via triple-resonance proton-decoupling and line-narrowing techniques. The method of Odom Ellis and co-workers2e depends on the dominance of the quadrupolar mechanism in spin-lattice and transverse relaxation for the "B nucleus. With the valid assumption T,= T2,measurement of T for boron hydrides allows a value of JBB to be obtained via fitting of calculated to experimental lineshapes. Upper limits for JBB extracted in this way are JBIBz = 1.0 Hz in B4H10; JB2B4 = 5.0 Hz JB2B3 = 0.0 Hz in B5H9; and JBB = 11Hz in B,H,CO.There is evidence for a correlation between boron-boron coupling constants and LMO difference map electron density; larger JBB values correspond to a build-up of electron density. This idea should stimulate further experimental and theoretical studies. Photoelectron Spectra of Substituted Pentaboranes. For electron-counting purposes the chief role of borane cage substituents is in dictating the electronic contribution of a cage fragment. A more subtle effect is their influence via conjugative and inductive effects on chemical reactivity and relative stabilities of cluster species. Such information has been sought by photoelectron (p.e.) studies of 1,2- and p-substituted pentaborane(9).The first band in the p.e. spectrum of B5H is due to ionization from the highest filled orbital (4e). Shifts in energy and splittings associated with this framework orbital reflect inductive (Sa)and conjugative (SE) interactions with substituents. For 2-substitution the conjugative effect also causes a removal of the degeneracy of the 4e orbital since only one substituent (X) .Ir-orbital is of the correct symmetry for interaction. In the p.e. spectra of 1-and 2-IB5H8 the second band correlates with 4e of B5H (at 1016.1 kJmol-') and is clearly split (SE = 41.5 kJ mol-') for 2-IB5H,; Sa = 19.3 kJ mol-' for 1-and 2-IBsH8 and SE = 54.04 kJ mol-' for 1-IB5H8. From measurements for 1-and 2-XB5H (X = C1 Br I Me or SiH,) and p-SiH3B5H8 conjugative interactions are clearly larger for 1-substitution while inductive effects are small and invariant to substitution.Consid- eration of core potentials (from a-values) and T-interactions led to the isomer stability predictions 2- >> 1-(X = F) 2- -1-(X = Cl) 1->2-(X = Br) 1>> 2 (X = I) in agreement with experimental observations. Comparison of 4e ionization potentials for p-SiH3B5Hs where inductive effects alone contribute with 1-and 2-XB5H8 (X = SiH3 or Me) values provides evidence for B -+ Si (p7r-d~)interactions in 1-and 2-SiH3B5H8. Stronger back-bonding in the 1-isomer agrees with bond-length data 3 J. A. Ulman and T. P. Fehlner J. Amer. Chem. Soc. 1976,98 1119. A.J. Carty,R. H. Cragg J. D. Smith and G.E. Toogood mentioned last year.Finally the utility of p.e. spectra as a measure of changes in framework electronic structure with substituent effects can be seen from relative values of Sac1(19.3 kJ mol-') us Sac, (-14.5 kJ mol-'). A C1 substituent withdraws electrons from the cage increasing the core potential of the framework; CH acts in the reverse sense. Relative acidities (1-ClB5H8 > 1-MeB,H8) correlate with these observations. Metalloboranes Carbaboranes and Related Compounds.-Hydrido -Transition -metal Complexes of Carbaboranes and Thiaboranes. Research on metallocar-baboranes continues as a leading activity in Group I11 chemistry and significant advances have been made in the area of hydrido-complexes of transition elements bound to dicarbaboranes.These show considerable promise as catalysts in hydroge- nation hydrogen-deuterium exchange and isomerization and hydroformylation reactions comparable and analogous to the versatile [Rh(Cl)(PPh,),] and [Ru(H) (Cl)(PPh,)3].4" Many of these complexes are synthesized by oxidative-addition reactions of dicarbaborane anions to co-ordinatively unsaturated transition-metal centres. Thus addition of 7,9- and 7,8-[C2BgH12]- to [Ru(H)(Cl)(PPh,),] produced respectively the dihydrido-species [2,2- (PP h3)2-2 ,2-H2- 2,1,7 -RuC,B,H (3) and [3,3-(PPh3),-3,3-H,-3 ~,~-RuC~B~H~~].~~ The structures of these compounds are described as seven-co-ordinate about ruthenium if the dicarbollide moiety is regarded as a terdentate ligand and the metal is formally d4. Both compounds are catalytically active and react readily with HCl or CO displacing H2and producing respectively [2,2-(PPh3)2-2-H-2-C1-2,1,7-RuC2BgHll], the six-co-ordinate [2,2- (PPh,),-2-CO-2,1,7-RuC2B9Hl1], and the corresponding 3,1,2-isomers.The 2,1,7- isomer (3) reversibly eliminates H2 upon heating to yield a five-co-ordinate d6 Rul* complex but the 3,1,2-isomer does not. Noteworthy is the absence of catalytic 4 (a)K. P. Callahan and M. F. Hawthorne Adv. Organometallic Chem. 1976,14182; (b)E. H. S. Wong and M. F. Hawthorne J. C.S. Chem. Comm. 1976,257; (c)T. E. Paxson and M. F. Hawthorne J. Amer. Chem. SOC.,1974,% 4674; (d)G. E. Hardy K. P. Callahan C. E. Strouse and M. F. Hawthorne Acta Cryst. 1976 B32,264; (e) C. W. Jung and M. F. Hawthorne J. C. S.Chem. Comm. 1976,499; (f)S. B. Miller and M. F. Hawthorne ibid. p. 786; (g) D. A. Thompson and R. W. Rudolph ibid. p. 770; (h)W. M. Maxwell V. R. Miller and R. N. Grimes J. Amer. Chem. SOC.,1976,98,4818. The Typical Elements activity for [3,3-(PPh3),-3-H-7-C,H,N-3,1,2-RuC2B9Hl0], which is six-co-ordinate about the metal. This may be contrasted with the behaviour of [3,3-(PPh3X-3-H- 3,1,2-RhC2B,H,,] which has been shown to be a good homogeneous Compounds similar to the dicarbollide hydrido-transition-metal species have been produced from other nido -and uruchno-~arbaboranes.~' However only monohydrido-compounds were detected. [Rh(Cl)(PPh,),] reacted with NaC,B,H, to yield [6,6-(PPh3),-6-H-6,2,3-RhC2B7H9] (4),and [Ir(Cl)(PPh,),] reacted with NaC,B,H, to give [1,1-(PPh,),-1-H-1,2,4-IrC,B,H1,].Interestingly reaction of [Ru(H)(Cl)(PPh,),] with NaC,B,H, produced a compound with no hydrides at all [6,6-(PPh3),-6,2,3-RuC2B7H9]. This is probably formed by reductive elimination of H from an undetected dihydrido-intermediate although it shows no tendency to add H2 nor does it show any catalytic activity in alkene hydrogenation in marked contrast to the corresponding [RuC,B,H ,] species. L I A novel reaction producing hydrido-metallocarbaboranes has recently been di~covered.~'Thermal rearrangement under mild conditions of closo -[3,3-(PPh3),- 3,l ,2-NiC2B9H1 ,] produced closo-[ 3,8-(PPh3),-3-H-3 1,2-NiC2B,H,,] in quantita- tive yield. Similar results were obtained with other nickel dicarbaboranes and in all cases the reactions proceed with high selectivity and without migration of carbon atoms.Hydrido-compounds of metallothiaboranes have been made by oxidative addition of various closo -and nido-thiaboranes to transition-metal compounds. 