摘要:

Kinetic Spectroscopy in the Far Vacuum Ultraviolet Part 3.-Oscillator Strengths for the 3s, 4s and 5s 3S-2p4 3P2Transitions ifi Atomic Oxygen BY MICHAEL AND LAWRENCEA. A. CLYNE* G. PIPER?, Department of Chemistry, Queen Mary College, Mile End Road, London El 4NS Received 20th May, 1976 Line absorption measurements for ns 3S-2p4 3PJ transitions have been made as a function of ground state oxygen 02p43PJ atom concentration. The results gave the following values for the oscillator strengths (f;:k)of the ns 3S-2p4 3P2transitions of oxygen : (4.5kl.O)~ (n = 3, h 130.22nni); (5.9k1.4)~ (n = 4, h 103.92nm); (1.5k0.4)~ (n = 5, h 97.65 nm). The agreement with the literature of the $value for n = 3 is good ; no previous measurements for the n = 4and n = 5 transitions appear to have been reported.Atomic oscillator strengths (f-values) or the associated transition probabilities (such as Aki,the Einstein coefficient for spontaneous emission) are necessary basic data in a number of different areas. Well-known oscillator strengths provide the required correlation between observed intensities of absorption (or of fluorescence), and the density of absorbing or emitting atoms. Thus, for example, quantitative chemical kinetic measurements may be performed, or the composition of planetary atmospheres may be modelled. Also, experimental f-values provide data both for theoretical work involving semi-empirical calculations, and for verification of ab initio calculations of oscillator strengths. Most resonance transitions of atoms of aeronomic interest occur in the vacuum ultraviolet spectrum, with its concomitant experimental difficulties.Therefore, only recently has a significant body of data on such resonance transitions begun to accuinu- late. Studies of transition probabilities at wavelengths shorter than the LiF cut-off (i.e., A < 105 nm) are quite rare because of acute experimental problems, although it is in this wavelength region that theoretically important, resonance-Rydberg series can be studied. In order to begin to fill the void of information concerning transition probabilities below the LiF cut-off, and more specifically those for resonance-Rydberg transitions, we have measuredf-values for the 3s, 4s and 5s 3S-2p4 3P2transitions in O(1) which appear at 130.22, 103.92 and 97.65 nm respectively (see table 1).We have used the line-absorption method for the determination of the f-value for all three transitions. (The method is applicable to the many other resonance transitions of 0 which lie between 92 and 110 nm). The apparatus employed collimated hole structures in lieu of windows to separate the source, absorber and detector. The source was a micro- wave discharge through a flow of helium with a trace of molecular oxygen. The 130.22 nmf-value was the same within experimental error as other recent experimental and theoretical results. The shorter wavelength Rydberg transitions (n = 4, 5) show a trend in f-value consistent with theoretical expectations. 7 present address : Physical Sciences Inc., Woburn, Mass.01801, U.S.A. 2178 M. A. A. CLYNE AND L. G. PIPER TABLEWA WAVELENGTHS AND ENERGIES OF ns 3S-2p4 3PJTRANSITIONS OF O(I) ground state 2p4 3s 3S0 130.217 76 795 130.487 76 636 130.603 76 568 4s 3S0 103.923 96 226 104.094 96067 104.168 95 999 5s 3S0 97.645 102412 97.796 102253 97.862 102 185 In this paper, we first consider the processes contributing to line broadening of the emitters and absorbers. A brief formulation of the line absorption method is then presented. The results section includes a description of the methods used to establish the optical density and temperature in the oxygen atom resonance lamp, followed by the results of the $value measurements. Finally, our experimental $values are compared with previous work.THEORETICAL LINE ABSORPTION METHOD FOR 0ns 3S-2p4 3PJ TRANSITIONS The raw data from which f-values were derived were measurements of fractional absorption, A, as a function of ground state 0 2p4 3PJatom concentration, N, using a resonance lamp. The method is based on well-established principle~,l-~ and it utilizes the relationship between the integral of the absorption coefficient at frequency v, k,, and the oscillator strength,f, for the corresponding transition : f = (mc/ne2N)k,dv. The expression relating A to k, is eqn (11), {laA = (Io-~trans)lIo = I(v)[l -exp (-k,Z)] dv}/Ia I(v) dv (11) --m -03 where I is the path length for absorption, and I(v) is the frequency distribution of the source emission line.The analysis used to determine values of ffrom measurements of A using eqn (I) and (11) has been given in full elsewhere '* '* and will be merely summarized here (in a section to follow). BROADENING OF OXYGEN ATOM LINES The definition of the line shapes of the emitters [I(v)] and absorbers, (k,,),and knowledge of the magnitudes of the line widths (FWHM), is central to the correct evaluation off-values in the line absorption method [see eqn (I) and (II)]. In some cases, such as the halogens F, Cl, Br, I, hyperfine nuclear splitting can broaden the lines and can lead to resolved multiplet structure ; this leads to an underestimate of f-values if the hyperfine splitting is ignored.'. In other cases, such as Ne, hyperfine isotopic splitting of lines can have the same effect.The oxygen l60atom lines are free from both nuclear and isotopic hyperfine effects. The observed profile of any non-reversed atomic line is considered to be inter- mediate between the limiting cases of a Gaussian, or Doppler profile, and a Lorentzian profile. In the present work, the experimental conditions were such that all factors leading to Lorentzian broadening were much less than those leading to Doppler broadening. The basis for this conclusion is briefly summarized as follows. KINETIC SPECTROSCOPY IN FAR VACUUM U.V. The Doppler width (AvD) due to thermal motions of atoms having mass A4 and at temperature Tis given by eqn (III),l AvD/cm-l = (2/LOc)(2RTIn 2/M)3 (111) A. is the wavelength of the line centre.Values for AvD at 298 K for the oxygen atom lines of interest are : 0.238cm-' (4.03x nm) for A 130.22nm, 0.299 cm-' (3.23x nm) for A 103.92nm, and 0.318 cm-l (3.03x nm) for A97.65 nrn. The phenomena leading to a Lorentzian line profile can be divided into two groups. These are : (i) natural broadening, which arises from the Heisenberg Uncertainty Principle ; and (ii) the several types of collision broadening, which include Lorentz, Holtzmark and Stark broadening.' For the case of a resonance transition (where the lower state has an infinite lifetime), the natural line width (AsN) reduces to the simple form of eqn (IV),9 z is the lifetime of the upper state (u) with respect to all transitions to all lower states (i), and rn is the electron rest mass.In the case of the 130.22nm transition (3s- 2p4), we need consider only transitions to the three Jlevels of the ground state. In conjunc- tion with the well-establishedf-value (0.048-see table 2), the value AvN = 3.01 x cm-l for the 130.22nm line is then obtained. Thef-value results given in table 3 and in ref. (10) established that the natural widths were AvN = 6.80 x cm-' for ?b 103.92nm and 2.27 x for 197.65 nm. It is clear, therefore, that even for the strongest 130.22nm line, AvN is two orders of magnitude less than AvD at 298 K. Contributions to the absorption from the natural line width can be safely neglected for all save extremely large absorbances involving radiation trapping (koZ > 10). TABLE2.-OSCILLATOR STRENGTHS FOR THE 130.22 nm, 3s-2p4, TRANSITION f-value method reference 0.045f0.010 0.047f 0.009 0.046f 0.001 0.050+ 0.009 0.049+ 0.011 line absorption line absorption lifetime (time-resolved) lifetime (phase shift) wall-stabilized arc this work 3 27 28 29 0.047f0.005 0.050f 0.0055 *> beam foil 30 0.0475 0.005 beam foil 31 0.052+ 0.005 0.0505 0.004 line absorption beam foil 32 33 * measured at 130.5 nm.The magnitude of Holtzmark or self-broadening, AvH, is dependent upon thef- value of the relevant line, its well as on the density of like atoms in the system : Av,t = 0.0229(8ne2/rnc')(gi/gu)NfAo. (V) The maximum value for AvH in our work was for the 1130.22nm line with N 2 10' ~rn-~,where its magnitude was 2 x cm-l.This value is clearly negligible com- pared with AV, (or AvN), and Holtzmark broadening can be neglected in this work. Lorentz or foreign-gas collisional broadening arises from perturbations to the energy levels of the emitting species by van der Waals interactions with the perturbing molecule or atom. Its magnitude is given approximately by the simple expression (IV) l2 : AV~= 8.34x ioy~/~)o-3(~~~)0.4~ (VI)t In ref. (4) this quantity (AvH)was inadvertently given as a factor of 2 greater. M. A. A. CLYNE AND L. G. PIPER 2181 where p is the reduced mass of the colliding species, and AC6 (erg cm6> is the difference between the dispersion coefficients for the upper-state perturber system and the lower- state perturber system.The small ground-state interaction was neglected, and the excited state broadening was estimated by calculating dispersion coefficients based upon the Slater-Kirkwood approximation. Since excited-state physical properties are not well known, we have had to make estimates of the excited oxygen atom polariz- abilities by the method of Slater 0rbita1s.l~ Although the accuracy of this method for excited states is expected to be low, the calculated line widths should be reasonably accurate, since AvL depends upon the polarizability only to the 0.4th power. Our calculated polarizabilities for the 3s, 4s and 5sexcited 3Soxygen atoms are 1.16x 4.82 x and 8.53 x m3 respectively. These values lead to Lorentz line widths of about 9.7 x 4.0 x and 4.3 x cm-l in the absorption cell (N 21 8 x 10l6 helium atoms ~m-~) for the 3s, 4s and 5s states respectively.In the lamp (N 21 1.4~lot7 helium atoms cnr3) the values of AvL are 1.5 x 6.7 x and 7.7 x cm-l in the same order. The results of these calculations show that although Lorentz broadening was always much less than Doppler broadening in our work, AvL and AvNbecome comparable in magnitude at helium pressures in the order of 65 000 Pa (500Torr). In fact, in flash photolysis-atomic resonance studies at J. 130.22 nm with much higher total pressures, the Lorentzian tail of the absorption coefficient curve (k,k, as a function of v) is expected to modify appreciably resonance absorption phenomena based on Doppler line models. For instance, at 1 atmos.pressure of He, AvJAvD = 1.2 for 1”130.22 nm. Stark broadening results when the local electric field near an electron or ion leads to a splitting in the energy levels of an atom with which the electron or ion is colliding. Most neutral atoms show a quadratic Stark effect, which is only of large magnitude for plasmas with high charged-particle densities. Unfortunately, the Stark effect giws line shapes which are difficult to describe analytically. But for weakly-ionized plas- mas, such as in low-power microwave discharges, one may employ the impact approxi- mation for electrons and ignore contributions from ions. The Stark broadening then gives rise to a Lorentzian whose width, Avs, is given by (VII),14 AvS = (38.8/2~)C~’/~Veil3 N, (VII) where C4 = 6.15 x times the Stark displacement (in cm-l) for a field of lo5V cm-’.The Stark displacement is 5.6 x 10’’ a,15 where Q (cm3) is the polarizability of the species of interest. N, (~m-~)is the electron density and Ye(cm s-I) is the mean electron velocity. Eqn (VII) and the polarizabilities, as estimated above, give Stark widths of 8.3 x 4.7 x and 7.0 x cm-’ for the 3s, 4s and 5s transitions, respectively. These results assumed an electron temperature of 5000 K, which is not a critical parameter, since Tenters the formula for Avs only to the one-sixth power. The electron density was taken to be 10l2~m-~,which is the maximum value expected for a low-power microwave discharge. We conclude that the estimates for Atis thus obtained are two to three orders of magnitude less than the Lorentz line widths, 4~~.In summary, the only parameter deterrning the spectral distributions of the emis- sion line and of the absorption coefficient is Doppler broadening, with a small (often negligible) contribution from Lorentz and natural broadening. DOPPLERLINE MODELS IN ABSORPTION MEASUREMENTS The determination of f-values from line absorption measurements with Doppler line models has been discussed previo~sly.’-~ We have used a computer program developed previously for this purpose.4* This program takes account of a limited contribution to the line profile from Lorentzian broadening, and includes integration KINETIC SPECTROSCOPY IN FAR VACUUM U.V. by Gaussian quadrature using the form of the Voigt profile given by Reiche.' The object of the program is to evaluate the optical depth in the absorber, koZ,as a function of fractional absorption, A, and absorber concentration, N.$values may then be directly determined from eqn (VIII), (VIII)mc koZ is a function not only of A and of N, but also of the optical depth kom in any self- reversing layer in the lamp, and in addition, of the ratio a2 of source and absorber temperatures; cc2 = TJT,. The parameters of importance in the present problem are summarized in eqn (IX) : koZ = g(A, N, konz,u>. (IX) Minor variables are B and C, equal to [J(ln 2). AvD/(Av,+ AvL)] for the absorber and emitter respectively ; these were included to account for small amounts of Lorentzian broadening.Neglect of Lorentzian broadening terms would amount to, at most, a 2 % reduction in thef-value ; they will not be discussed further. The experimental measurements were sets of values of A and N. The objective was thus first to determine the best values of the secondary parameters k,m and a, and then to compute the corresponding koZ value for each pair of A, N values [see eqn (IX)]. The two-layer model was used to calculate kom, based on final values of the oscillator strength. Since the self-reversal in the source was always minimized, k0m was always < 1, and the function of eqn (IX) was, therefore, rather insensitive to k,m. This matter is discussed more fully below. The parameter a, equal to J(T,/T,), is a more important one in determining koZ (and hence $values), and this quantity is additionally very uncertain for absorption experiments with most resonance lamps.It was practicable in our work to develop a technique for determining a,as described below. No physical significance is attached to ain this analysis, the object of which was to parameterize the frequency distribution of the source. An analogy with this approach is the common use of an equivalent Boltzmann temperature to characterize an energy distribution which may not be an equilibrium distribution. EXPERIMENTAL The apparatus for studies of atomic resonance phenomena in the far vacuum ultra- violet has been described previously.16 In outline, it consisted of a resonance lamp, an absorption cell through which known concentrations of 0 "PJatoms flowed, and a mono- chromator.The lamp was a 2.45 GHz discharge in helium, to which was added a trace of oxygen for the studies on the weaker 103.92 nm and 97.65 nm lines. Traces of residual oxygen or water in the helium left after purification with a refrigerant trap at 77 K, sufficed for the studies on the strong 130.22 nm line. The monochromator was a 1 m normal-incidence type (Hilger and Watts E760) and the grating was a Pt-overcoated replica blazed at 90nm in the first order, with 600 line mm-l and three equal, separately-ruled areas in total 96x 56 mm (Bausch and Lomb). The detector was an E.M.I. 9789Q photomultiplier cell, and a sodium salicylate phosphor, showing a mean dark count of 1.5 s-' at 290 K and at 850 V e.h.t.All solid window materials absorb strongly below 105 nm ; hence collimated hole struc- tures (Brunswick Corporation) were used to separate the lamp from the absorption cell, the absorption cell from a buffer volume, and the buffer volume from the monochromator [see fig. 1 of ref (16)]. The narrow parallel channels of the collimated hole structures restricted the diffusion of gas between the sections of the apparatus, whilst allowing 40 % transmission M. A. A. CLYNE AND L. G. PIPER 2183 of on-axis light. Off-axis light (>5" off-axis) is not transmitted, thus reducing scattered light from the lamp below detectable limits. Ground state oxygen atom concentrations were determined by using the N+ NO reactions to produce 0 'PJatoms in the presence of a large excess of N 4Satoms (from a microwave discharge in N2+Ar).With [N 4S] > 2x lo'' ~rn-~,the reaction, N+NO 4 N2+0, was >99 % complete within 10 nis under the conditions used. The concentration of 0 'PJ absorbers, N, was then simply taken to be (F,,ICF) x [MI ; where FNois the flow (mol s-') of nitric oxide added, CFis the total mass flow rate, and [MIthe total concentration in the absorp- tion cell. A small correction to N was required because there was some gas flow into the absorption cell, from the lamp and from the buffer volume. All these flows could be measured, but there remained some uncertainty regarding the appropriate total mass flow rate to be used in the absorption cell, which uncertainty we estimate to be kl3 %.A second correction was necessary, in this case, for the path length over which absorption took place. This arose because of the existence of a small dead volume in the absorption path, and once again some uncertainty, in this case about the true path length, remained. We took the path length to be the diameter of the flow tube (3.4 cm) plus one-half of the length of the side-arm (0.75 cm). The maximum error introduced was 5 18 %. It appears, from the excellent agreement with the literature of our $value for the 130.2 nm transition, that neither of these uncertainties introduced serious error, or alternatively, that the errors cancelled out. Fig. 1 shows part of the spectrum of the oxygen atom resonance lamp, between 95 and 105 nm, using FWHM resolution of 0.07 nm.As well as the very strong 3s 'S-2p4 'PPJ triplet near 130 nm, and the much weaker 4s 'S---2p4'PJ and 5s 3S-2p4 'PJ triplets, many other (some fairly intense) resonance multiplets were observed. Most of these would be feasible for $value determination, although complete spectral resolution within the 3D-3P mu1tiplets would not be practicable. 3d'D -2p' n I--I~~ I 105 100 95 nm FIG.1.-Spectrum of far-u.v. oxygen atom resonance lamp, showing 3s-2p4, 4s-2p4, 5s-2p4 and other resonance multiplets of 0. h 93 to 98 nm (300 Hz full-scale); h 98 to 105nm (lo00 Hz full-scale). RESULTS LINE REVERSAL AND THE DETERMINATION OF k,m The extent of self-reversal in the lamp, as measured by k,m, could be determined experimentally.The observed oxygen atom emission (ns3S-2p4 3P,, ,,) are triplets, 21 84 KINETIC SPECTROSCOPY IN FAR VACUUM U.V. with a single upper state emitting to a ground state consisting of three separate J sub-levels. The intensity ratio of this triplet is 5 :3 :1 for emission to J = 2, 1,O in the absence of self-reversal. Small amounts of self-reversal will reduce the intensity ratios (3Pz: 3P1:3P0),since the lowest J = 2 level possesses a much greater Boltzmann population (74 %) at 300 K than the intermediate J = 1 level (20 %) and the highest J = 0 level (6 %). Thus the fractional absorption is greatest for the J = 2 transition and least for the J = 0 transition. The computer program based on the two-layer model was used to calculate relative lamp intensities (3P2: 3P1: 3P0)as a function of kom.The results were then compared with experiments and the appropriate kom value for the J = 2 transition was deter- mined. (The procedure is similar in principle to that described by Braun and Car- rington l' and Kaufman and Parkes 2). The lamp temperature was taken to be 1000 K, in accordance with the present results for a (see below), and thef-value for the 130 nm multiplet was the mean value of table 2. The experimental intensity ratio for the 3s 3S-2p4 3PJ(130 nm) was 4.6 : 2.9 :1, which corresponded to kom = 0.15 for the 3S-3P2 line. Anticipating the results of the following sections, we found that inclusion of this amount of self-reversal in the analysis resulted in a 6 % upwards correction to the finalf-value.Because of lack of intensity, we were able to fully resolve only the triplet of the 3s 3S-2p4 3PJtransition between 130.2 and 130.6 nm. Therefore, to determine kom values for the weaker 4s-2p4 and 5s-2p4 triplets, measurements of konzfor the 3s-2p4 triplet were made. This value of komwas then multiplied by the appropriate ratio of $values to obtain k,m for the other triplets ; e.g., for the 4s-2p4 triplet, kom (103.92 nm) = kom(130.22) x (f(103.92)/f(l30.22)). For the 103.92 nm studies, higher concentrations of oxygen atoms in the lamp than for the 130.22 nm work were used, resulting in a measured 3P, : 3P1: 3P0 intensity ratio for the 3s-2p4 triplet equal to 3.5 :2.7 :1.This gave kom = 0.6 for the 130.22 iim line, and hence kom = 0.08 for the 103.92 nm line. At still higher lamp oxygen atom concentration, similar results for the 97.65 nm line, 5s-2p4, gave kom = 0.07 derived from the datum kom = 2.2 for the 103.22 nm line. The small amounts of self-reversal for the two higher energy transitions led to negligible corrections in the finalf-values for the 103.92 nm and the 97.65 nni transitions. f-VALUE FOR THE 130.22nm LINE, AND THE DETERMINATION OF cc In fig. 2, we have plotted values of kol(derived from measurements of A via compu- tation-see above), against I?, for the 130.22 nm line ; Nis equal to X[O 3PJ]. Accord-ing to eqn (VIII), this plot should be linear over the whole range of kol,if the correct choice of a has been made.As shown in fig. 2, the plot of kolagainst N is linear for a = 1.8, but not for a = 2.5 (positive curvature), nor for ct = 1.O (negative curvature). Since direct measurement of a is inappropriate, we used the linearity of kolagainst N plots to determine cc. The value of a was chosen by minimizing the quadratic term in least squares polynoinial fits of kol against N which were generated for different choices of a. Our data extended to sufficiently high kolthat a could be determined to better than 0.1. It was found unnecessary to correct the results for self-reversal in the lamp. One effect that could invalidate analysis would be significant contributions to the light signal in the presence of absorbing 0 atoms from fluorescent scattering.2 Some of the light absorbed by the 0 atoms in the absorption cell would be re-emitted in the direction of the detector, thus increasing the transmitted light signal.This re-emission n,ould have an increasingly large effect on the absorption measurements as the optical M. A. A. CLYNE AND L. G. PIPER depth is increased. The determination of A would thus be low, leading to an under- estimate of the optical depth, k,Z, in the absorption cell. The effect of fluorescent scattering is readily observed in plots of koZ against N, for data taken using a non-collimated lamp, at optical depths as low as 1.5 to 2.0.2 The collimated hole struc- tures used in our apparatus so severely restricted the fields of view from the lamp. and A A N/1OI2 atoms ~rn-~ FIG.?.-Variation of optical depth k,l with atom concentration for the 130.22nni line, showing vari-ous choices of a.N/lO'* atoms ~m-~ FIG.3.-Variation of kolwith N for the 130.22 nm line: determination off-value. (x = 1.8 1. f = 0.045k 4%. of the detector, that an insignificant number of re-emitted photons is expected at the detector. This expectation was verified directly : no resonance fluorescence cocld ever be seen under conditions similar to those of the absorption experiments. The present value. x = (1.8 f 0.I), is, therefore, likely to be free from major sysrem-atic errors. When this value of c( was used with our experimental absorption results at 3, 130.2niii (sce below), the resultiiigjlvalue was within 10 0); of most of the other KINETIC SPECTROSCOPY IN FAR VACUUM U.V.recent determinations off(see table 1). This finding adds extra weight to our method for determining c(. Fig. 3 shows a plot of kolagainst N, with a = 1.8, for the absorption experiments at 130.22 nm. The plot is a composite of six independent experiments, each including about 20 data points. Some of the scatter in the data shown (fig. 3, 4 and 5) results from slight changes in the residual 0-atom concentration present in the N atom flow before NO is added. The small positive intercepts in fig. 3 (also in fig. 4) are attributed to the residual 0 atom concentrations. The final result,f = (0.045 +0.004)(2a)t, was the mean value obtained from least mean squares fits (of koZagainst N plots) to each of the six separate experiments. VALUES FOR THE 103.92 nm AND 97.65 nm LINES Fig.4 and 5 show plots of kolagainst N, with ci( = I .8, for the absorption experi- ments at 103.92 nm and at 97.65 nm. Seven independent sets of experiments in each case were carried out. The analysis for the 4s-2p4 103.92 nm line was exactly as described for the 130.22 nm line, and the result was f = (0.0059 +0.0007)*. 34I I 'c 2.0-' T-N/10I2atoms ~m-~ FIG.4.--Variation of kol with N for the 103.92nm line: determination of $value. (a= 1.8). f = 0.0059 i-5.5 %. The scatter of the 97.65 nm, 5s-2p4 data, was considerably greater than thzt of the 130.22 nm and 103.92 nm results, as expected on account of the low count rates used (I, 21 22 Hz at 97.65 nm).In this case, the data were analyzed in two ways. First, the residual 0 atom concentration was measured using the (already calibrated) 130.22 nm absorption, and all the 0 atom concentrations in the 97.65 nm studies were cor- rected accordingly. This results in the full line through the origin shown in fig. 5. However, there appeared to be a slight deviation, marginally significant, of our data from this line at high N. Therefore, we fitted the data by a linear least squares proce- dure, to give the broken line (and finite intercept) also shown in fig. 5. This intercept, if significant, suggests that the residual N may have been slightly overestimated. t This is the statistical uncertainty. The overall uncertainty is taken to be the square root of the sum of squares of the uncertainties in I (k18 %), N (i-13 %) and in the gradient kol (20 = 8 %).Thus the overall uncertainty for the 130.22 nm $value is k 23 %.* Overall uncertainty is +25 %. M.A. A. CLYNE AND L. G. PIPER 2.0,. , I,, , , , , , . , N/10l2atoms CM-~ FIG.5.-Variation of k,l with N for the 97.65 nm line: determination off-value. (a= 1.8). &lope = 0.0016rtll %,fkol/[o]= 0.0014+5 %. However, since the error limits of the gradients of both lines (fig. 5) overlapped, we took the mean of these gradients to give the best estimate offfor the 97.65 nm line : f = (0.0015 0.0004).+ DISCUSSION The finalf-values for the 3s-2p4, 4s-2p4 and 5s-2p4 3S-3PJ transitions are sum- marized in table 3.The quoted error limits include allowance for uncertainty in mass flow rate and absorption path length (see Experimental section). They are probably unduly conservative, in view of the excellent agreement of thef-value for the 3s-2p4 transition with recent literature (table 2). The relative f-values should be reliable to TABLE3 .