7-[SB,,H,,]-adds to [Rh(Cl)(PPh,),] to give [RhH(PPh,),(SB,,H,,)] which func- tions as a hydrogenation catalyst.4g A different reaction occurs when closo-1- SB,,H, or closo-1-SB,H reacts with [Ir(Cl)L,] (L = PPh or AsPh,). The addition in this case produces a B-Ir exodeltahedral cr-bond in [2-(IrL,HCl)- l-SB,H,-,] (n= 9 or 11). These may be viewed as trigonal-bipyramidal iridium compounds with trans H-Ir-C1 bonding and are analogous to the B-cT-carbaboranyliridium com-plexes mentioned last year. All the hydride compounds referred to above are characterized by the presence of terminal metal hydrides with no evidence for interaction between the hydride and the carbaborane or thiaborane ligand.In contrast the hydrogen in cluso-[Co(H)- (Me2C2B4H4),] is considered to be associated with nearby boron atoms as well as with cobalt in a face-bonded arrangement. Though this has not been fully con- firmed four-centre H-B bonding has been found in CB,H and is also proposed for [1,2,4-(q 5-C5HS)Fe"(H)C2B4H6].4h The cobalt compound is converted by acidified THF into the nido closo-[(Me,C,B,H,)Co(H)(Me2C2B4H4)], where the cobalt (Scheme 1)resides in both a nido- and a closo-cage. Treatment of this compound with NaH-THF removes the proton attached to the metal but it may be replaced by treatment with aqueous or anhydrous HCl.This suggests that the metal-bound A.J. Carty,R.H. Cragg,J. D. Smith and G.E. Toogood 7’n Scheme 1 hydrogen is protonic rather than hydridic in character and that these compounds are formally different from the hydrido-metallocarbaboranes. However as noted by the authors ‘The chemical consequences if any of this formal distinction between metal-proton and metal-hydride metallodicarbaboranes have yet to be estab- lished’.4h Metalloboranes and Carbaboranes Containing Metal-Metal Bonds. Insertion of a second metal atom into a monometallocarbaborane frequently occurs at a position adjacent to the first metal. Also direct insertion of several metal atoms simultane- ously into a carbaborane often leads to products containing two or more metal atoms adjacent to one another.It is thus clear that metal-metal bonding is of considerable importance in determining the structures of polymetalloboranes carbaboranes and related compounds. Some interesting examples of the production of metal-metal-bonded carbaboranes include the dicobalt species [2,11-(Co-q5-C,H,),-1-CBgH10]-,5a produced by the cage-opening reaction of closo-l-carba-decaborane(lO)(l-) with cobaltocene and sodium amalgam in THF (Scheme 2) and (a)C.G. Salentine C. E. Strouse andM. F. Hawthorne Inorg. Chem. 1976,15,1832;(b)R. N. Grimes A. Zalkin and W. T. Robinson ibid. p. 2274; (c)V. R. Miller and R. N. Grimes J. Arner. Chem. SOC. 1976,98 1600; (d)K. Wade Adu. Znorg. Chem. Radiochem.1976,18 1and references therein; (e) R. W. Rudolph Accounts Chem. Res. 1976,9 446. The TypicalElements 127 the first trimetallocarbaborane containing nickel [(Ni-r) 5-C5H5)3CB5&],5" made by reaction of 2-~arbahexaborane(9) with nickelocene and sodium amalgam in THF. The basic structure of the trinickel species is shown in (5); it may be described as a distorted monocapped square antiprism with the three metal atoms occupying three of the four positions in the open face of the nido-compound. Reaction of cZ~~~-[CO(H)(M~,C,B,H,)~] with [Co(q5-C5H5)(CO),] produced a mixture of compounds two of which where characterized as a dicobalta-and a tricobalta-carbaborane respectively (both with metal-metal bonds) [1,2,4,5-(q5-C5H5)2C02(Me2C2B3H3)] (6) and [(q5-C,H5)Co(Me2C2B3H3)Co(H)-8 (Me,C,B3H3)Co(q'-C,H5)] (7).," Structural data are now available for the two isomers 1,8,5,6- and ~,~,~,~-[(CO-~~-C,H,)~C~B~H,]~~ mentioned in last year's Report.These show that the tendency to metal-metal bond formation is opposed by repulsive interactions between hydrogens of neighbouring C,H5 groups. At higher temperatures the steric factor is dominant so that the 1,8,5,6-isomer is favoured. Conversely at lower temperatures the metal-metal-bonded species is more stable. Clearly metal-metal bonding is not the only important interaction in the species and the metal-metal-bonded compounds initially formed in many reactions often rear- range to form other isomers5a where the metals are not adjacent to one another and occupy sites of higher co-ordination.However the gap between the boranes and carbaboranes on the one hand and the fully metallated clusters on the other is obviously narrowing as is evident from a recent study5' where the tri- and tetra- cobaltaborane clusters [(Co-)) 5-C5H5)3B3H5] [(Co-q 5-C5H5)3B4H4] and [(Co-))5-C5H5),B,H,] (8) were prepared. These compounds represent the first examples of 4 128 A.J. Carty R. H. Cragg,J. D.Smith and G.E. Toogood clusters with as many metal as non-metal atoms in the cages. The CO~ species is the first tetrametalloborane and the first with an isolated boron not attached to other boron atoms. The range of cluster types even now available provides both a challenge and an opportunity to bonding theorists and significant advances can be expected following the initial work of Wadesd and Rudolph." Early Transition -metal Carbaboranes.Metallocarbaboranes incorporating titanium were described in last year's Report. This work has been greatly expanded in a significant paper6 which also includes the first reported metallocarbaboranes of zirconium hafnium and vanadium. New Cr'l and MnII compounds were also prepared. The work provides a guide as to which formal oxidation states and electronic configurations may be required for the isolation of new stable electron- deficient metal carbaborane complexes. Highlights from the paper include the following neither (Et4N)2[4,4'-Ti-(1,6-C2B10H12)2] (A) nor its more stable 1,6- dimethyl relative (B) showed any tendency to expand the co-ordination sphere of the titanium atom and both were unreactive in solution to one atmosphere pressure of H2 N2 or CO or to PPh3 in marked contrast to titanocene which reacts immediately with such molecules.Electronic rather than steric factors may be responsible for the additional stability. The ZrII and Hf" analogues of (B) were produced by reaction of MCl with [Na2C2Me2BloHlo] in THF followed by isolation as their tetraethylam- monium salts. Both underwent extremely facile thermal carbon atom rearrange- ments (e.g. 90-95 "C under N2 in vacuo ;or 75 "C for 10h in MeCN solution for zirconium). In the case of zirconium the rearrangement was observed to proceed through the 1,8-isomer to the thermally most stable 1,12-isomer.For hafnium the rearrangement was so rapid that only the 1,12-isomer was detected. By contrast the titanium compounds showed little or no rearrangement under the same conditions. The relative rates for the rearrangements may be related to the strength of the bonding of the metals to the carbaborane cage the more diffuse 5d orbitals of hafnium binding more weakly than the corresponding 4d and 3d orbitals of zirconium and titanium. A mixed C5H5/C2BloH12-Ti" complex was isolated in the form of (Et4N)[4-(q5-CsHs)-4-Ti- 1 ,6-C2B 10H12] (C) and an unstable intermediate thought to be neutral [(CsH,)Ti(C2BloH12)] was also noted. The compound (C) was analogous to (A) in its lack of reactivity towards N2 H2 or CO and this provides further evidence of the powerful stabilizing influence of the carbaboranyl ligand compared with the cyc- lopentadienyl ligand.The VII Cr" and MnII analogues of (A) and (B) possess unexpectedly one two and one unpaired electrons respectively pointing to a different MO scheme for the carbaboranyl compounds compared with the biscyc- lopentadienyl complexes. Different ligand-field strengths for [q5-CsHs]and q 6-C2BloH12are indicated. Titanacarbaboranes incorporating the q '-cyclo-octatetraenyl ligand are now known. Reaction of [(TiClC#&] with Na2C2BlOHl2 yielded (Et4N)[4-(q8-C8H8)- 4-Ti-1,6-C2BloH12] a Ti(''') species oxidation of which by H202 produced the neutral Ti'" complex. The latter showed virtually no tendency to undergo thermal rearrangement and this perhaps indicates that whereas four-electron-deficient com- plexes may undergo polyhedral rearrangement two-electron-deficient ones (the 6 C.G. Salentine and M. F. Hawthorne Inorg. Chem. 1976,15 2872. The Typical Elements Ti'" complex is formally a 16-valence-electron system) may not. The isolation of metallocarbaboranes of general "formula [Ti(C,H,)(C2B,H,+2)] with unusual heteroatom positions can thus be predicted. With [C,B,Hl J2-neutral titanacar- baboranes of formula [Ti(q8-C6Hg)(C2B9Hl1)] were obtained which were completely air stable and did not melt or decompose at up to 300°C in air. Electrochemical studies showed that the Blo complexes [q6-C2BloH12]2- are easier to reduce than those of the B ligand [qS-C,B,Hl,]2- which implies that the B, ligand may donate less overall electron density to the metal centre than does the B ligand.This seems reasonable in view of the larger bonding face of the former which delocalizes the six electrons over a larger area. The behaviour of these ligands towards chromium underlines this fact. Whereas C2B10H12 can stabilize both Cr" and Cr''' [C2B9H1J2- could only stabilize Cr"'. Electron-hyperdeficient metalloboranes and Metallocarbaboranes. The structural consequences of clusters containing less than 2n +2 skeletal bonding electrons have been investigated in [Me4C4B,H,FeCo(q 5-C5H5)] which possesses only 2n (n = 14) skeletal ele~trons.~" The structure (9) involves a BH group simultaneously capping triangular faces in two polyhedra. The net effect is of two capped pentagonal bipyramids sharing an edge.With two extra electrons the structure would presum- ably have involved the fusion at the iron atom of a seven-vertex pentagonal- bipyramidal FeC2B4 cage to an eight-vertex dodecahedra1 FeCoC,B polyhedron. The two-electron deficiency of the compound has resulted in the shifting of one BH group to a capping position as noted previo~sly'~ in [1,6-(775-C5H,)2-1,6,2,3-Fe&B,&] which is also a 2n skeletal electron system and in the metal carbonyls [os,(Co)l,] and [Os,(CO),,]. This behaviour is accountable on the basis that capping a face of a closed polyhedron (at least in some cases) does not increase the 7 (a)W. M. Maxwell E. Sinn,and R. N. Grimes J. Amer. Chem. Soc. 1976,98,3490;(b)F. P. Callahan W. J. Evans F.Y. Lo,C. E. Strouse and M. F. Hawthorne ibid. 1975,97 296; (c)W. M. Maxwell E. Sinn,andR. N. Grimes J.C.S. Chem. Comm. 1976,389; (d)M. McPartlin C. R. Eady B. F. G. Johnson and J. Lewis ibid. p. 883. A.J. Carty,R. H. Cragg,J. D.Smith,and G. E. Toogood number of bonding orbitals so that an n-vertex capped polyhedron would require the same number (2n) of skeletal bonding electrons as an uncapped polyhedron of (n -1)vertices. Other 2n-electron systems studied include [Co3(qS-C,H,),B,H4] which is inferred on the basis of n.m.r data and the counting rules to be capped octahedral and the more complicated [CO,($-C,H~)~B~H~] where the n.m.r. data support a DZd dodecahedral structure which can be reconciled with the counting rules by assuming ‘partial’ bonding interactions between ‘formally’ non-bonding metal atoms or by assuming that the dodecahedral structure observed is merely a time-averaged geometry resulting from a fluxional rearrangement of the expected capped peri- tagonal bipyramid.The D2dstatic structure (8) is An indication that electron-counting rules do not tell the whole story has been presented in the recent structural investigation7‘ of the isomers of [Fe2(q5-C,H,),Me,C,B,H,] which has shown that at least two of them do not have the closo-structures predicted for these 14-vertex polyhedra with 30 skeletal electrons. One has an open pentagonal face as in (10) and the other a four-membered open face. This also provides a very rare example in metallocarbaborane chemistry of isomers having different gross polyhedral geometries.At elevated temperatures both rearrange but the structures of the products are not yet known. It is interesting to note that the closo-structure predicted for [H20~6(C0)18] is also not observed (see p. 241). Instead the nido monocapped square pyramid is found. However as the authors point out closo and nido versions of the same polyhedron will accommodate the same number of skeletal electron^.^^ It is not clear that either The Typical Elements of the iron 14-vertex polyhedra7‘ represents a nido tricapped version of the expected closo bicapped hexagonal antiprisms! Monometulloborunes. Examples of metal atoms forming part of a small borane cluster are still few in number but an interesting series of compounds is now available whose structures can all be related to pentaborane(9) and indeed many of them are prepared from it.Virtually every possible insertion or replacement possibility is represented among these compounds. Within the Fe(CO),-boranes we find [Fe(CO),(B,H,)] which has the apical BH of pentaborane(9) replaced by the Fe(CO) group,8a [Fe(CO),(B,H,)] and [Fe(CO,)(B,H,)]- in which an Fe(CO) group has inserted into the basal belt of the pentaborane to produce a pseudo-B,H, structure,8b and [Fe(CO)3{B,H,(CO)2}] which has the closo-octahedral structure like [B,H,]’-in which the B unit bonds in a polyhupto fashion to the Fe(CO) unit.,‘ To round out the other known structures [Co(qS-C,H,)(B,H,)] has involved the replacement of a basal BH group in pentaborane(9) by CO(~’-C,H,),~~ and [Be(BH4)(B5H10)](11)*=is comparable to [Fe(C0),B5H9] except that it contains two Be-H-B bridge bonds whereas it is possible that the iron compound has no Fe-H-B bridge at all (at most it has one).It seems likely that such a variety of compounds will not be confined to pentaborane-based species. n Metal complexes of the large boranes and their anions continue to attract attention. Perhaps the most interesting work recently has involved [BlOHl2]’-. This is known to co-ordinate in several ways in different compounds and it now seems that the mode of attachment may vary for a given compound depending upon the conditions. Thus [TlMe2(B10H12)]- whose structure has been determined by X-ray methods involves q4-bonding in the solid state whereas it appears to be q2when the compound is dissolved in donor solvents.8f A similar co-ordination change has been postulated for [Ir(CO)(PPh,)2(B,oH,2)]-which undergoes intramolecular H-D exchange in acetonitrile solution.It is suggested that the original q4-binding decreases to q2thereby releasing co-ordination sites on the metal for uptake of D2.8g 8 (a)N. N. Greenwood C. G. Savory R. N. Grimes L. G. Sneddon A. Davison and S. S. Wreford J.C.S. Chem. Comm. 1974 718; (6)T. P. Fehlner J. Ragaini M. Mangion and S. G. Shore J. Amer. Chem. Soc. 1976 98 7085; (c) J. A. Ulman and T. P. Fehlner J.C.S. Chem. Comm. 1976 632; (d)L. G. Sneddon and D. Voet ibid. p. 118; (e)D. F. Gaines and J. L. Walsh ibid. p. 482; (f) N. N. Greenwood and J.A. Howard J.C.S.Dalron 1976,177;(g)A. R. Siedle and L. J. Todd,Znorg. Chem. 1976,15,2838. 132 A.J. Carty,R.H. Cragg,J. D. Smith and G.E. Toogood Non-metal Heteroatom Boranes. Some notable advances in the chemistry of phospha- and thia-boranes have been made this year. Phosphaundecaboranes of formula 7-B10H12PR (R = Me Et Pr" or Ph) have been prepared by reaction of NaH decaborane and RPC12 followed by protonation. Me4N salts of the [7- Bl,HllPR]-anion were also produced.'" Reaction of the neutral phosphorus compounds with CoCl and C,H in basic solution gave [Co(q5-C,H,)(q-7- B,,H,,PR)] and the unsubstituted [Co(q5-C,H,)(q-7-BloHloP-)], which can be readily alkylated in high yield. The thiaboranes 6-SB9HIl and 7-SBloHlz when pyrolysed gave a variety of polydeltahedral thiaboranes as well as the cluso-1-SB9H9 and -1-SBllHll.These polydeltahedral species contain clusters linked through two-centre B-B bond^.'^ There is no evidence for B-B links with vertex orders other than 5 i.e. no linkage through apical borons. This contrasts with the clusters formed by pyrolysis of CZB4- and C2B,-carbaboranes. However similar coupling occurs photochemically for 2,4-C2B5H7." Coupling of thiaborane polyhedra has also beer accomplished via oxidation of [7-SBl,Hl,]2- by Ag' in ben~ene.'~ The structures of twelve- eleven- ten- and nine-vertex thiaboranes appear to parallel those of boranes and carbaboranes of the same skeletal electron count (a sulphur cage fragment provides four framework electrons and an ex0 lone pair).Thus [6-SB,Hlz]- is arachno 6-SB,Hll is nido and 1-SB9H9 is CIOSO.~~ Finally it is worth noting that the ultimate stereochemistry of products from the electrophilic halogenation of 1-SB9H9 cannot be simply predicted from a knowledge of charge distribution in the cage. Cage rearrangements play an important Triple-decker Sandwich Complexes containing Boron. In last year's Report the potential significance of various boracarbocycles as ligands was pointed out. The electronic (six ?r-electrons) analogy between the anions [C5BH6]- and [C,H,]- has already been exploited in the synthesis of borabenzene complexes. This year has seen the characterization of complexes derived from l-phenyl-2-ethylbor01e~~" and 3,4-diethyl-2,5-dimethyl-1,2,5-thiadibor0lene.~~~The borole derivative [Mn2(CO),(PhBC4H3Et)] is formed in the reaction of l-phenyl-4,5-dihydroborepin with [Mn2(CO),,] in boiling mesitylene.The rearrangement of a seven-membered boracarbocycle to a five-membered system is interesting when viewed in the light of facile valence tautomerism for other seven-membered carbocycles. The structure consists of a triple-decker sandwich (12) with the manganese atoms occupying the apices of a pentagonal bipyramid."" A complex (13) also having a triple-decker structure is produced from the 1,2,5-thiadiborolene-[Mn2(CO)lo]reaction.lob Apart from (12) and (13) only three other triple-decker sandwiches have been characterized namely the [Ni2(C,H&]+ ion"' and 1,7,2,3- and [1,7,2,4-(q5-C5H5)2C02C2B3H5].Possible routes to multidecked sandwich complexes incor- lad 9 (a)J. L. Little Inorg. Chem. 1976,lS. 114; (b)W. R. Pretzer and R. W. Rudolph ibid.,p. 1779; (c)J.S. Plotkin and L. G. Sneddon J.C.S. Chem. Comm. 1976,95; (d)D. A. Thompson W. R. Pretzer and R. W. Rudolph Inorg. Chem. 1976,15,2948; (e)W. R. Pretzer and R. W. Rudolph J. Amer. Chem. SOC. 1976 98 1441; (f) W. L. Smith B. J. Meneghelli N. McClure and R. W. Rudolph ibid. p. 624. lo (a)G. E. Herberich J. Hengesbach U. Kolle G. Hiittner and A. Frank Angew. Chem. Internat. Edn. 1976,15,433; (6)W. Siebert and K. Kinberger ibid. p. 434; (c)A. Salzer and H. Werner ibid.,1972.11 930; (d)R. N. Grimes D. C. Beer L. G. Sneddon V. R. Miller and R. Weiss Inorg. Chem. 1974,13 1138; (e)W. Siebert G. Augustin R.Full C. Kruger and Y. H. Tsay Angew. Chem. Internat. Edn. 1975,14,262; (f)W. Siebert R. Full C. Kruger and Y.H. Tsay 2.Naturforsch.,1976,31b 203; (g)P. S. Maddren A. Modinos P. L. Timms and P. Woodward J.C.S. Dalton 1975 1272. The Typical Elements 133 ' Ph porating carbaborane anions and metal fragments have however been ~uggested.~" It is significant that for the clusu frameworks of (12) and (13) each Mn(CO) unit contributes one electron; the 14 additional electrons required according to the 2n +2 rule are then contributed by four-carbon units (12e) and a boron fragment (2e) in (12) or two-carbon units (6e) two boron fragments (4e) and a sulphur atom (4e) in (13). The general co-ordination behaviour of the 1,2,5-thiadiborolene ligand now seems well In (13) and in the nidu-compounds [Fe(CO),- (Et,C,Me,B,S)]'o' and [Ni(CO)2(Et,C,Me,B,S)]'of all atoms of the C,B,S ring interact with the metal atoms and the components of the ring contribute 14 electrons to the framework count.The sulphur atom presumably has an exo-polyhedral electron pair as in thiaboranes and their derivativesg" It is interesting to speculate on the possible replacement of S in the thiadiborolene ring with a PR moiety. Presumably a similar series of metal carbonyl complexes containing cyclic R2C2Rr2B2PRrr ligands is feasible. We also note the co-ordinating behaviour of the duroquinone analogue 1,4- difluoro-2,3,5,6-tetramethyl-2,5-diboracyclohexa-1,4-diene which forms T-complexes such as [Ni(C0)2(C4Me4B2F2)] [Ni(C,Me,B,F,),] and [Fe(CO),-(C,Me,B,F,)] with firs t-row metals.log Alkylboranes (see also p. 2 12).