-COMPARISON OF $VALUES BETWEEN EXPERIMENT AND THEORY inverse cube extrapolation Kazaks Armstrong Wilson and n flexperimen t of expt. Kelley z1 a Kelle), 21 e; al.20 and Purdum 22 Nicolet 25 3 0.045 +O.OlO 0.049 0.059 0.047 0.056 0.030 0.047 4 0.0059+ 0.0015 0.0054 0.0066 0.0067 0.008 0.0063 0.0022 5 0.0015~0.005 0.0015 0.0017 0.00175 0.003 0.0029 5.8 x 6 6.4~ 6.6~ 6.8~ 0.0015 0.0017 2.2~ 7 3.2~10-4 3.2~10-4 3.3~10-4 sx 10-4 7~ 10-4 8 1.8~ 10-4 1.9~ 10-410-4 1.9~ 10-4 5~ 10-4 1.3~ 0 based on calculated transition energies ; b basdd on true transition energies.within the statistical uncertainties given above. Table 2 lists our value for the oscilla- tor strength of the 130.22nm transition, along with a comparison of nine other recently reported values for this quantity. The mean of the ten values listed is (0.048k0.004) (2a), where the mean was obtained by weighting each value by the inverse of the reported error limits. The f-value for the 130.2 nm transition is thus known to good precision. The results listed in table 2 were obtained by a number of different methods, but no one method appears to show a consistent difference from the results obtained by other methods.Transition probabilities obtained by various lifetime t Overall uncertainty is +_ 33 %. 21 88 KINETIC SPECTROSCOPY IN FAR VACUUM U.V. measurement methods have at times been regarded with a certain scepticism l8 since cascade froin longer-lived upper states sometimes masks the true lifetime of the state under study. Thus, the measured lifetime may be too long, resulting in an oscillator strength which is too small. This cascade problem evidently does not affect the more recent lifetime determinations, since they yield results consistent to within a few per cent with values obtained from other methods. In the hydrogen atom, oscillator strengths for any Rydberg series fall off as r3.19 For hydrogen-like transitions in a series, the oscillator strengths would vary with n as indicated by eqn (X),” wheref, is the oscillator strength of the transition from the state with principal quan- turn number n,fr is a constant and 6, is a quantum defect.This equation can be rearranged to give a linear relationship (XI) between the inverse cube root of the .f-value and the principal quantum number : fn-f = f;-+as, +f y%l. Our experimental data are plotted according to eqn (XI) in fig. 6. The straight line through the points is derived from least squares fit, which gave values off* = 0.0384 and 6, = 2.08. Our experimentally-determined parameters of the inverse cube law, allowed the calculation of the oscillator strengths of the higher-lying transitions in the series.Since oxygen has been the subject of several theoretical studies, an experi- mental check is provided for the calculated values offfor the principal resonance series of oxygen. 113.-11 Li %I2345670 n FIG.6.-Rydberg series oscillator strength (f)ns 3S-2p4 3P2. Variation of f-3 with principalquantum number 11. Table 3 lists our experimental $values, the values corresponding to our best-fit parameters to the inverse cube law, and those from several theoretical studies. Both Kelley 21 and Armstrong and Purdum 22 list values of a2,rather than thef-value for M. A. A. CLYNE AND L. G. PIPER the transition. The ,f-values listed in table 3 from these authors were calculated according to eqn (XIE) : 23 f= 0.333AE.S/g, (XII) where AE is the energy difference between the two states involved in the transition in Rydbergs, g is the statistical weight of the lower state, and S is the absolute line strength of the transition, which is given by s = S(L)S(M)a2.(XIII) In eqn (XIII), S(L)is the relative line strength of the particular line, S(M)is the multi- plet strength, and o2 is the term which accounts for overlap in the radial matrix elements of the two states involved in the transition. S(L) and S(M)were taken from the tables of Shore and Meiizel which are based upon L-S The results of Kelley 21 are in excellent agreement with the present results, based upon the inverse cube root extrapolation, especially if one takes the true transition energies rather than those calculated from Kelley's Hartree-Fock-Slater wave func- tions.The values of Kazaks et aL2' based upon an independent particle model, are too large. For n > 5 their values are about a factor of 2.5 larger than our own numbers. The results of Armstrong and Purdum 22 based in part upon the Coulomb approximation, are about a factor of two larger than the present results for n > 5. Wilson and Ni~olet,~' on the other hand, report values which are about a factor of 2.5 smaller than the present results. Their values are taken from a report by Armstrong, Johnston and Kelley.26 We thank S.R.C. for an equipment grant and a postdoctoral fellowship held by L. G. P. A. C. G. Mitchell and M. W. Zemansky, Rrsonatrce Radiation and Excited Atoms (Cambridge U.P., London, 1971).F. Kaufman and D. A. Parkes, Trans. Faraday Soc., 1970, 66, 1579. C.-L. Lin, D. A. Parkes and F. Kaufman, J. Chem. Plzys., 1970, 53, 3896.'P. P. Bemand and M. A. A. Clyne, J.C.S. Faraday 11, 1973, 69, 1643. 'M. A. A. Clyne and L. W. Townsend, J.C.S. Faraday 11, 1974, 70,1863. H. G. Kuhn, Atomic Spectra (Longmans, London, 2nd edn, 1969). J. Tellinghuisen and M. A. A. Clyne, J.C.S. Faraday ZZ, 1976, 72, 783. A. P. Stone, Proc. Phys. Soc. (London), 1959,74,424. H. E. White, Introductiori to Atomic Spectra (McGraw Hill, New York, 1934). lo Thef-values used for this calculation were : 0.163 for X 1.3167 pm (4s 3S-3p "J) and 0.0162 for A 725.6 nm (5s 3S-3p "J) (W. L. Wiese, M. W. Smith and B. M. Glennon, Atomic Transition Probabilities, Vol.1, NSRDS-NBS 4, 1966). Also we calculated f = 0.42 for the A 4.1054 pm (5s 3S-4p 3P~)transition from L-S coupling calculations using the Coulomb approximation and L-S coupling line and niultiplet strengths. [See ref. (23) and (24)]. l1 P. R. Berman and W. E. Lamb, Jr., Phys. Rev. A, 1969, 187, 221. l2 R. J. Hood and G. P. Reck, J. Chern. Phys., 1972, 56,4053. J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liqitids (John Wiley, New York, 1954). l4 C. W. Allen, Astrophysical Quantities (Athlone Press, London, 2nd edn, 1955). l5 E. Merzbacher, Quantum Mechanics (John Wiley, New York, 1961). l6 (a)P. P. Bemand and M. A. A. Clyne, J.C.S. Faraday 11, 1976, 72, 191 ; and (b) Chern. Pltys. Lefters, 1973, 21, 555.l7 W. Braun and T. Carrington, J. Quant. Spectr. Rad. Transfer., 1969, 9, 1133. See, for example : C. Laughlin and A. Dalgarno, Phys. Ret.. A, 1973, 8, 39, and E. H. Pinning-ton, A. E. Livingston and J. A. Kernahan, Phys. Rev. A, 1974, 9, 1004. l9 W. L. Wiese and A. W. Weiss, Phys. Rev., 1968, 175, 50. 2o P. A. Kazaks, P. S.Ganes and A. E. S. Green, Phys. Rec. A, 1972, 6, 2169. 21 P. S. Kelley, J. Quant. Spectr. Rad. Transfer, 1964, 4, 117. 22 B. H. Armstrong and K. L. Purdum, Phys. Rer., 1966, 150,51. KINETIC SPECTROSCOPY IN FAR VACUUM U.V. 23 G. K. Oertel and L. P. Shomo, Astrophys. J. Supp. Ser., 1968, 16, 175. 24 B. W. Shore and D. H. Menzel, Astrophys. J. Supp. Ser., 1965, 12, 187. 25 K. H. Wilson and W.E. Nicolet, J. Quant, Spectr. Rad. Transfer, 1967, 7, 891. 26 B. H. Armstrong, R. R. Johnston and P. S. Kelley, Lockheed Missiles Space Co. Report No. 8-04-64-2 (1964). 27 G. M. Lawrence, Phys. Rev. A, 1970,2, 397. 28 M. Gaillard and J. E. Hesser, Astrophys. J., 1968, 152, 695. 29 W. R. Ott, Phys. Rev. A, 1971, 4,245. 30 J. Martinson, H. G. Berry, W.S. Bickel and H. Oona, J. Opt. SOC.Amer., 1971, 61, 519. 31 W. H. Smith, J. Bromander, L. J. Curtis, H. G. Berry and R. Buchta, Astrophys. J, 1971, 165, 21 7. 32 T. T. Kikuchi, Appl. Optics, 1971, 10,1288. 33 D. J. G. Irwin, A. E. Livingston and J. A. Kernahan, Nucl. Instr. Methods, 1973, 110, 105. (PAPER 6/959)

ISSN:0300-9238    

DOI:10.1039/F29767202178

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Infrared Spectra and Hydrogen Bonding of Monoalkali Salts of Malonic Acid and their Dialkyl Derivatives BY (MRs.) A. A. BELHEKARAND C. I. JOSE* National Chemical Laboratory, Poona, India Receiued 24th May, 1976 Infrared spectra of monoalkali salts of malonic acid showed that the strong inter-molecular hydrogen bonding in these salts varied from an unsymmetric type in Li and Na salts to a symmetric type in the K, Rb and Cs salts. In the monopotassium salts of dialkyl malonic acids, strong sym- metric intra molecular hydrogen bonds were found in the diethyl and di n-propyl derivatives (but not in dimethyl) which inhibits the dissociation of the second carboxylic group and explains the large Kl/K2values observed in water. Recent studies on the monoalkali salts of malonic acid showed that while a sym-metrical intermolecular hydrogen bond is present in the potassium salt an un- symmetrical hydrogen bond exists in the sodium salt.2 Albertsson et aL3 recently found from detailed X-ray crystallographic investigations an unsymmetrical inter- molecular hydrogen bond in the monopotassium salt (sodium salt was isostructural) of oxydiacetic acid and a symmetrical hydrogen bond in the rubidium salt (caesium and thallium salts were isostructural).We have, therefore, extended our infrared studies to other alkali ions Li, Rb and Cs with a view to investigating the influence of ionic radius on the nature of hydrogen bonding in mono alkali salts of malonic acid. A more than hundred fold increase in the ratio of the first and second dissociation constants of malonic acid on dialkyl (other than methyl) substitution has been attri- buted to strong hydrogen bonding of the carboxylic OH and carboxylate ion from limited infrared studies4-6 in heavy water.But since aqueous system the does not favour the determination of the inter- or intramolecular nature of H-bonding, we have analysed the spectra of monoalkali salts of dimethyl, diethyl and di n-propyl malonic acids in the solid state as well as in dimethyl sulphoxide. EXPERIMENTAL The various monoalkali salts of malonic acid were prepared by standard procedures. The dimethyl malonic acid was a recrystallised Fluka product. The diethyl (m.p. 125°C) and di n-propyl (m.p. 161°C) were synthesised and crystallised from toluene and chloroform.Deuteration of the salt of dialkyl malonic acids was carried out and spectra recorded in Nujol, hexachloro butadiene mulls and in dimethyl sulphoxide as described before.2 RESULTS AND DISCUSSION The infrared spectra of solid mono- Li, Rb and Cs salts of malonic acid are com- pared with the spectrum of the sodium salt in fig. 1. It can be seen that the spectrum of the lithium salt is very similar to that of the sodium salt while the spectra of rubi- dium and caesium salts resemble one another and are comparable with that reported 2191 2192 H-BONDINGOF MALONIC ACID DERIVATIVES for the potassium salt.' The Li and Na salts are characterised by hydroxyl absorp- tions at -2750, 2500 and 1850cm-', carboxyl and carboxylate absorptions at 1750-1700and 1580-1 550 cm-I respectively with well-defined absorptions at lower frequen- cies.On the other hand, the spectra of Rb and Cs salts do not show any hydroxyl absorptions in the region 2800-1900 cm-'. A broad band at 1720 cm-l ascribable to hydroxylic and carboxylic absorptions together with ill-defined and broad absorptions below 1300cm-l are found, as in the potassium salt. The bands shown by the sodium and lithium salts are characteristic of Unsymmetrical hydrogen bond of double inini- mum potential type (Hadzi type 18) while the band pattern shown by the rubidium, caesium and potassium salts are indicative of single minimum potential type (Hadzi type 118) symmetric hydrogen bonds. In the case of the potassium salt, this has been established both by X-ray and neutron diffraction analyses.Preliminary crystallo- graphic investigation of the sodium salt showed it to be orthorhombic with space group Pbca, 2 = 8 and cell dimensions of a = 6.79k0.03 A, b = 10.30+0.02 A and c = 16.l8+0.06 A, 2 = = y = 90". The potassium salt was monoclinic with space group Czl,. I I I I I 1 3800 3500 3000 2500 2000 1500 1000 600 frequency lcm- FIG.1.-Infrared spectra of monoalkali salts of malonic acid, lithium (-----), sodium (-.-.-),rubidium (-...), caesium (-). In the case of the monoalkali salts of oxydiacetic acid,3 an increase in the symmetry of the structure, resulting in a change from an unsymmetrical to a symmetrical hydro- gen bond, has been found in going from the potassium to the rubidium salt.The monoalkali salts of malonic acid represent the second case, where the change from an unsymmetrical to a symmetrical hydrogen bond takes place in going from the sodium to potassium salt. A detailed crystallographic investigation is being undertaken to throw more light 011 the structural aspects. The infrared spectra of mono-potassium salts of dimethyl, diethyl and di n-propyl malonic acids are shown in fig. 2. The spectra of the mono-potassium salt of diethyl and di-n-propyl malonic acid are quite different from that of the monopotassium salt of dimethyl malonic acid, which resembles the spectrum of monosodium salt of malo-nic acid (fig. 1). The monopotassium salt of dimethyl malonic acid shows carboxylic and carboxylate absorptions in the Characteristic regions of 1700 and 1580 cm- and absorptions at 2500 and 1900cm-', characteristic of a hydroxyl group involved in double minimum potential type of hydrogen bonding.In the monopotassium salts of diethyl and di-n-propyl nialonic acid on the other hand, there are no bands ascribable to OH group above 1650cm-', as show-n by deuteration. There was some decrease in the intensity of bands near 1600 cm-', but the shifted band could not be located. Deuteration also showed changes in intensity of bands in the region 1000-750 cm-' and gave rise to new bands at 641 and 613 cni-l A. A. BELHEKAR AND C. I. JOSE 2193 at least with the diyropyl monopotassium salt.The absence of bands ascribable to ~~II above 1650 cm-I and thc changes in the intensities of bands near 1600 and 1000-750 on deuteration and carboxyl absorptions near 1650 cm-' are suggestive of a strong hydrogen bond of a symmetrical type.8 In order to get more information, the spectra of these two salts were recorded in dimethyl sulphoxide in the region 3700-1500 C1Ti-l. There was no difference in the band position even after 5 fold dilution (2.5 to 0.5 x,),indicating that the symmetrical hydrogen bond is unaffected in dimethyl sulphoxide and, therefore. must be intramolecular in nature. Strong support for this conclusion I 3800 3500 3000 2500 2000 1500 1000 600 frequency /cm- FIG.2.