-Unlike trimethylaluminium which is dimeric Me,B is a monomer in the gas phase.llQ Mulliken"' originally postulated the existence of hyperconjugation in Me,B to account for its monomeric nature but subsequent high-precision electron diffraction studies revealed 'IQ [B -C = 157.83(11) C-H = 111.38(15) pm] no evidence for hyperconjugative bond- shortening. Semi-empirical MO calculations'lc indicated that .rr-type (B2g2-C2p,) interactions in Me,B and Me,Al were of similar magnitude and less than 10% of the cr-bonding. Thus hyperconjugation does not explain the molecularities of these two species. These latter studies llQ*c suggest that in Me,B there is an essentially vacant 11 (a)L.S. Bartell and B. S. Carroll J. Chem. Phys. 1965,42 3076; (6)R. S. Mulliken Chem. Rev. 1947 41,207; (c)A.H. Cowley and W. D. White J.Amer. Chem.SOC., 1969,91,34; (d)M.K. Murphy and J. L. Beauchamp ibid. 1976,98 1433; (e)J. C. Haartz and D. H. McDaniel ibid. 1973,95,8562; (f)H. C. Brown and N. Ravindran ibid. 1976,98,1785; (g)H. C. Brown and N. Ravindran ibid. 1976,98,1798; (h)A. Pelter K. Rowe D. N. Sharrocks K. Smith and C. Subrahmanyan J.C.S. Dalton 1976 2087. A.J. Carty,R.H. Cragg,J. D. Smith and G.E. Toogood B2p orbital in contradistinction to boron halides BX where conjugative ?r-eff ects are definitely present. Ion cyclotron resonance (ICR) mass spectrometric studies have now been used to shed further light on the role of this empty B2p orbital in the acid-base chemistry of Me,B .'Id As expected for a very electron-deficient species the parent radical-ion Me,B' appears in very low abundance in positive-ion single- resonance ICR mass spectra.Ionization occurs from a strongly bonding (T~-~ orbital in Me3B resulting in a weak B-C bond in the ion. From photoionization measure- ments the one-electron B-Me bond dissociation energy in Me,B' is only 32.63 kJ mol-' [cf. D(B-Me) in Me,B =372.4 kJ mol-'I. The only negative ion observed in Me,B by electron impact is [Me,B=CH,]- isoelectronic and presum- ably isostructural with Me2C=CH2 and [Me2N=CH2]+. This is the first time that a boron-stabilized carbanion has been identified as a stable isolated gas-phase species. Trimethylborane is not protonated in ion-molecule reactions with strong proton donors.Instead production of Me2B' occurs via reaction (2). In sharp contrast the gas-phase acidity of Me,B has been placed in the series CD30H <C2HsOH<PH3< Me3B <ASH,; Me3B is apparently comparable in acidity to HF and CF3CH20H. MH++Me3B +Me2Bf +M +CH4 (M =CH4 C2H4 H2S,or CH20) (2) SF5-+HF+Me2BCH2 < SF,-+Me3B 10% Me2BF2- +Me +SF4 (3) SF5-+Me3B +Me3BF-+SF4 (4) ICR techniques have also been used to determine relative Lewis acidities for boron halides"' and Me3B.'Id For example the formation of Me2BF2- and Me3BF- can occur via fluoride-ion transfer in the gas phase [equations (3) and (4)]. Towards fluoride ion the Lewis acidity varies as Me2FB>Me3B>SF4.Upper limits for AH;[Me,BF,-] and AH;[Me,BF-] are <-776.1 f48 and -603.8 f48 kJ mol-' respectively considerably less than the value of 1728 kJ mol-' for AH;[BF,-]. As expected heats of formation increase with increasing fluoride substitution on boron. It will be of interest to see how Lewis acid strengths of R3B towards F-and H- are sensitive to changes in the R group. Although hydroboration is covered in Section B of Annual Reports it is pertinent here to mention some notable advances in the syntheses of organo(ha1ogeno)- boranes. Partially alkylated or alkenylated halogenoboranes are potentially valu- able precursors for mixed organoborane syntheses. Brown and Ravindran"' have shown that BH,Cl,OEt hydroborates a variety of alkenes quantitatively at 0 "C giving the corresponding R2BC1 compounds.Internal alkynes react rapidly with BH2Cl in diethyl ether at 0 "C giving dialkenylchloroboranes cleanly. Furthermore from reactions of internal alkynes with BH2Cl in THF at 0 "C intermediate alkenyl- chloroboranes can be isolated. Convenient procedures for the synthesis of alkyl- and alkenyl-dichloroboranes [e.g. equation (5)]have also been described."g BHC12,0Et2+BCl +alkene -+BC13,0Et2+alkyl-BC1 (5) Finally mention should be made of a high-yield synthesis of dialkylbromoboranes from trialkylboranes by conversion of the latter into dialkyl(methy1thio)boranesand subsequent reaction of the thio-compounds with bromine at low temperatures."" The Typical Elements 135 Boron Analogues of Amino-acids.-Recognition by Parry and co-workers several years ago,lza,b of the structural consequences of replacement of an oxygen atom by an isoelectronic BH group led to the synthesis of several families of boron analogues of carbon oxides oxoacids and organic compounds.Thus isoelectronic CO and BH,CO react with KOH yielding K2C03 and potassium boranocarbonate K2[H3BCO2] respectively while the compound originally formulated as H3BC0,2bJH3 is actually ammonium boranocarbamate NH4[H3BCONH2] the counterpart of ammonium carbamate. Consideration of the isoelectronic nature of BH2- and CH (or BH- and CH) allows the prediction of a series of dipolar boron analogues of the zwitterionic a-amino-acids. The zwitterionic forms of glycine H,kCH,CO,-and alanine MeCH(fiH3)C02-have boron counterparts H,&BH,CO,H and MeBH(kH,)CO,H.Interest in these boron species derives principally from their potential biological activity when compared with the enorm- ous significance of the a-amino-acids in biochemistry. Development of boron-amino-acid chemistry will be stimulated by a recent report describifg the synthesis characterization and activity of Me,&BH,CO,H (cf.betaine Me3NCH2C0,-) and Me3kBH,CONHEt.'2' The synthetic route to these compounds is shown in equa- tion (6). Me3NBH2CN Et3OBF4 Me,NBH,CNEt+ BF4-Me,NBH,CONHEt p Me3NBH,C0,H (6) The acid Me3&BH2C02H is a crystalline solid stable in air and water. Water stability is biochemically significant but perhaps not unexpected in view of the known hydrolytic stability of the borane cations Me,NBH,O,C(CH,) NMe,' and Me3NBH2&Me2CH2C0,Et.12dIn the crystal Me3&BH2CO2H exists as .the hydrogen-bonded dimer similar to other simple carboxylic acids. Both the acid and the N-ethylamide exhibited significant antitumour activity in preliminary tests with mice. Serum cholesterol levels in mice were reduced following dosage with Me,N- BH2C02H or Me3NBH2CONHEt perhaps an indication of antagonism between betaine a cofactor in liver cholesterol synthesis and the boron analogue. m-Bonding and Valence Angles in Boron-Oxygen Compounds. A great deal of interest has been focused on the role of B-X p?r-p?r bonding in the ground-state structures and properties of boron halides. For the lesser known simple boron- oxygen compounds such as B (OR) relatively little accurate structural information is available to assess B -0 p?r-p.rr bonding contributions despite theoretical predic- tions of increasing ?r-bond orders in B-X bonds in the order B-R <B-halogen < B-SR <B-OR <B-NR,.This year precise electron diffraction data have been accumulated for B(OMe) and Me,BOBMe,.'36 The latter is particularly inter- esting since the bent twisted configuration (C symmetry) confirmed by diffraction maximizes B-0 bonding and had been predicted earlier by Lanthier and Graham13C 12 (a)J. C. Carter and R. W. Parry J. Amer. Chem. Soc. 1965,87,2354;(b)L. J. Malone and R. W. Parry Inorg. Chem. 1965 6 817; (c) B. F. Spielvogel L. Wojnowich M. K. Das A. T. McPhail and K. P. Hargrave J. Amer.Chem. Soc. 1976 98 5702; (d) N. E. Miller Inorg. Chem. 1976 15 1735 and references therein. 