--Infrared spectra of monopotassium salts of dialkyl rnalonic acid : dimethyl ( .-..), diethyl (-----), di-n-propyl (--). was found in a p.m.r. study of the monopotassium salt of diethyl nialonic acid in dimethyl sulphoxide. The carboxylic proton showed a chemical shift of 19.50 6 with respect to tetramethyl silane which was independent of concentration in the range 3-1 % (Varian T.60). Proton resofiance shifts of 15.40, 15.03 and 15.16 6 with respect to water have been reported lo for symmetric intramolecular hydrogen bonds in potassium and sodium hydrogen maleates and potassium hydrogen phthalate respec- t ively in dimethyl sulphoxide. The symmetrical intermolecular hydrogen bond in potassium hydrogen malonate on the other hand has been found to change over to an unsymmetrical type in dimethyl sulphoxide.Thus it is clear that the dissociaticn of the second carboxylic group in dialkyl (other than dimethyl) is suppressed by its participation in a strong intramolecular hydrogen bonding with the carboxylate ion as found in the solid, and which is unperturbed in a dipolar aprotic solvent like dimethyl sulphoxide and is reflected in large K,/K, values (> 100) in water. With a view to understanding the differences in hydrogen bonding behaviour between the monoalkali salts of dimethyl malonic acid on the one hand and the diethyl and di-n-propyl inalonic acids on the other, we made their molecular models (Cour- talds). In the dimethyl derivative the two methyl groups do not interfere in the rota- tion of the carboxylic and carboxylate groups which, therefore, may form either an inter- or intra-molecular hydrogen bond.In the diethyl and other higher dialkyl derivatives, the rotation of the carboxylic and carboxylate groups is restricted and the bulky alkyl groups inade intermolecular contacts difficult. Thus intramolecular inter- action would be favoured with dialkyl substituted coinpounds larger than the methyl. S. G. Sime, J. C. Speakman and R. Parthasarathy, J. Clienr. Soe. A, 1970, 1919; IM.Curry and J. C. Speakman, J. Chem. SOC..4, 1970, 1923. A. A. Belhekar and C. 1. Jose, Ind. J. Chem., 12, 1974,997. J. Albertsson, I. Grenthe and M. Herbertsson, Acta Cryst, 1973, B29, 2751, 2539.'D. R. Lloyd and R. H. Prince, Proc. Chem. SOC.,1961,464.'D. Chapmcn, D. K.Lloyd and R. H. Prince, J. Chenr. SOC.,1964, 550. 2194 H-BONDINGOF MALONIC ACID DERIVATIVES E. S. Hanrahan, Spectrochim. Acta, 1966, 22, 1243.'M. Conrad, Ann. Chem., 1880, A204, 134. D. Hadzi, Pure Appl. Chem., 1965, 11,435. S. Y. Natu and M. C. Takwale, unpublished results. lo S. Fordn, J. Chem. Phys., 1959, 31, 852. (PAPER 6/987)

ISSN:0300-9238    

DOI:10.1039/F29767202191

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Perturbation Expansion for Onsager’s Linear Law for Wien Dissociation of a Weak Electrolyte BY DAVID P. MASONAND DOUGLASK. MCILROY* Department of Applied Mathematics, University of the Witwatersrand, Jan Smuts Ave., Johannesburg, South Africa Received 14th June, 1976 The partial differential equation governing the distribution function for oppositely charged ion pairs in a weak electrolyte in the presence of a uniform applied electric field, is separated into two ordinary differential equations. By means of a perturbation expansion in terms of the field dependent parameter &, where ,9 is proportional to the magnitude of the applied field and q is the Bjerrum association distance, these ordinary differential equations are solved to first order in pq.Using this result, the linear law for the relative increase in the dissociation constant due to the application of the external field is derived. This result agrees with Onsager’s well known closed form expression to first order in ,8q. The possibility of extending this method to terms of higher order in ,9q is discussed. Interest in the theory of Wien dissociation has been renewed lately by develop- ments in the theory of the propagation of the nervous impulse,‘-’ in the theory of the dissociation of weak electrolytes at interfaces * and in the theory of the dissociation of ion-exchange resins and soluble polyele~trolytes.~ Onsager lop developed the theory of Wien dissociation for the case of simple weak electrolytes in a uniform external electric field.He found that the relative increase in the dissociation constant Kas a function of the applied field intensity X is given by where q = -e,e2/2DkT > 0, J, is the ordinary Bessel function of order one and in a weak electrolyte whose ions have charges el, e2, diffusion coefficients kTq, mobility coefficients mi in a medium of dielectric constant D and absolute tempera- ture T; k is Boltzmann’s constant. Apparently the full derivation of eqn (1) has never been published. Furthermore, the above-inentioned applications of Wien dissociation involve modifications and extensions of Onsager’s result to, e.g., the case of non-uniform applied electric fields ’9 or to the case of ion-exchange resins and soluble polyelectrolytes where a charged ion may accept more than one counterion ; in the latter example very large Wien dissociative effects have been observed due to a large charge (-10 electron charges) on one of the ions.g The first step in establishing mathematical theories of these effects is evidently to find a conceptually simple derivation, if possible, of Onsager’s result, eqn (1).Onsager notes that the “ most remarkable feature of eqn (1) is the proportionality with the absolute value of the field ” ; the aim of this article is to try to obtain, as a 2195 2196 WIEN DISSOCIATION first step in deriving the complete result of eqn (I), the linearized version of eqn (l), riz referred to by Onsager as the "linear law ", via a perturbation expansion. Apart from its intrinsic interest: eqn (3) holds for a considerable range of Xand, in particular in the low field intensity range for all but the lowest field intensities.Further, eqn (3) has been employed, rather than the closed form (I), in some theoretical models.12 An attempt has been made by Onsager and Liu l3 to derive eqn (3) using a perturbation expansion of the ion pair distribution function, employing the field independent Bjerrum association distance q as expansion parameter. They succeed in deriving the linear law but their approach is not mathematically systematic or easy to justify physically. Our perturbation technique is different. The expansion parameter which we use is the field dependent dimensionless parameter pq which arises naturally in the partial differential equation for the distribution function when the quantities in that equation are made dimensionless.Using the technique of separation of variables, this partial differential equation is split into two ordinary differential equations which are both solved to first order in Pq using perturbation methods. This allows us to obtain the ion pair distribution function to first order in pq and so to derive eqn (3). The possible extension of this method to obtain K(X)/K(O)to orders higher than the first in Pq, is examined. MATHEMATICAL FORMULATION The partial differential equation governing the function f(r, 6) which describes the distribution of oppositely charged ion pairs separated by distance I' at angle 8 to Sin an electrolytic solution is l1 div(grad f) = (grad f) [grad(2q/r +2fir cos O)].(4) Implicit in the derivation of this equation is the assumption that Kq 4 1 (3 where IC-~ is the Debye length of the electrolytic solution. Inequality (5) impliesthat for small r the screening effect of the ionic atmospheres is negligible ; further we may clearly take the field free interaction between ion pairs to be coulombic ( = eiej/Dr)up to some I' = r' such that q < r' < li-l (6) without significant error. In spherical polar coordinates (r, 8, 4)eqn (4) becomes Derivatives with respect to 4 have beer, set equal to zero in eqn (7) due to symmetry about the electric field vector. To determine a suitable dimensionless expansion parameter, and also to simplify the notation, we make the quantities which occur in eqn (7) dimensionless and normalize the distribution function.Since the characteristic length in the problem is the Bjerrum association distance q we will work with the dimensionless variable 7 = r/q. In this work we will look only for that solution to eqn (7) which corresponds to the distribution describing undissociated ion pairs. These dissociate with rate constant K(X)A where A is the association rate constant given by A = 8n(cr>,+ cr>,)kTq (8) D. P. MASON AND D. K. MCILROY (obtained, following Onsager by considering that solution to eqn (7) which describes dissociated ion pairs). It can be shown easily that, in the absence of an applied electric field, the solution to eqn (7) satisfyingf= 0 at r = co is f = vtjK(o)(e2’?-1) (9) where vij is the number of bound ion pairs; thus we normalise the distribution function by defining f =f/v,,K(O) thereby avoiding the frequent occurrence of the constant vtjK(0)in the sequel.Eqn (7) then becomes where E = pq. To simplify the notation further we drop the bar onfand r, it being understood in the subsequent analysis that f is normalised and r is dimensionless. The parameter E,which arises naturally in eqn (lo), is dimensionless, and proportional to the magnitude of X through eqn (2). Thus it is a suitable perturbation expansion parameter. We therefore seek a solution forfin the form f =fo+Ef*++2f2+ . . * (11) We next consider the boundary conditions. Through inequalities (5) and (6) we may effectively extend r’ to infinity and thereby impose the boundary condition lim fir, 8) = 0.(12) r-co To determine the boundary condition for small r, we consider fin the region r -a where a is the mean diameter (divided by q)of the ions. Due to local equilibrium in this region (this is not strictly true if el fe, # 0, but the error in assuming equilibrium in this case is small, being of the order of that already made in neglecting the hydro- dynamic interaction of the ions 11) f must correspond to a Maxwell-Boltzmann distribution in the combined Coulomb and external field. Thus for r -a f(r,0) = B exp (~EYcos 8 +2/r) (13 where B is a constant. For the idealised case a = 0, this condition can be written as lirn e-2/r f(r, 0) = I r-0 where we have taken B = I so as to correspond to the field-free solution [eqn (9) normalised] which should be exactly satisfied in this limit.This is basically the boundary condition used by Onsager lo to derive eqn (1). On expanding both sides of eqn (14) in powers of Ewe obtain the boundary condition(s) at r = 0 to all orders : Iim e-’/“ f,= 1, (154r+O lim e-2’r fn = 0, for n I. (15b)r+O Now the net rate of entry of ion pairs into the interior of an arbitrary closed surface surrounding a central ion is, from the equation of continuity for .fi Gauss’ divergence theorem and eqn (8), given by where we have taken the arbitrary surface to be a sphere of radius r. To complete the solution and obtain K(X)/K(O)we next consider the rate at which ion pairs dissociate ; recalling that -fhas been normali3ed this is given by -K(X)Av,, = K(0)vij afdV6.#?I WIEN DISSOCIATION and so from eqn (16) which on expandingfin powers of E yields Thus the problem is to solve the partial differential eqn (1 0) for fto each order in E using the boundary condition (12) at r = KI and a boundary condition for small r such as (13) or (14) and then to calculate K(X)/K(O)to the corresponding order in E using eqn (17b).SEPARATION OF VARIABLES In its present form eqn (10) is not separable in r and 6 but becomes so if we make the transformation O f(r,e) = g(r,e) exp (EY cos e) (18) whence eqn (10)transforms to which is clearly separable in r and 8. Now for large r the asymptotic solution of eqn (10) is (from the Appendix) Nf I /rexp [E~(COS 8-l)].(20) The expansion off in powers of E will, therefore, be clearly non-uniform in r for cos 8 # 1. This evidently implies that the factor exp [~(cos 6-l)] must be removed in order to make our expansion valid for large r. Furthermore since the Maxwell-Boltzmann distribution (13), expanded in powers of E, diverges for all orders in E as r -+0 due to the factor e2/', this suggests that we should also remove the factor e2/' from the function we intend to expand. This is supported by the limit form (15) of the boundary condition for small r. Thus we set f(r, 0) = h(r,0) exp [E~(COS 1) +2/r], 8-or g(r,6) = h(r,0) exp (-~r+2/r), where h is the function we will expand in powers of E.Thus eqn (19) becomes a2 h dh d 2h ahr27+2(~-1-~~2)-+~(E-E~+ECOSe)h+-+cot 8 -= 0. ar dr a2 ae We next look for a solution to eqn (22) in the form h(r,0) = R(r)Z(B). Then we can write eqn (22) as ~r2~+~(r--1--Ei2~-+2&(1-r)RdR dr D. P. MASON AND D. K. MCILROY The left hand side of eqn (23) is a function of r only, while the right hand side is a function of 8 only. Thus each side must equal a constant, a say, so that eqn (23) splits into the ordinary differential equations d2R dRr2-+2(r-1-w2)-+(2~-22~r--x)R = 0,dr2 d7. and By setting p = cos 8, eqn. (25) can be rewritten as d2Z dZ(l-p2) 2-2p -+(2&p+a)Z = 0. d.u dP We shall solve eqn (24) and (26) to each order in E by seeking expansions of R and 2 in the form R = Ro+&R,+ .. . (27) 2 = ZO+&Z,+ . .. (28) in terms of which fis, from eqn (21), f(r,8) = exp [~(cos +&(ROZ,8-1) +2/r][RoZo +RL&) +O(c2)1 (29) ZERO ORDER We next calculate K(X)/K(O)to zero order in E. First consider eqn (26) and substitute eqn (28) for 2. Then to zero order eqn (26) is d2Zo dZ,(1 -p2) --2p-+aZ, = 0. dP2 dP We can always write u = v(v+ 1) for some real number v so that eqn (30) is Legendre’s equation ; l4 it is well known that if v is not an integer there are solutions of eqn (30) which are regular at p = + 1 and solutions which are regular at p = -1, but there are no solutions regular at both p = + I and p = -1. As we require solutions regular at both p = + 1 and p = -I, we conclude that v must be an integer.Furthermore when v is an integer, the only solutions regular at p = +_1 are the Legendre polynomials. Now the zero order solution forfmust be the same as the field-free solution eqn (9) which is independent of 8. We must therefore take v = 0, thus determining that sc = 0 and 2, = AoPo where Po, the Legendre polynomial of order zero, is I, and A. is constant. Consider next eqn (24). On setting a = 0 and substituting eqn (27) for R we obtain to zero order in E, d2Ror2 -dr2 +2(r-1) dR0 -= 0dr which on integrating twice gives Ro = Coe-2/r+Do, where Co and Do are constants. Thus by eqn (29) .fo = ZoROe2/r= Ao(Co+ Doe2Ir). WIEN DISSOCIATION Without loss of generality we can incorporate A.in Coand Do and so take AD = I. It follows from the boundary condition (12) at r = co that Do = -Coand from the boundary condition (15a) at r = 0 that Co = -1. Thus fo = e21r-1 (32) which is the same as the field-free solution as we of course require. eqn (32) into eqn (17) gives K(X)/K(O)= 1 to zero order. Substituting We conclude this section by noting that Zo= 1 and Ro = 1 -e-2/r: both of which will be required in the first order calculation. FIRST ORDER On substituting eqn (28) into eqn (26) and setting x = 0, as previously determined, we obtain the first order perturbation equation d2Zl dZ1(1-p2) --211 -+2p& = 0. (33)dP2 dP Since Zo = 1 this can be rewritten as Its solution, after two integrations, is 1 +p2, = /[+A, In-+B, 1-11 where A, and B1 are constants.For Z1 to be finite at p = f1, we require that Al = 0. Thus 2, = p+B1. Consider next eqii (24) from which by substituting for R from eqn (27) wc obtain the first order perturbation equation d2R, dR1 dR0 ).* -+2(r-1) __ = 2r2-+2(r-1)Ro.dr2 dr dr Since Ro = 1 -e-2/r this becomes We will solve this equation in two stages, first regarding it as a first order differential equation in dR,/dr whose integrating factor is clearly r2e2jr. Thus where c,is a constant. On noting that and that D. P. MASON AND D. K. MCILROY 2201 we find on integrating eqn (35) that R~ = -re-"i' +r+Cl e-2i'+D1 (36) where C1 and D1are constants. To determine these constants of integration we first consider the boundary condition at Y = 0.On expanding the exponential in eqn (29) in powers of E and using eqn (36) recalling that 2, = cos 8+B1we obtain fl = (rcos 0+cos O+B1+Dl)e2/r-rcos O-COS 8-Bl+C1. (37) This expression forf, does not satisfy eqn (13), according to whichf, should behave like 2r cos 8e2" for small Y. Also, condition (15) is not satisfied, for from eqn (37) we have lim (e-2/r fl) = cos O+Bl +D,. r+O However, if we modify the boundary requirement for small r slightly, we can determine B1 and D1.Instead of eqn (1%) we shall impose the weaker condition that where fl = J fl(r, 0) d8 is the mean value offl over the range 0 < 8 < n. This no condition will be satisfied by eqn (37) provided B1+D1 = 0. We examine this boundary condition more fully in the next section.We next consider the boundary condition at Y = co. It follows from eqn (12) and (21) that h(r, 0) must tend to zero as Y tends to infinity, at least when cos 0 = 1. By eqn (29) we see, therefore, that e2/r(RoZ1 +RIZo) must tend to zero as r tends to infinity at least when cos 8 = 1. As e2/'RoZ1 tends to zero as r tends to infinity, this in turn implies that e2IrR1 must tend to zero as r tends to infinity. On expanding the exponential in e2/'R1 in powers of l/r we see by eqn (36) that this implies that C1+ D1= -2. Since from the above B1+ D1= 0, it follows that C1-B1 = -2 and so from eqn (37) fi = cos 8(r+ I)(e2jr-1) -2. (39) The two boundary conditions imposed above give only two relations between the three constants B1, C1 and D1,from which we can obtain B1+D1 and C1-B1.This is all that we require as it is only in this combination that these constants occur in fl. Unlike fl, the functions Z1 and R1have no direct physical significance. If we want to proceed to second order where Z1 and R1will be required at an inter- mediate stage in the analysis, we can take B1 = 0 without loss of generality and so obtain C1and D1. The last step in the calculation is to use eqn (32) and (39) in eqn (17b) to obtain the first order contribution to K(X)/K(O). We find that 4 1:r$+j$fl-! -2 cos 8 fo the surface-dependent terms in eqn (40) giving zero contribution. We therefore obtain to first order in 1 which is Onsager's linear law eqn (3).WIEN DISSOCIATION DISCUSSION It should be emphasized that the expansion off in powers of E is not valid for large r, asfmust be zero at r = co but each of the functionsfl,f2, . . . are not. For exampIe,f, given for eqn (39) tends to ~(COS 8 -1) as r tends to infinity. In the above analysis we overcame this difficulty by making the transformation, eqn (21), and instead of expandingfwe expanded h which as we saw has an expansion which is valid for large Y, and is also well behaved in the limit as r tends to zero. In this work we do not requiref, for large or small r as it is used only in eqn (176) for K(X)/K(O) where we are free to choose the surface of integration, and so r. We can, therefore, use eqn (39)forf1 if we choose for convenience a sphere of radius of order of magnitude 1, and indeed we saw above that the result of the calculation was independent of r. Onsager lo emphasizes that the proper choice of boundary condition for small r is mostly a matter for conjecture and that the final result of the calculation should be rather insensitive to this choice.This observation is supported by our calculation, where we were not able to satisfy exactly the boundary condition of eqn (15). To examine more closely the behaviour of ourf, for small r, and also to gain insight into its physical significance, consider the radial flow of ion pairs from the origin. which is proportional to Expanding this in powers of E, we find that to first order Now if we use the Maxwell-Boltzmann distribution (13) expanded in powers of E we find that J:l) = 0.On the other hand, if we use the terms in eqn (32) and (39) proportional to e21r, which are the dominant terms for small r-we obtain J!l) = cos 0e2ir, which is non-ze.ro in gener21 YowevPr '= the flow of ion pairs over a small sphere surroundinl 1;'' we find that I = 2.n I: J$IJr*sin 6 db = V. This illustrates physically the difference between the two boundary conditions. In the one, the radial flow of ion pairs is zero in all directions for small r, while in the other it is only the integral of this flux, I, over a small sphere surrounding th-which is zero. If we try to extend the foregoing analysis to higher orders, u __.LlZS as eqn (26) for 2with a = 0 does not have a second order s ..liicn is finite at p = 5 1.Our perturbation technique cannot, therefore, be used to obtain higher order terms without modification. One approach which we considered was to expand the separation constant in powers of E, writing a = a, +&al-i-~~a,+ . . .. It turns out that for 2,and Z1 to be finite at p = 5 1 we require a, = al= 0 so that the results derived above remain unaltered. But we found that the equation for Z2 has a solution which is finite at p = k1 if and only if r2 = -3. With this value for a2,we were able to integrate the equation for R2and so obtainf,, but when this result was substituted into eqn (17a) we obtained the contribution 1919 E~ for the second order term in K(X)/K(O)instead of (12/9)c2 as found by Onsager." As we D.P. MASON AND D. K. MCILROY believe that Onsager's result is correct, we conclude that the necessary modification to the technique must be more fundamental. CONCLUSIONS We have given a simple derivation of the linear law for the dissociation of a weak electrolyte in an applied electric field. The method cannot, however, be used without modification to obtain terms of higher order than the first in the expansion of K(X)/K(O)in powers of pq. ' D. K. McIlroy, Math. Biosci., 1970, 7,313. D. K.McIlroy, Math. Biosci., 1970, 8, 109. D.K.McIlroy, Math. Biosci., 1970, 8, 417. D. K. McIlroy, Math. Biosci., 1970, 9, 135. D. K. McIlroy, Math. Biosci., 1975, 26, 191. D. K.McIlroy and D. P. Mason, J.C.S. Faraday 11,1976,72,590.'D. K.McIlroy and B. D. Hahn, 1976, no. 6, A. Math. Reprint series (University Witwatersrand). * G. G. Susbielles and P. Delahay, J. Phys. Chem., 1968, 72,841. U. Schodel, R.Schlogl and M. Eigen, 2.phys. Chem. (N.F.), 1958,15, 350. lo L. Onsager, Solutions of the Mathieu Equation of Period 47, Ph.D. Thesis (Yale University, 1935).L. Onsager, J. Chem. Phys., 1934, 2,599. H. S. Harned and B. B. Owen, Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 3rd edn., 1958), p. 145. l3L. Onsager and C. T. Liu, 2.phys. Chem., 1965, 228,428. l4 M. G.Smith, Introduction to the Theory of Partial Diflerenfial Equations (Van Nostrand, London, 1963, p. 204. (PAPER 6/1138) APPENDIX ASYMPTOTIC SOLUTION OF EQN (lo) FOR LARGE Y We look for a solution of eqn (19) in the form 0) = P(Y)Z(@. Then f(r, 0) = exp (E r cos 0)p(r)Z(0) where p(r) satisfies d2P dPr2 -+2(1+r) --(e2r2+a)p = 0,dr2 dr where a is the separation constant. Consider large r; the most important terms in eqn (A2)are 2d2P dP Y ---z+2r --E2r2p = 0.dr dr To remove the first derivative from eqn (A3) let p = S/r. Then eqrl (A3) becomes WIEN DISSOCIATION which can be solved immediately for S and we obtain, since p = S/r, where A and B are constants. In view of eqn (12) we must take A = 0. Thus by eqn (Al),fbehaves like 1f --exp [w(cos 8-I)]r for large r.

ISSN:0300-9238    

DOI:10.1039/F29767202195

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Molecular Rotations in the Plastic Phases of c&& and C6F12 BY ALAN J. LEADBETTER,?* A. TURNBULLAND (IN PART) P. M. SMITH Department of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS Received 22nd June, 1976 Incoherent quasi elastic neutron scattering experiments at relatively high momentum transfer have been made on the plastic crystalline phase of CsF9H3 at -295 K. These data are consistent with a rotational diffusion motion with a rotational diffusion constant Dr= 3 x 1O'O s-'. However, analysis of the intensities of the quasi elastic scattering together with results obtained earlier at lower momentum transfer and a lower temperature indicate the existence of an appreciable librational component of the total mean square vibrational displacements.This indicates that the molecules spend a significant fraction of time librating about a quasi-fixed orientation. It is concluded that the overall rotational motion is that of an itinerant librator. Preliminary coherent inelastic scattering measurements have also been made on a single crystal of C6FI2in its plastic phase at -295 K. A very low energy excitation has been observed and it is suggested that this may be associated with cooperative reorientational motions of the molecules. The fluorinated cyclohexane derivatives C6FI2, C6F11H and C6F9H3,like their parent cyclohexane, have plastic crystalline phases between about 175 K and the melting points (Y320 K). The molecular rotational motions in these materials have already been studied by neutron scattering spectroscopy and from incoherent scattering experiments on C6FgH, (and also, but less surely, for C6FI1H)it was concluded that jump reorientations of about 60" are the predominant rotational motion, at least at the lower temperatures.At the higher temperatures (-300 K) the simple jump model fitted the data less well and it was suggested that the rotational motion is here becoming more diffusional in nature. In the range of momentum transfer (hQ) previously studied the incoherent quasi-elastic scattering cross section is not very sensitive to the details of the molecular reorientation, so further ineasure- nients have been made to higher values of Q at T N 295 K in order to investigate the rotational motions more closely; further analysis has also been carried out on the previous data.Incoherent scattering experiments can only give the self correlation function for the reorientational motions ; simple geometrical considerations show that such motions must be strongly cooperative in these materials so a preliminary investigation has been made of the scattering from a single crystal of C6F1, which is almost purely coherent in nature and thus contains information about the cooperative molecular motions. EXPERIMENTAL The high Q incoherent quasi elastic scattering experiments were carried out on the triple axis spectrometer on the DIDO reactor at A.E.R.E. Hanvell. An incident energy of 16 meV was used and the experimental energy resolution was 0.9 meV (FWHM) as determined by scattering from vanadium.