13 (a)G. Gundersen J. Mol. Structure 1976,33,79; (6)G. Gundersen and H. Vahrenkamp ibid. p. 97; (c) G. F. Lanthier and W. A. G. Graham Chem. Comm. 1968 715. 136 A. J.Carty,R. H. Cragg,J.D. Smith and G.E. Toogood from n.m.r. studies. The BOB angle is large (144.4') (cf. COC 111.5' in Me20) and the B-0 bonds [135.9(4) pm] are even shorter than in B(OMe) [136.7(4) ~m1.l~~ Comparison with the Schomaker-Stevenson modified B -0 single bond length of 143 pm shows that considerable B-0 multiple bonding exists in these molecules. The shorter B-0 distance in the anhydride may reflect the availability of two B2p7r orbitals for two oxygen lone pairs as opposed to one orbital for six pairs in B(OMe),.Large valence angles at oxygen in Me2BOBMe and B(OMe) (121.4') can of course be rationalized uia VSEPR theory where B-0 multiple bonding is expected to increase B -O/B -0 and B -O/C-0 bonding pair repulsions. Boraphosphanes. Polyboraphosphanes containing a P-B backbone have been the subject of much research aimed at producing high molecular weight polymers resistant to thermal decomposition and to oxidative and hydrolytic attack compar- able to those of the cyclic oligomers. Condensation polymerization of the latter has appeared to be a promising approach to the synthesis of stable high polymers but this requires the selective placement of two or more potentially reactive substitutents on a preformed cyclic unit.The only consistently successful reaction of this kind involves the halogenative replacement of the hydrogens on boron. Unfortunately the halogens in the fully halogenated species have proved to be inert in attempted substitution reactions. Recently however partially halogenated trimers have been successfully synthesized and their halogens found to be readily replaceable. Stoicheiometrically controlled halogenation of [Me2PBH2I3 has been achieved by refluxing with N-halogenosuccinimides in benzene solution. The halogenation selectivity increased with increasing atomic number and was apparently sterically controlled. It proceeded in a stepwise fashion whereby non-geminal substitution occurred preferentially. 14a Nucleophilic displacement of halogen in the mono- halogenated species readily For example a 67% yield of the 2-formoxy-derivative could be prepared according to equation (7).Acetoxy-compounds were also prepared. The extent and position of substitution within these cyclic trimers and also in the corresponding tetramers is clearly indicated by "B n.m.r. and the ring dynamics have been investigated by a multinuclear ('H "B 13C ,'P) variable-temperature n.m.r. study. 14' Me,P ,PMe Me,P /PMe B B H2 2 Aluminium Gallium Indium and Thallium Aluminium and Gallium Borohydrides.-Methylaluminium borohydrides are of interest because of the contrasting structures and properties of the parent com- pounds AlMe (dimeric alkyl bridged) and A1(BH4X (monomeric bidentate 14 (a)M. H. Goodrow and R. I. Wagner Inorg.Chern. 1976 15 2830; (b)M. H. Goodrow and R. I. Wagner ibid. p. 2836; (c)M. A. Sens J. R. Odom and M. H. Goodrow ibid. p. 2825. "'*' gallium complexes with five-co-ordinate stereochemistry. The Typical Elements 137 borohydrides). The mixed compounds AlMe,(BH,) and AlMe(BH,) have been synthesized in essentially quantitative yields via reaction (8). n AIR3+ (3 -n)AI(BH4) -B 3A1(BH4)3-nRn n = 1 or 2 (8) The dimethyl compound is a crystalline solid below the melting point (14 "C) is air sensitive and decomposes slowly above 0 "C while the monomethyl compound is a liquid above -76 "C. Both compounds are monomeric with i.r. spectra characteris- tic of bidentate BH groups; methyl bridges are absent. It is interesting that the stability of AlMeCBH,) to disproportionation is greater than that of the dimethyl compound.This feature is enhanced in the higher alkyl homologues where AlR,(BH,) (R = Pr" or Bu') cannot be obtained pure via redistribution reacti~ns.''~ All of these compounds are fluxional in solution; rapid exchange of bridge and terminal hydrogens occurs even at low temperatures. Relatively little is currently known about gallium borohydrides. It is significant therefore to mention that the novel compound HGa(BH,) has now been prepared from Ga,Cl and LiBH and from HGaCl and LiBH at -45 0C.15c Vibrational spectra for the solid and vapour as well as for the molecule trapped in dinitrogen or argon matrices are consistent with a Czomolecular structure in which each gallium atom is co-ordinated to a single hydrido-ligand and four hydrogen atoms from two bidentate BH groups.The single hydride ligand gives rise to an n.m.r. resonance at T -4.8. This compound joins a relatively small group of structurally characterized Monomeric Aluminium Trich1oride.-By analogy with BC13 the predictable struc- ture for monomeric AlCl is trigonal planar (D3h).However a low-precision electron diffraction study16" was interpreted in terms of a C3"molecule slightly distorted from planarity (LClAlClll8 * 1.5"). In a subsequent matrix-i.r. investiga- tion both symmetric (382.2 cm-') and asymmetric Al-Cl (594.7 cm-') stretching frquencies were observed inconsistent with a planar molecule. 