-f present address: Department of Chemistry, University of Exeter, Stocker Road, Exeter, EX4 4QD. 2205 MOLECULAR ROTATIONS IN THE PLASTIC PHASES The sample of C6F9H3 used for these measurements comprised 94.1 % of the 1 Ha, 4 He/2Ha isomer with 5.6 % of the 1 Ha/2Ha, 4 Ha form. It was contained in aluminium foil (0.05 mm) and was in the form of a flat powder slab of thickness such that about 10 % of the incident beam was scattered. Measurements were made at 295 K and at Q values (eelastic = 4n:sin O/A) of 1.7, 2.2, 2.7 and 3.2A-1 with data being collected in steps of 0.2 meV in the energy transfer range 3-4 meV and thereafter in steps of 1meV up to 7 meV. The triple axis experiment gives directly the double differential cross section d2a/dfidE which is converted after background subtraction to the symmetrised scattering law as follows : where k, and kl are respectively the incident and scattered wave vectors.A cylindrical single crystal of C6F12 of dimensions approximately 2.5 cm diam. x 5 cm height was grown in a silica tube by the Bridgman-Stockbarger method. It had a mosaic spread of -0.5" but the quality of the crystal deteriorated during the experiment as a result of some flow taking place in the tilted specimen. The scattering was determined by time of flight experiments using the double chopper spectrometer (4H5) on the DIDO reactor at Harwell, and the rotating crystal spectrometer (RXS) on the HERALD reactor at A.W.R.E.Aldermaston. The energy resolutions of the two spectrometers were -0.4 meV and 0.3 meV (FWHM) respectively. RESULTS AND DISCUSSION 1. C6FgH3 The scattering law data are shown in fig. 1. For C6F9H3the incoherent scattering cross section of the protons is about 3.5 times greater than the total cross section of all other nuclei combined, so we make the approximation that the observed scattering may be described by the incoherent scattering law. For a proton in a molecule which rotates about its centre of mass and undergoes vibrational (including perhaps librational) motions independently of the rotations the scattering law may be written 2* (powder sample) Sincoh(Q9 W) = e-""[skc(Q, m) +SE'(Q, where 2W = Q2(u2)/3is the Debye Waller exponent and (u2) may in general contain displacements due both to translational and rotational vibrations (librations). The first term in brackets is the quasi-elastic scattering due to the rotational motions of the molecule and the second is a convolution of the inelastic scattering due to the vibrations with the rotational scattering law.The intensity of the inelastic term is proportional to Q2 so that this term becomes very important at the higher Q values of the present experiments4 In the absence of a complete theoretical description of the scattering in the near elastic region, we attempt to separate out the quasi elastic scattering and identify this with SFncoh(Q,w) e-2w. In order to obtain an internally consistent separation the following procedure was adopted.For the lowest Q data where the inelastic background is relatively small, an empirical extrapolation was made from the wings of the quasi elastic region as shown in fig. l(a). The shape of the background was then assumed to be independent of Q and its magnitude was determined at higher Q values by scaling the low Q background to the high Q data at hco = 3.5 meV where the contribution from vibrational modes should be dominant. The results are shown in fig. I@), (c) and (d). As a check on this procedure the Q-depen- dence of the resultant quasi-elastic intensities (Ise)are compared in fig. 2 with those obtained previously at lower Q using a higher resolution spectrometer ; the two sets of data were normalised at Q = 1.7A-l.The agreement is good enough to suggest that A. J. LEADBETTER, A. TURNBULL AND P. M. SMITH the above procedure is reasonable. Since Iqe= SEcoh(Q,w) e-QZ<u2)/3 then fig. 2 gives (u2), the total mean square displacement of the average proton. Values have also been obtained from the previous experiments at other temperatures; all are shown in fig. 3. (u2) is approximately proportional to the temperature, as expected for a harmonic solid at high temperature (T 2 0,/3). A comparison of these results with values calculated from the observed frequency distribution using harmonic lattice vibration theory is of interest, and throws light on the nature of the molecular reorientations. Thus if the molecule is considered to undergo rotational motion during an average time zRand to librate about a fixed orientation during an average time zL,then if zL $ zRthis implies a jump reorientation mechanism and the existence of well-developed librational modes, so that the total mean square vibrational displacement will contain translational, librational and internal vibration components, i.e., (u2) = <U+) 4-<u:> f (uT>.(1) If on the other hand zR 9 zL this implies a rotational diffusion, since there will be strong interaction with neighbouring molecules which will prevent free rotation and there will be no well developed librational motions, so that (u2> = (U;)+<U;). For the high temperatures of this experiment then, for harmonic vibrations where and d is the distance of the proton from the molecular centre.For approximate calculations we may neglect (u;) because the internal modes are of high frequency compared with the whole-molecule vibrations and (u2) cc CO-~ for Fzw 2 kT and (u2)cc w-l for tio $ kT. Values of or2and 3have been estimated from the (amplitude weighted) frequency distribution obtained earlier, assuming first that there are no librations, when (?I-+ -34 cm-l and, secondly, that the lowest frequency modes are predominantly librational with a Debye tail of translational modes when {oL2>-*-20 cm-l and (COT>-*The resultant values of (u2) according to eqn (1) to (5) are-40 cm-l. shown in fig. 3. The very good agreement with the assumption of translational plus librational displacements must be regarded as partly fortuitous in view of the un- certainties and approximations of the calculation, but nevertheless the results certainly confirm that the molecules spend an appreciable fraction of their time librating, although it is not possible to give a quantitative value for zL/zR.Turning now to the shape of the quasi-elastic scattering law SYncoh(Q,w), this may be conveniently described in the present case using Sears’s formulation for an isotropic rotator MOLECULAR ROTATIONS IN THE PLASTIC PHASES Rw /nieV -3 0 3 I I I If II.I-1 L -6 -3 0 3 6 Q / 10 s-tLm /meV -3 0 3 1---I I LI I 1 L -6 -3 0 3 6 0/10'2 s-' FIG.1.-C6F9H3 : Scattering Law S(Q, w) on an arbitrary scale plotted against w at the following values of Q/A-' : (a)1.7 (b)2.2 (c) 2.7 (d)3.2 0Experimental data ; -.-. -inelastic background ; -_-jump rotation model with average jump angle # = ~r/3and TL = 3.7 x lo-'* s ; -rotational diffusion model with D,= 3.3 x 1O'O s-I. A. J. LEADBETTER, A. TURNBULL AND P. M. SMITH where j,(Qd) is a spherical Bessel function F,(w) = ‘se-ia*F,(t)dt and F,(t)depends on the nature of the rotational motion. We previously fitted the data at lower Q using Ivanov’s result for a jump model ~,(t)= exp [-7; ‘(1--I&] sin (I ++)42, = (21+ 1)-412 where d, is the average jump angle. A good fit to the data except at high Tand high Q was obtained using 4 = 7113. 0 I J 246810 Q2/A-2 FIG.2.-Quasi elastic intensities for present data on C6F9H3 obtained using a triple axis spectro- meter (0)compared with previous results obtained with a higher resolution time-of-flight spectro- meter (2).The intensity scale is arbitrary and the two sets of data were normalised to each other at Q = 1.7A-’.TiK FIG.3.-Mean square displacements for the average proton in C6F9H3as a function of temperature {.:uz> = <u2>/3:. The dashed line represents values calculated assuming contributions from only translational vibrations and the solid line for translational plus torsional vibrations (librations) ; eqn O)-W For continuous rotational diffusion F,(t) = exp [ -Z(Z+ l)D,t] where D,is the rotational diffusion constant D,= (4’)/6t. The experiments described here (and indeed also the earlier experiments at lower Q)are of low resolution in the sense that no experimental separation is possible of the purely elastic scattering 6(w)from the true quasi-elastic so that no direct check is possible or whether the rotation is in fact isotropic.The effect of the poor resolution is, in fact, to make the experimental curvcs approximate quite closely to the results of folding a single Lorentzian with the resolution function. 11-70 MOLECULAR ROTATIONS IN THE PLASTIC PHASES Calculations have been made for both of the above models using parameters (7, and D,)which give good fits to the low Qdata and the results are shown in fig. 1. These model cakulations are also summarised in a different way, together with all the data for 295 K, in fig.4. In this figure are compared the effective widths of experimental and model scattering laws obtained as the width of the single Lorentzian function which, when folded with the experimental resolution function, gives the best fit both to the data and also to the model scattering law folded with the resolution function. These comparisons show clearly that the rotational diffusion model gives a better description of this new high-temperature, high-Q data than the jump model. The Debye-Waller calculations discussed above show, however, that the molecules also spend a significant fraction of their time librating in a fixed orientation. The present low resolution data do not permit accurate determination of zL/zRbut higher resolution experiments should make this possible or, alternatively, reveal the in- adequacy of the simple models discussed here.It does, however, seem likely that the overall rotational motions of the C6F9H3 molecules are describable as those of an itinerant librator and regardless of the detailed nature of the rotational motions we may characterise them by a time z for rotation through an angle of 71/3 using z = (7~/3)~/6D,,with 0,= 3.3 x 1O1O s-I giving z = 5.5 x 10-l2 s which may be compared with zL = 3.7 x s for the residence time between jumps for the n/3jump model. 1 3 Q1A-l FIG.4.-Effective half-widths of the quasi elastic scattering law for CsF9H3 plotted against Q. 0,present triple axis results (cf. fig. 1); 0, previous time of flight data ;---jump model with C$ = 7~/3and 7~ = 3.7 x lo-'' s ; -rotational diffusion model with D,= 3.3 x 1O1Os-l.2*CtiF12 The results of the measurements on single crystals of C6F12at TN 295 K are shown in fig. 5. The scattering shows peaks or shoulders in the near elastic region which vary in position with Q. The energy of these features is plotted against reduced wave vector 4 (4 = lQ-27~21,where 7 is a reciprocal lattice vector) in fig. 6. The inelastic features were only observed when 4was approximately in a 550 direction. The ~(q)relation for the excitations appears to resemble that for a typical acoustic phonon branch of the spectrum. However the implied sound velocity of 0.24 km s-1 is nearly an order of magnitude smaller than expected by comparison with other A.J. LEADBETTER, A. TURNBULL AND P. M. SMITH 221 1 molecular crystals. Furthermore, the frequency distributions determined for C6F12, C6FIlH and C6F9H3 from polycrystal specimens shows a first strong peak at o 2 30 cm-l compared with a zone boundary frequency of the observed excitations of -lOcm-l, and in any case these modes near 30cm-l have been assigned as librations. We speculate, therefore, that what has been observed here are propagating .. .'.*. * :. -I 11-3 45 1.5 0 -065 -14 I b ,*.. ......s:*... "*... , ..,urn. 5 0 -2.5 tiw /meV (b) FIG.5.-Time-of-flight spectra for a single crystal of CsFlz at different scattering angles. (a)Double chopper spectrometer (4H5) ; (b) Rotating crystal spectrometer.The arrows indicate estimated positions of Q-dependent peaks and shoulders. (1 meV = 8 cm-'). MOLECULAR ROTATIONS IN THE PLASTIC PHASES reorientational excitations. The fact that they are observed only in the 5CS direction supports this interpretation because the molecules are much less closely packed in this plane than in the other high symmetry planes COO and (tt, and hence should a&' FIG.6.--w(4) relationship for low energy excitations observed in C6F12.I,double chopper spectro-meter ; 0,rotating crystal spectrometer. find rotation easier in this direction. Much more work must be done with higher resolution instruments on this and related systems before a better understanding of the cooperative rotations in plastic phases can be achieved, and we are undertaking such a programme of work.We thank the S.R.C. for financial support and members of the University Support Groups at A.E.R.E. and A.W.R.E. for inuch willing help. A.T. acknowledges financial support from the Carnegie Trust and P. M. S. from the S.R.C. We thank I.S.C. Chemicals Ltd. for donation of the samples. A. J. Leadbetter, D. Litchinsky and A. Turnbull, Neutron Inelastic Scattering (I.A.E.A. Vienna, 1972) p. 231. T. Springer, Springer Tracts in ModernPhysics (Springer-Verlag, Berlin-New York, 1972),vol. 64. P. A. Egelstaff, J. Chem. Phys., 1970, 53, 2590. C. G. Windsor, Chemical Applications of Neutrort Scattering ed. €3. T. M. Willis (O.U.P. London, 1974), chap. 1. E. N. Ivanov, Soviet Phys. JETP, 1963,18, 1041.'V. F. Sears, Canad. J. Phys., 1966,44, 1299. (PAPER 611205)

ISSN:0300-9238    

DOI:10.1039/F29767202205

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Generalized Treatment of Alkanes Part 5.-Branching and Buttressing Effects R. SOMAYAJULU~BY GOLLAKOTA AND BRUNOJ. ZWOLINSKI* Thermodynamics Research Center, Texas Engineering Experiment Station, Texas A&M University, College Station, Texas 77843, U.S.A. Received 19th May, 1975 The generalized treatment of the alkanes proposed by the authors has been further refined to include corrections for the buttressing and branching effects. In addition, the increments in both the zero point energies and the enthalpy of the reactants are shown to be additive. Several specialized schemes for the estimation of the enthalpies of formation of alkanes have been developed recently.' Scott has modified one of these procedures by introducing additional corrections for the effect of buttressing and for the presence of conformers other than the ground state conformation at 298.15 K.Furthermore, according to Scott, the molar zero point energy of formation, AEzp, and the change in enthalpy of reactants, A(Hig8 -HE) 3cV~(H;g8-H$)B, should not be additive in B the same kind of structural features on which the enthalpy of formation in the vibrationless ground state, AH,"'(O), depends. According to C~ttrell,~ the zero point .energy and A(Hi98 -Hi) are approximately additive and their nonremoval from AHa (heat of atomization) does not complicate the correlation of chemical binding energies with structure. We may likewise expect the zero point energy of formation and A(Hig8-Hg) to be additive. We therefore examined critically the procedure developed by Scott to see whether any evidence has been adduced to make it worth- while to depart from the normal practice of partitioning of the enthalpies of formation without the removal of the zero point energy of formation and the A(Hi98 -HE).The enthalpy of formation at 298.15 K is normally assumed to be AH,"(298.15K) = AH,"'(O)+AE,,+A(H;98 -Hg). Scott, on the other hand, proposes 298.15 AHF(298.15 K) = AH,"'(O)+AEzp+lo AC,.' dT+HCO,f (2) .in which AC;' applies to the formation of alkane in the ground state conformation, and Hconfis the conformational enthalpy at 298.15 K. Based on the steric terms that are involved in the branched alkanes, one can make a reasonable estimate of lIconf, but it is difficult to evaluate the first three terms of eqn (2).Scott tried to circumvent this difficulty by rearranging eqn (2) as follows : AHF(298.15 K) = AH, +AH2 +Hconf (3) 'in which AHl represents the enthalpy of formation in the vibrationless ground slate plus the additive portions of the second and third term of eqn (2), while AH2 t present address : 1-8-217/2 Prendergast Road, Secunderabad, India, 5oooO3 2213 2214 GENERALIZED TREATMENT OF ALKANES represents the nonadditive portions of the second and third terms of eqn (2). The calculation of AH1 and AH2 being difficult, Scott made the assumption that AH2 = O.O443[3C,"(400K) -5C,"(300K)] kcal K cal-I. (4) According to Scott, AH1 is the only term that can be correlated with molecular structure and the other two terms are nonadditive.To test the validity of the above assumptions, we have first determined a set of parameters which are necessary for the correlation of the enthalpies of formation at 298.15 K and tested whether the same set of parameters can be used for the correlation of AH2 and Hconf. Our results have indicated that both AH2 and Hconfare additive to a high degree of accuracy on the same kind of structural features on which the enthalpy of formation at 298.15 K depends. This leads us to the inevitable conclusion that nonremoval of AH2 and Hconffrom AH," (298.15 K) does not affect the correlation of the enthalpy of formation at 298.15 K. Furthermore, Scott has not provided any evidence to show that the zero point energy of formation and the A(Hig8-Hg) are nonadditive.DEVELOPMENT OF A NEW GENERALIZED EQUATION To develop a new equation for the correlation of the enthalpies of formation, enthalpies of vaporization, etc. of the alkanes we select the following generalized equation ignoring the Wsccsand elkl terms from the generalized eqn (2A) developed in Part 2 : AH," = Woao+ WlUl+ W2a2+ W3a3+ W4a4+ Ylpl+n23y23+n24y24+n33y33+ n34~34+n44~44+Q2k2+ Q3k3 (5) where Wo = 2n+2 = the number of C-H bonds, W1= n-1 = the number of C-C bonds, W2 = n2+3n3+6n4 = the number of C-C-C angles, W3 = n22+ h23 +3n2, +4n33 +6n34+9n44 = the number of C-C-C-C structural features, and W4 = 72222 +n2j2 +n242 +2n2,, +2n2,, +2n243 +3n2,,+ 3n234+ 3~1244f 4n323+%33 +4n343+6n423+6n433 +6n443 +9n424+9n434f9n444 = the number of C-C-C-C-C structural features (expressed as a function of the numbers nijk's of certain C-C-C angles) ; and where Y1= n3+4n4 = the number of nonbonded CCC trios or the CCC-C triatoms and n23 = the number of C2-C3 bonds, n24 = the number of C2-C4 bonds, n33 = the number of C3-C3 bonds, n34 = the number of C3-C4 bonds, n44 = the number of C4-C4 bonds; and where Q2 = the number of carbon atoms with five carbon atoms as second neighbours and constituting one 1,5 H .. . H interaction, Q3 = the number of carbon atoms with six carbon atoms as second neighbours and constituting two 1,5 H .. . H interactions, and the coefficients a,, a,, a2, a3, a,, pl, 723, 724, y33, y34, y44, k2 and k3 are the contributions of the respective structural features.Using the terminology of the generalized treatment, Scott's eqn (22) of ref. (2) for the correlation of the enthalpy of formation at 298.15 K may be written as follows : AHt(298.15 K) = Woao+ Wla1+ W2a2+ YlPl+n23~23+~~24~24+n33~33+ n34~34+n44~44+Q2k2 + Q3k3 +Q33k33+ Q34k34 f Q44k44 + AH2 +Hconf. (6) The correspondence between the generalized eqn (5) and Scott's eqn (22)is as f'ollows : NO = HCH; = HCC;a2 = &cC; = HTrie;y23 = a; y24 = 2afc; y33 = H33; yS4 = H34; y44 = H44; k2 = b; and k3 = 2b+H4., G.R. SOMAYAJULU AND B. J. ZWOLINSKI The three terms Q33k33, Q34k34, and Q44k44found in eqn (6) appear to be valuable in accounting for the effect of overcrowding in some highly branched alkanes.Such overcrowding occurs whenever the following CCC angles are present : C2C3C3; c2c3c4; c2c4c3; c2c4c4 ; c3c3c3; c3c3c4; c3c4c3; c4c3c4; c3c4c4,and C4C4C4. The overcrowding effect also called the buttressing effect was previously corrected by us by means of only one term elkl. For the purpose of our new generalized equation we accept the above three buttressing terms. The buttressing terms associated with each of the above ten CCC angles are shown in table 1. TABLE1.-SUMMARY OF THE BUTTRESSING TERMS CiCjC, buttressing terms The numbers Q33, Q34, and Q44 may be calculated using the following relation- ships : Q33 = n233 +4n333 +311334 Q34 = n234fn243+2n334+3n344+4n343+6f1434 Q44 = n244 +2n344 +6n444 where the nijk's represent the numbers of the corresponding cicjck angles in the branched alkanes.These numbers may also be calculated using the structural analysis indicated by Scott. We have found that AH, and Hconfof eqn (6) are represented adequately by means of the following equations with the stipulation that the coefficients in each case correspond to the property under consideration : AH2 = WOaO + Wlal+ W2a2 + w3u3 + w4x4 + ylpl + n23y23 + n24y24 + n33y33 + n34~34+n44~44+ Q2k2 -I-Q3k3 + Q33k33 -I-Q34k34 + Q44k44. (7) Hconf = W3%+ w4x4+n23y23 +n24y24+n33y33 +n34Y34+n44Y44+ Q2k2 + Q3k3+ Q33k33 + Q34k34 + Q44k44-(8) We may therefore estimate AHf"(298.15K) directly without sacrificing any accuracy by means of the following equation containing 16 parameters : AHf"(298.15K) = Woao+ Wlul+ W2a2+ W3u3+ W4x4+ YlP1+n,3y,3+ n24~24+n33~33+n34~34+n44~44+Q2k2 i-Q3k3 + Q33k33 + Q34k34 -F Q44k44-(9) Eqn (9) contains the same number of parameters as does Scott's eqn (6) for the correlation of AHf"(298.15K) and for all practical purposes yields more or less the same results.Further modification of eqn (9) has been found necessary for comparison with a study of the carbon-13 nuclear magnetic resonance chemical shifts in iilkane~.~ This GENERALIZED TREATMENT OF ALKANES study has revealed that the sum of the carbon-13 chemical shifts of all the carbon atoms in a given alkane molecule, hereafter called the molecular shift, behaves in general in much the same way as the enthalpy of formation and depends to a large extent on the same kind of structural and nteric factors that influence the enthalpy of formation.A more accurate representation of the molecular shift requires, in addition to the parameters present in eqn (9), the following : (1) a corrective term k, for each of the side branches higher than the methyl; (2) a corrective term 634 For each of the C4-C-C--C structural features in the molecule ; and (3) a corrective term 844 for each of the C4-C-C-C-C structural features in the molecule. Tests have shown that these additional terms are quite important even in the treatment of the enthalpy of formation. Our final equation for the enthalpy of formation therefore is AH,"(298.15 K) = Woao+ WiaI + W242 + W333 + W4~4+ W34S34 + W44844 + YIPI+n23y23 +n24y24+u33733 +7134Y34+n443'44+ QO~O+ Q2k2 + Q3k3+ Q33k33 + Q34k34+ Q44k44 (10) in which Qo = the number of side branches other than the methyl branch and W34 = the number of C4-C-C-C structural units in the molecule IV4, = the number of C4-C-C-C-C structural units in the molecule.Eqn (10) contains 19 parameters and it is the most accurate of all the equations for the correlation of the enthalpy of formation of the alkanes. Similar equations may be written for the other properties of the alkanes. RESULTS AND DISCUSSION The enthalpies of formation at 298.15 K are available for 84 alkanes (five gaseous alkanes, 76 liquid alkanes, and three solid alkanes). For 48 of these alkanes they agree with the selections of Cox and Pil~her.~ For the first five members through C4, they are taken from the recent flame-calorimetric work of Pittam and Pilcher.6 For three isomeric pentanes, two isomeric octanes, and 11 isomeric nonanes the values of Good 7-9were used.For one nonane, three isomeric decanes, one undecane, two isomeric dodecanes, and one isomeric hexadecane the values of Desai were used. For 2,2,3,3,5,5,6-heptamethylheptanethe value quoted by Seifer, Smolenskii, and Kocharova was used. For three alkanes (2,3-dimethylpeiitane, 3,3-dimethyl- pentane, and 3,4-dimethylhexane) the values were adjusted to agree with the enthalpies of isomerization quoted in ref. (2). For n-undecane and n-dodecene our selected values agree with the selections of the API Research Project &.I2 For n-hexadecane our selected value is an average of two experimental values quoted in ref.(5). The enthalpies of vaporizatioii are available for 48 alkanes (45 liquid alkanes and three solid alkanes). The values for 42 of these alkanes were taken from the AH44 tables.12 The values for three isomeric nonanes are from the ERDA Energy Research Center. The values for n-dodecane, n-hexadecane, and n-octadecane are from Morawetz.14 For the three solid alkanes (2,2,3,3-tetramethylbutane, n-octadecane, and n-dotriacontane) the auxiliary information concerning their enthalpies of fusion was taken from the ref. (5) and (12). For the determination of all the parameters of eqn (1 1) using the multiple linear regression, we also needed the enthalpies of vaporiza- tion of methane, 2,2,3,34etramethylpentane, and 2,2,4,4-tetramethylpentane which are key compounds for the determination of the parameters a,, k44,and k3,respectively. Methane with a critical temperature of 190.55 K remains a gas at 298.15 K, no matter what the applied pressure may be, and has been treated as a hypothetical fluid with G.R. SOMAYAJULU AND B. J. ZWOLINKSI 2217 zero enthalpy of vaporization at 298.15 K for the purpose of this study.* For 2,2,3,3-tetramethylpentane the enthalpy of vaporization assumed by us is the same as that employed by For 2,2,4,4-tetramethylpentane, however, our selected value for its enthalpy of vaporization is based on several past correlations referred to in Part 2 and differed from that assumed by Scott, and Cox and Pilcher by 0.1 kcal mol-l.This, therefore, constitutes a minor difference between the two methods in the predicted values for compounds requiring the parameter k3. Multiple linear regression was employed to determine two equations, one for the enthalpy of formation of the liquid alkanes (84 alkanes) and another for the enthalpy of vaporization of liquid alkanes (5 1 alkanes). While generating these expressions eight lower members with low experimental uncertainty were given the weight 2 in the regressional analysis. For obtaining more meaningful equations for the prediction +ofproperties in the high molecular weight range, we used the data for 15 high molecular weight alkanes with higher experimental uncertainty. These molecules were also allowed to participate in the regressional analysis but with a weight of 0.5.All other alkanes with reasonable experimental uncertainty were given uniformly a weight of 1. The equation for the enthalpy of formation of gaseous alkanes is obtained by combining the above equations for the enthalpy of formation of the liquid alkanes and the enthalpy of vaporization of liquid alkanes. TABLE2.-vALUES OF THE PARAMETERS AT 298.15 K AHf(liquid)/ AH,/ 3.Hl"(gas)l AH21 Hconll C;/ccal parameter kcal mol-1 kcal mol-1 kcal mol-1 kcal moI-1 kcal mol-1 K-1 mol-1 2u0-0!1 -13.1835 -2.3720 -15.5555 -0.481 5 4.4857 2ao+a, -4.61 57 2.3720 -2.2437 -0.1164 4.0436 a2 -2.0043 -0.8484 -2.8527 -0.1353 1.3358 Q3 0.4691 -0.2367 0.2324 -0.0090 0.2180 -0.3048 0.0274 -0.1031 -0.0757 -0.01 97 -0.0110 0.3503 0.6807 0.2310 0.91 17 0.1026 -0.9878 d34 0.0216 0.1217 0.1433 -0.0378 0.001 1 -0.21 65 844 -0.0165 -0.0696 -0.0861 0.0472 -0.0529 -0.3345 0.0432 0.2301 0.2733 0.0556 -0.3284 -0.0833723 0.1567 0.5233 0.6800 0.0549 -0.6402 0.6914724 0.6501 0.7363 1.3864 0.1750 -0.8250 -0.2350Y33 1.1238 1.3373 2.461 1 0.1126 -1.2778 0.7177Y34 2.1332 2.2684 4.401 6 0.0775 -1.9624 2.5224Y44 k0 0.0535 0.0619 0.1154 -0.1298 0.1811 0.2077 k2 1.8871 -0.0838 1.8033 0.1297 -0.0819 -1.1561 k3 4.6911 -0.2039 4.4872 0.1796 0.0647 -0.4580 k33 0.01 74 0.0529 0.0703 -0.0203 0.01 18 0.1028 k34 0.0793 0.0866 0.1659 0.08 19 0.0055 0.2452 k44 0.9300 0.2808 1.2108 0.0592 0.1880 0.1171 average devn.k0.2075 +0.0259 0.2105 k0.0346 &0.04oO f0.3021 standard devn. -+0.3829 0.0540 k0.3865 k0.055 1 f0.0632 f 0.4788 Values of the parameters determined by multiple linear regression for the calcula- tion of several properties, uiz., standard enthalpy of formation, standard enthalpy of vaporization, conformational enthalpy, AH2, and ideal gas heat capacity of the alkanes at 298.15 K are given in table 2. In table 3 are given the values of the four * Strictly speaking, methane is outside the correlation procedure. However, including the ideal gas value for methane proved necessary to avoid disparity in the linear regrcssion of the standard enthalpies in the liquid and in the ideal gaseous state at 298.15 K. 2218 GENERALIZED TREATMENT OF ALKANES fundamental parameters according to the triatomic additivity, group additivity, bond additivity, and the special additivity of the Allen-Skinner type.The values estimated on the basis of the parameters given in table 2 are compared with experimental values in table 4. The word "experimental " has to be qualified with respect to the confor- mational enthalpies and heat capacities since the values used for comparison in table 4 are those calculated by Scott.2 The variables of eqn (10) for alkanes are recorded in table 5. TABLE3.