166 Recent more detailed Raman and i.r. work in the Al-Cl stretching region by Beattie Blayden and Ogden,',' has shown that the symmetric Al-Cl stretch does not appear in the i.r.spectrum of Ar-isolated AlCl,. Moreover the 'vl' Raman frequency is -392 cm-'. Thus the band at 382.2 cm-' in Lesiecki and Shirk's i.r. spectrum166 is not due to the symmetric stretch of non-planar AlCl but probably arises from an impurity molecule (see below). These results were essentially confirmed in a new investigation by Shirk and Shirk.16' There is now general agreement on the vibrational frequencies and planar structure of AlCl,. Significantly evidence has also been presented from spectra of AlC13 codeposited with N2in Ar that bands at 599 and 385 cm-' are due to the dinitrogen adduct AlC13N,.'6d These frequencies are similar to those originally attributed to non-planar AlC1 in the initial i.r.study.'66 All-electron ab initio SCFMO calculations (and p.e. spectra) on AlCl and AlClMe l5 (a)P. R. Oddy and M. G. H. Wallbridge J.C.S. Dalton 1976 869; (b) P. R. Oddy and M. G. H. Wallbridge ibid.,p. 2076; (c)A. J. Downs and P. D. P. Thomas J.C.S. Chem. Comm. 1976,825; (d)A. T. McPhail R. W. Miller C. G. Pitt G. Gupta and S. Srivastava J.C.S. Dalton 1976 1657; (e)K. Dymock and G. J. Palenik J.C.S. Chem. Comm. 1973 884. l6 (a)E. Z. Zasorin and N. G. Rambidi Zhur. strukt. Khim. 1967,8,391;(b)M.L. Lesiecki and J. S. Shirk J. Chem. Phys. 1972,56,4171;(c) I. R. Beattie H. E. Blayden and J. S. Ogden ibid. 1976,64,909;(d) J. S. Shirk and A. E. Shirk ibid. 1976,64 910; (e) M. F. Lappert J. B. Pedley G.J. Sharp and M. F. Guest J.C.S. Faraday II 1976 72 539. 138 A.J.Carty,R. H. Cragg,J.D.Smith and G.E. Toogood (as well as their dimers A1,Br6 and Ga,Cl,) show that A1 3d orbitals make a significant contribution to bonding whereas C1 3d orbitals act only as polarization functions. Aluminium Fluoride and Oxide Species in Molten Cryolite.-Although extensively studied by a wide variety of physical techniques owing to its industrial importance the nature of the oxide fluoride and mixed oxide-fluoride species present in cryolite-alumina melts is still a matter of debate. Recently Raman spectroscopy has been used to identify complexes present in pure cryolite and related A careful analysis of Raman spectra of melts for a range of NaF AlF3 ratios allowed identification of bands due to [AlF,]- tetrahedra and [A1F6I3- octahedra; relative concentrations of these ions which vary with composition can be estimated from line intensities.These studies suggested that in molten cryolite the dissociation [A1F6I3-$ [AlF,]-+ 2F- occurs to the extent of 25'/0 refuting an earlier claim'7c that [A1F6I3- dissociated to AlF3 and 3F-. It is interesting that support for this premise has been forthcoming from theoretical calculations which predict that in the gas phase [A1F6I3- would decompose to [AIF,]- and 2F- with a net release of 723.5 kJ m~l-'.'~~ When A1203 is added to cryolite the dissociation in equation (9) is commonly presumed A1203 S 2(A10)++02-(9) An alternative suggestion is equation (10) In the presence of F-ion mixed oxide-fluoride complexes of aluminium would be expected but in fact none of these species has been unequivocally characterized.Raman spectra of Al,O,-AlF,-NaF melts as well as A1203-pure cryolite melts show that polarized bands at 530 and 460cm-' and depolarized bands at 310 and 185 cm-' arise from species with AI-0-A1 bridges. Hence it seems that equation (10) may better represent the reaction of A1203 in molten cryolite. Stereoisomerization of Aluminium p-Ketoeno1ates.-The stereochemical non-rigidity of tris-(P-ketoenolato)aluminium(rIr) and related tris-chelates has been recognized for more than a decade.lsa Establishment of exact mechanisms of stereoisomerization in the aluminium P-ketoenolate series originally described by Fay and Piper,"" has however proven elusive.New kinetic data have been obtained for tris-(2,6-dimethylheptane-3,5-dionato)aluminium(111) Al(dibm), and bis-(1,1,1,5,5,5-hexafluoropentane-2,4-dionato)(2,6-dimethylheptane-3,5-dionato)aluminium(Irr) Al(hfa),(dibm) and information obtained from all previous 17 (a) B. Gilbert G. Mamantov And G. M. Begum J. Chem. Phys. 1975,62 950;(6) B. Gilbert G. Mamantov and G. M. Begum Inorg. Nuclear Chem. Letters 1976,12,415;(c)J. L.Holm Inorg. Chem. 1973,12 2062; (d)D. R.Armstrong Inorg. Chim. Acra 1976,17 125. 18 (a)R.C. Fay and T. S. Piper Inorg. Chem. 1964,3,348;(b)M.Pickering B. Jurado and C*S. Springer jun. J. Amer. Chem. Soc. 1976,98,4503;(c) J. R.Hutchison J. G. Gordon and R. H. Holm Inorg. Chem. 1971,10 1004; (d)I.JoniiS and B. Nordkn Inorg. Nuclear Chem. Letters 1976,12 33; (e)S. S. Eaton G. R. Eaton R. H. Holm and E. L. Muetterties J. Amer. Chem. Soc. 1973,95 1116; (f)D.J. Duffy and L. H. Pignolet Inorg. Chem. 1974 13 2045. The Typical Elements 2H n.m.r. studies of AI1Ir-P -ketoenolates has been reassessed."' Stereoiso-merization of Al(dibm) is a first-order reaction and occurs intramolecularly paralleling observations for other Al"' P-diketonates. Furthermore all reliable activation enthalpies for Al(P -ketoenolate) isomerizations with the possible exception of Albmhd) (pmhd = l-phenyl-5-methylhexane-2,4-dionato) and Al(acac) lSd(see below) lie in the narrow range 77.0-95.8 kJ mol-' suggesting a single isomerization mechanism. Conversely AS+ values lie in the range 41.2-57.3 kJ mol-' for hfa chelates and close to zero or negative for non-fluorinated chelates [Al(pmhd) and Al(acac) excepted].Permutational analyses and 'H n.m.r. patterns establish that only one rearrangement involving simultaneous interchange of terminal groups within two of the three bidentate ligands and enantiomerization of the metal centre is consistent with all reliable 'H n.m.r. studies. This is the effective steric course of the reaction'" (the permutation consistent with experiment) and does not determine the mechanism or 'physical pathway followed by the molecule during reaction'. Nevertheless certain intramolecular non-bond-rupture mechanisms are inconsistent with the single estab- lished steric course. The trigonal squash (Stiefel and Brown) and trigonal twist (Bailar) mechanisms are ruled out for the AIM-diketonate) and Al(hfa),(dibm) molecules considered.The final mechanistic choice for the isomerization process in non-fluorinated P-diketonates of aluminium rests heavily on the similar small (or negative) AS) values for A1@-diketonate), Al(tropolonate) and M(NN-dialkyl dithiocarbamate)3.1'f The tropolonates and carbamates rearrange via trigonal twist mechanisms. By contrast in [Co(P-diketonate),] complexes where bond-rupture processes dominate positive entropies are found. Thus for non-fluorinated aluminium diketonates considered by Springer et af.,"' the combination of steric course and activation parameters points to a rhombic (Ray-Dutt) twist mechanism. The generality of these conclusions for all non-fluorinated derivatives cannot however be taken for granted.Thus the 'H n.m.r. behaviour and activation entropy for Al(pmhd)3'8c do not allow unambiguous selection of a twist or bond rupture mechanism. Very recently in a nice piece of experimental work Al(acac) was resolved into optical isomers by low-temperature column chromatography on D-lacto~e-A1~0~,~'~ The absolute configuration was established from the circular dichroism (c.d.) spectral pattern. The enantiomer with a positive sign of the low-energy c.d. band has the absolute configuration A. Kinetic data for inversion of A-Al(acac) gave activation parameters E = 131f5 kJ mol-' AH' = 130f.5 kJ mol-'. These values are close to those for Al(pmhd),."" Inversion instability of Al(acac) is due to a large positive activation entropy,'8f disfavouring a twist mechanism.For the fluorinated diketonate complexes activation entropy evidence is strong for bond-rupture mechanisms. Assuming that (a) cleavage of A1-0 bonds always occurs at the fluorinated end of the chelate ring (b) the co-ordinated oxygen atom of a unidentate ligand is less electronegative than the oxygen atoms of a chelate ring and (c) a unidentate ligand is a better .rr-donor than a bidentate ligand relative energies for various five-co-ordinate intermediates can be estimated. The favoured intermediates in the common bond-rupture mechanism for Al(hfa),(dibm) Al(tfa), Al(tfa),(acac) and related molecules have a square-pyramidal-apical stereochemistry .140 A.J. Carty,R. H. Cragg,J. D. Smith and G.E. Toogood Indium(1) Complexes.-Until recently the chemistry of the lower oxidation state of indium was poorly developed."" Interest in the chemistry of In' stems not only from the stereochemical significance of inert-pair effects but also from the potential utility of In' compounds as abnormally good ionic cond~ctor~.~~~ Several routes to anionic complexes are now available [equations (11)-(14)]:19c [Me2bipy]Xz+InX(s) h'eoH~ [Me2bipy][InX3] ([Me2bipy12' =NN-dimethyl-4,4'-bipyridinium dication X = C1 Br or I) (11) [Me2dppe]12+ In(C,H,)+ HI C6H6 b [Me2dppe]In13+C5H6 ([Me2dppeI2' = 1,2-bis(methyldipheny1phosphonio)ethanedication) (12) [Et,N]X+ HX + In(C,H,) EtoH-C6H6b [Et,N][InX,] +HC&(X = C1 Br or I) (13) Et,NI + I + In EtOH-C& In Et,N[InI,] (14) Vibrational spectra and force-constant calculations for the solid trihalogenoindate(1) complexes are indicative of trigonal-pyramidal stereochemistry; the lone pair is thus stereochemically active as in the isoelectronic [SIX,]- series.For the dichloroin- date(1) species Raman and i.r. frequencies correlate satisfactorily with v1and v2for bent triatomic SnCl in argon or dinitrogen matrices. There is however a large frequency difference between the bending modes v2,for [InC12]- and SnC1,. The implication from these studies is for the existence of discrete [InX312- and [InX,]- ions in the crystal lattices of the In' complexes a conclusion which contrasts with the propensity of [SnXJ and SnX to form halide-bridged polymers in the solid.X-Ray data are awaited with interest. The large monopositive cations In' and T1' in sites of low co-ordination number should by analogy with Ag' and Cu' iodide systems exhibit high ionic mobilities. The postulate of high ionic conductivity for salts containing these cations has been tested by the synthesis and characterization by powder-X-ray Raman and conduc- tivity techniques of In4Cd16 In2ZnI, Tl,ZnI, and T14Cd16.19b Raman data for M,Cd16 and M,ZnI (M=In or TI) are consistent with the presence of Cd16 octahedra and ZnI tetrahedra respectively; the co-ordination number of M' (M = In or T1) in these compounds was unspecified but covalent interactions with halide ions must be at most very weak. Variable-temperature Raman spectroscopy can via line-broadening provide a sensitive indication of the existence of high- temperature disordered phases.The findings of Shriver Whitmore and co-worker~~~~ show that M2Zn14 (M = In or Tl)and In,Cd16 undergo sharp order- disorder phase transitions at elevated temperatures; the disordered phases have high electrical conductivities with In' and Tl' ions the probable conducting species. Transition Metal-Indium Bonds.-Clusters of the type [{Mn(CO),},InX] (X= C1 or Br) were originally synthesized by Graham and co-workers.200 Crystals of these compounds have now been made via insertion of indium(r) halides into the metal- metal bond of [Mn2(CO),,] in a bomb reactor. All three compounds have the same 19 (a)A. J. Carty and D.G.Tuck Progr. Znorg. Chem. 1975,19,245;(b)R. L. Ammlung D. F. Shriver,M. Kamimoto and D. H. Whitmore J. Solid Stare Chem. in press; (c) J. J. Habeeb and D. G.Tuck J.C.S. Dalron 1976 866; (d)J. G. Contreras and D. G. Tuck Inorg. Chem. 1972,11 2967. 20 (a)W. A. G. Graham J. Hoyano and D. J. Patmore Inorg. Nuclear Chem.Letters 1968,4,201;(b)H. J. Haupt W. Wolfes and H. Preut Inorg. Chem. 1976 15 2920. The Typical Elements structure (14) with bridging halides and tetrahedrally co-ordinated indium atoms.20b Although the structures resemble that of In216 there are some interesting differences which reflect the bulk of the Mn(CO) ligands. Thus the In(p-X)In angles are obtuse in [{Mn(C0)5}21nX]2 and acute in In216 (86.3') while the non-bonded distances In.-.In and X. -X are in the sequences In. -.In > X. -.X for [{Mn(CO)5}21nX]2 and X. -.X > In-In for 1n216. In addition the In(p-X)In angles increase as I < Br < C1 for [{Mn(CO),},InX],. All of these structural changes can be rationalized on the basis of non-bonded repulsions between equatorial CO groups of pairs of Mn(CO) ligands above (or below) the In,X2 ring. These observations lend credence to the view expressed in last year's Report of an analogy between transition-metal carbonyl fragments and very bulky alkyl groups. Finally we note the relative invariance of LML angles in halide-bridged Group 111 dimers with change in electronic and steric properties of terminal ligands L.'Ob ""n N.M.R. Chemical Shifts as a Probe of Binding Constants for Alkali-metal Ions.-The use of Tl' as a probe of alkali-metal ion behaviour in biochemistry is based on chemical similarities between Tl' and M' (M=alkali metal) together with the availability of physical methods (e.g.Tl n.m.r. relaxation times TI' luminescence) to locate T1' ions. A method has been developed for determining relative binding constants of alkali-metal ions in a variety of solvents via 1'chemical shift measurements.21u Since Tl' shifts are sentitive to ligand binding sites,"' the method is capable of providing information on solvation effects ion selectivity and the types of ligand atoms involved in complexation. As an example the selectivity sequence for 18-crown-6 towards M' in MeOH is K' >Rb' >Na' Cs' TI' whereas in DMF the sequence is K' >Rb' > Cs' TI' > Na' owing to stronger Na' solvation in this solvent.(a) J. J. Dechter and J. I. Zink J. Amer. Gem. Soc.,1976,98,845; (b)J. J. Dechter and J. I. Zink ibid. p. 2937.

ISSN:0308-6003    

DOI:10.1039/PR9767300120

出版商:RSC    

年代:1976

数据来源: RSC