-vALUES OF THE FUNDAMENTAL PARAMETERS a AHF(liq., 298.15 K)/ AHt(298.15 K)/ AH,O(gas; 298.15 K)/ parameter kcal mol-1 kcal mol-1 kcal mol-1 a0 -4.449s 0.0000 -4.4498 a1 4.2839 2.3720 6.6559 -2.0043 -0.8484 -2.8527QZ P1 0.6807 0.2310 0.9 107 6111 -4.4498 o.ooO0 -4.4498 Q112 -2.2525 0.3953 -1.8602 6122 -1.0575 0.3665 -0.6910 0222 -0.1928 0.1444 -0.0484 B -0.3856 0.2888 -0.0968 B1 -3.6715 0.3472 -3.3243 Bz -3.1 172 0.6174 -2.4998 B3 -2.7869 0.8107 -1.9762 GI -11.2073 1.1859 -10.0214 G2 -6.6200 1,5236 -5.0964 G3 -3.3653 1.2439 -2.1214 G4 -0.7712 0.5776 -0.1936 --CH,-incremen t -6.1235 1.1838 -4.9397 for n > 5 a The parameters have been defined in part 3 as well as in the adjoining communication.Internal consistency for interrelated properties determines the number of significant figures quoted above. But for a few compounds the calculated enthalpies of formation agree with the experimental enthalpies of formation within the assigned experimental uncertainty.The compounds for which the deviations are large are usually compounds with large experimental uncertainties and such compounds have been given a weight of 0.5 in the regressional analysis. The calculated values of AH; differed from the experi- mental values by slightly more than the experimental uncertainty in the case of the following compounds for which a weight of 1 was given: 2,3-dimethylbutane, 2,2-dimethylbutane, 2-ethyl-3-methylpentane, 3-ethyl-3-methylpentane, 2,3,3-tri-methylpsntane, 3,3-diethylpentane, and 2,2,3,4-tetramethylpentane. Some of these compounds were excluded from regressional analysis by Scott. By allowing several of these compounds to participate in the regression, we feel we have obtained a better correlation procedure for the calculation of the enthalpies of formation of the alkanes.The predicted enthalpies of formation also yielded satisfactory enthalpies of isomeriza- tion in agreement with the equilibrium data as shown in table 6. The calculated conformational enthalpies compare favourably with the values calculated by Scott. The comparison between the heat capacity values calculated by Scott and those estimated by us is also satisfactory as is our procedure for the estimation of AH2. In view of the above results we feel that our correlation is a good prediction of the enthalpies of formation of the alkanes. Our correlation for the enthalpies of vaporization yielded better results than previously. TABLE4.-cOMPARISON OF EXPERIMENTAL AND ESTIMATED VALUES AHi(liq., 298.15 K)/kcal mol-1 AH,(liq., 298.15 K)/kcal mol-1 Hpnnp/kcalmol-1__...compound a 0bs.b est. devn. 0bs.C est. devn. calc.4 est. devn. ca1c.e est. devn. 1 -17.80+0.10f -17.80 0.00 0.000 0 0.000 0.000 0.00 0.00 0.00 8.53 8.53 0.00 2 -22.30+0.07f -22.41 0.1 1 2.264 2.3 72 -0.108 0.00 0.00 0.00 12.57 12.57 0.00 3 -28.99 f0.12f -29.03 0.04 3.965 3.896 0.069 0.00 0.00 0.00 17.44 17.95 -0.51 4 -35.22f 0.16f -35.19 -0.03 5.191 5.183 0.008 0.25 0.22 0.03 23.30 23.03 0.27 2m3 -36.87 & 0.15 f -36.98 0.1 1 4.799 4.802 -0.003 0.00 0.00 0.00 23.13 23.68 -0.55 5 -41.48 f0.14 h -41.31 -0.17 6.395 6.366 0.029 0.45 0.43 0.02 211.69 28.45 0.24 2m4 -42.76k0.14 h -42.62 -0.14 6.030 6.082 -0.052 0.09 0.1 1 -0.02 28.41 28.37 0.04 22mm3 -45.49k0.15 h -45.57 0.08 5.345 5.322 0.023 0.00 0.00 0.00 28.89 28.77 0.12 6 -47.45k0.18 -47.43 -0.02 7.555 7.550 0.005 0.66 0.63 0.03 34.08 33.88 0.20 2m5 -48.91 f0.24 -48.71 -0.20 7.160 7.163 -0.003 0.25 0.30 -0.05 33.99 34.14 -0.15 3m5 -48.37 f0.24 -48.23 -0.14 7.255 7.260 -0.005 0.23 0.20 0.03 33.49 33.40 0.09 22mm4 -5 1.10 f0.24 -50.62 -0.48 6.651 6.659 -0.008 0.00 0.01 t -0.01 33.81 33.92 -0.11 23mm4 -49.58 & 0.24 -49.02 -0.56 6.985 7.021 -0.036 0.00 0.05 t -0.05 33.32 33.33 -0.01 7 -53.59 & 0.22 -53.56 -0.03 8.739 8.734 0.005 0.86 0.84 0.02 39.48 39.30 0.18 2m6 -54.86 f0.27 -54.84 -0.02 8.325 8.347 -0.022 0.47 0.51 -0.04 39.32 39.57 -0.25 3m6 -54.12 k 0.46 -54.32 0.20 8.391 8.340 0.051 0.39 0.40 -0.01 39.10 39.1 8 -0.08 3e5 -53.67 k0.33 -53.76 0.09 8.425 8.396 0.029 0.53 0.47 0.06 39.67 39.00 0.67 22mm5 -56.95 k0.37 -56.67 -0.28 7.764 7.758 0.006 0.09 0.20 -0.11 39.84 39.83 0.01 23mm5 -54.47 0.30 i -54.58 0.1 1 8.191 8.148 0.043 0.11 0.14 -0.03 38.44 38.82 -0.38 24mm5 -56.07+0.29 -56.09 0.02 7.872 7.856 0.016 0.17 0.17 0.00 40.81 40.18 0.63 33min5 -55.5820.30 i -55.65 0.07 7.901 7.892 0.009 0.03 0.02 0.01 39.62 39.43 0.19 223mmm4 -56.53 f0.33 -56.19 -0.34 7.669 7.669 0.000 0.00 0.03 -0.03 39.02 38.76 0.26 8 -59.82f0.42i -59.68 -0.14 9.915 9.918 -0.003 1.07 1.05 0.02 44.88 44.73 0.15 2m7 -60.95f0.36 -60.96 0.01 9.484 9.531 -0.047 0.67 0.72 -0.05 44.75 44.99 -0.24 3m7 -60.31 k0.33 -60.45 0.14 9.521 9.524 -0.003 0.60 0.61 -0.01 44.41 44.60 -0.19 4m7 -60.14 k0.33 -60.42 0.28 9.483 9.421 0.062 0.55 0.60 -0.05 44.70 44.95 -0.25 3e6 -59.84 f0.32 -59.85 0.01 9.476 9.476 0.000 0.69 0.67 0.02 45.32 44.77 0.55 221~11116 -62.59 1-0.32 -62.81 0.22 8.915 8.872 0.043 0.32 0.35 -0.03 45.00 44.92 0.08 23min6 -60.37 f0.40 -60.68 0.31 9.272 9.229 0.043 0.28 0.34 -0.06 44.00 44.60 -0.60 24mm6 -61.43 5 0.33 -61.70 0.27 9.029 9.034 -0.005 0.31 0.27 0.04 45.96 45.22 0.74 25mm6 -62.23 20.40 -62.24 0.01 9.051 9.143 -0.092 0.27 0.39 -0.12 44.33 45.26 -0.93 33mm6 -61.55 50.32 -61.70 0.15 8.973 8.992 -0.019 0.12 0.20 -0.08 45.62 45.34 0.28 34mm6 -59.91f0.40 i -60.15 0.24 9.316 9.275 0.041 0.21 0.24 -0.03 43.58 44.31 -0.73 23me5 -59.65 0.35 -60.07 0.42 9.209 9.234 -0.025 0.51 0.41 0.10 45.90 44.87 1.03 33me5 -60.43& 0.35 --60.60 0.17 9.081 9.085 -0.004 0.12 0.19 -0.07 44.93 45.49 -0.56 223mmm5 -61.40 & 0.40 -61.65 0.25 8.826 8.848 -0.022 0.13 0.11 0.02 44.37 44.53 -0.16 TABLE4.-contd.mol-1 Ci/cal K-1 mol-1hH",(liq., 298.15 K)/kcal mol-1 AHG(liq., 298.15 K)/kcal mol-1 HCoM/kcal compounda 0bs.b est. devn. 0bs.C est. devn. ca1c.d est. devn. talc.= est. devn. 224mmm5 -61.9440.37 -62.11 0.17 8.402 8.386 0.01 6 0.02 -0.02 t 0.04 45.03 44.85 0.18 233mmm5 -60.59 4 0.38 -61.11 0.52 8.897 8.886 0.011 0.07 0.03 0.04 44.70 44.86 -0.16 234mmm5 -60.954 0.43 -60.87 -0.08 9.014 9.040 -0.026 0.25 0.10 0.15 45.79 44.80 0.99 2233mmmm4 -62.3620.28i -62.36 0.00 8.410 k 8.410 O.OO0 0.00 0.00 0.00 44.74 44.74 0.00 9 -65.6420.24 1 -65.80 0.16 11.101 11.102 -0.001 1.27 1.25 0.02 50.29 50.15 0.14 4m8 -66.82 k0.21 m -66.54 -0.28 10.605 0.08 50.02 50.38 -0.36 22mm7 -68.88 20.24 -68.93 0.05 10.056 0.52 0.56 -0.04 50.49 50.3 5 0.14 223mmm6 -67.57 20.22 I -67.76 0.19 9.871 n 9.859 0.01 2 0.31 0.25 0.06 49.87 49.97 -0.10 224mmm6 -67.6020.24 -67.74 0.14 9.478 " 9.494 -0.016 0.14 0.02 0.12 50.06 49.55 0.51 225mmm6 -70.11 20.241 -70.23 0.12 9.580 n 9.599 -0.01 9 0.13 0.18 -0.05 49.68 50.28 -0.60 233mmm6 -67.18 & 0.24 I -67.16 -0.02 9.986 0.16 0.21 -0.05 50.68 50.77 -0.09 235mmm6 -67.88 & 0.24 1 -68.05 0.17 9.910 9.923 0.19 0.21 -0.02 50.49 50.64 -0.15 244mmm6 -66.974 0.22 -67.14 0.17 9.620 0.04 -0.02 t 0.06 50.74 50.36 0.38 334mmm6 -66.33 f0.22 I -66.57 0.24 10.066 0.20 0.1I 0.09 50.00 50.63 -0.63 33ee5 -65.82 4 0.41 -65.52 -0.30 10.174 0.41 0.35 0.06 51 .80 51.91 -0.11 223mme5 -65.18 4 0.22 1 -65.13 -0.05 9.903 0.16 0.28 -0.12 48.71 49.70 -0.99 234mem5 -64.47& 0.22 I -64.43 -0.04 9.992 0.18 0.28 -0.10 49.66 50.14 -0.48 2233mmmm5 -66.51 20.39 -66.38 -0.13 9.840 0 9.840 0.17 0.1 7 0.00 50.68 50.85 -0.17 2234mmmm5 -66.3720.31 -65.92 -0.45 9.761 -0.02 49.54 49.73 -0.19 2244mmmm5 -66.92 0.34 -67.14 0.22 9.020 0 9.020 0.000 0.00 0.00 0.00 51.29 51.29 0.00 2334mmmm5 -66.434 0.42 -66.39 -0.04 9.950 0.04 52.17 51.14 1.03 10 -71.92 20.25 -71.93 0.01 12.276 12.286 -0.010 1.48 1.46 0.02 55.70 55.5s 0.12 2m9 -74.04 20.58 -73.21 -0.83 11.898 1.13 55.56 55.84 -0.28 5m9 -73.58 20.41 -72.67 -0.91 11.789 1.01 55.32 55.80 -0.48 335mmm7 -72.84& 0.20 m -72.76 -0.08 10.728 0.02 55.64 55.06 0.58 2233mmmm6 -72.534 0.26 m -72.45 -0.08 10.870 0.30 56.59 56.42 0.17 2255mmmm6 -77.32 0.23 m -78.25 0.93 9.916 -0.14 * 54.60 54.63 -0.03 11 -78.06k 0.50 C -78.05 -0.01 13.469 1.68 1.67 0.01 61.11 61.00 0.1 1 2n110 -79.22 & 0.30 m -79.33 0.1 1 13.082 1.34 61.27 2255mmmm7 -83.90 20.70 -83.28 -0.62 11.150 -0.13 1 60.14 3355mmmm7 -77.80+ 0.70 -77.23 -0.57 1 1.348 -0.10r 61.63 22445mmmmm6 -78.60+ 0.70 -77.66 -0.94 11.108 -0.09 * 61.56 12 -84.16 0.50 C -84.17 0.01 14.65P 14.653 -0.003 1.89 1.87 0.02 66.52 66.43 0.09 3366mmmm8 -89.104 0.80 -88.31 -0.79 12.384 -0.13 f 65.64 22446mmmmm7 -83.6220.22 m -83.67 0.05 11.912 -0.08 2 67.39 22466rnmrnmm7 -87.202 0.27 -87.24 Q.04 1 1.728 -0.17 t 65.70 TABLE4.-contd.4466mmmm9 -88.70f0.80 -89.32 0.62 13.547 0.27 73.45 3 355meme7 -86.20 0.80 -87.1G 0.94 13.594 0.14 73.09 -2233556(7m)7 -93.10+0.80'! -93.52 0.42 13.872 ,0.25 76.48 5577mmmmll 103.60-t 1.10 -101.60 -2.00 15.776 0.58 83.63 4466meme9 -99.104 1.10 -99.25 0.15 15.793 0.51 84.91 16 -108.8120.50r -108.67 -0.13 '9.45p 19.389 0.061 2.71 2.70 0.01 88.16 88.12 0.04 2ml5 -109.8540.36 m -109.95 0.10 19.001 2.37 88.39 18 -120.80+ 1.20 k -120.92 0.12 21.70p 21.756 -0.056 3.12 3.12 0.00 98.98 98.97 5b22 -170.50f1.70 -170.02 -0.48 30.579 4.37 143.12 1 1b22 -171.104 1.70 -170.02 -1.08 30.579 4.37 143.12 1ld21 -201.302 2.10 -200.64 -0.66 36.498 5.41 170.24 32 -204.83 2 1.50S -206.64 1.81 38.330 6.02 174.72 174.92 average deviation k0.21 k0.026 +0.04 -t0.30 standard deviation k0.38 k0.054 I0.06 0.48 a The style of writing the molecular formulae is from Part 2.b All observed values are taken from ref. (5) if not indicated otherwise. C Taken from ref, (12) if not indicated otherwise. d Taken from ref. (2). e Taken from ref. (2). f Taken from ref. (6). The values given in ref. (6) are for the gaseous compounds. They have been changed into the values for the liquid compounds using the appropriate values for the enthalpies of vaporization taken from ref. (12) except in the case of methane which remains a gas at 295.15 ISno matter what the pressure may be. Since our correlation requires methane as a key compound for the determination of the coefficient x0, we considered methane as a hypothetical fluid with zero enthalpy of vaporization at 298.15 K, B See footnote (f).Methane is considered to be a hypothetical fluid with zero enthalpy of vaporization at 298.15 K. h Taken from ref. (7). i Based on the enthalpy of isomerization data given in ref. (2). j Taken from ref. (8). Enthalpy of vaporization for the solid is changed into the enthalpy of vaporization for the liquid using the enthalpy of fusion taken from ref. (12). 1 Taken from ref. (9). m Taken from ref. (10). n Taken from ref. (13). 0 For 2,2,3,3-tetramethylpentane,and 2,2,4,4-tetramethylpentane no experimental enthalpies of vaporization are available. These compounds are key compounds with respect to our correIation and their enthalpies of vaporization are necessary for the determination of the coefficients kG4and k3.For the purpose of this correlation the enthalpies of vaporization for these two compounds were made to agree with the best predictions made by several other correlations mentioned in Part 2. p Taken from ref. (14). (1 Taken from ref. (11). The value is our selection based on the three experimental determinations cited in ref. (5)and the API selection. S Enthalpy of formation of the solid is changed into the enthalpy of formation of the liquid using its enthalpy of fusion quoted in ref. (5). t 2,ZDimethylbutane has three identical conformations and its conformational enthalpy is zero. Our correlation predicts, however, a conformational enthalpy of 0.03 kcal mol-' for this molecule. This happens mainly because ours is a correlation procedure but not a basic procedure from statistical mechanics for the calculation of the conformational enthalpy.In some cases our correlation procedure may even predict negative values for the conformational enthalpy. All cases marked by f correspond to one of these two cases. This is not an anomaly. 2222 GENERALIZED TREATMENT OF ALKANES TABLE5.-vARIABLES FOR SOME ALKANES n w2 W3 W4 WS YI 00 Q2 Q3 Q33 Q34 Q44 W34 W44 n23 n24 n33 n34 n44 1 1 0 00000000000000000 2 2 0 00000000000000000 3 3 1 00000000000000000 4 4 2 10000000000000000 2m3 4 3 00010000000000000 5 5 3 21000000000000000 2m4 5 4 20010000000010000 22mm3 5 6 00040000000000000 6 6 4 32100000000000000 2m5 6 5 32010000000010000 3m5 6 5 41010000000020000 22mm4 6 7 30040000000001000 23mm4 6 6 40020000000000100 7 7 5 43200000000000000 2m6 7 6 43210000000010000 3m6 7 6 53110000000020000 3e5 7 6 63011000000030000 22mm5 7 8 43040000001001000 23mm5 7 7 62020001000010100 24mm5 7 7 44020000000020000 33mm5 7 8 61040000000002000 223mmm4 7 9 60050000000000010 8 8 6 54300000000000000 2m7 8 7 54310000000010000 3m7 8 7 64310000000020000 4m7 8 7 65210000000020000 3e6 8 7 75211000000030000 22mm6 8 9 54340000001101000 23mm6 8 8 74220001000010100 24mm6 8 8 65220000000030000 25mm6 8 8 54420000000020000 33mm6 8 9 74140000001002000 34mm6 8 8 84120002000020100 23meS 8 8 85021002000020100 33me5 8 9 93041000000003000 223mmmS 8 10 83050000101010010 233mmm5 8 10 92050000100001010 234mmm5 8 9 84030004000000200 224mmm5 8 10 56050100002011000 2233rnmmm4 8 12 9 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 1 9 9 7 65400000000000000 4m8 9 8 76410000000020000 22mm7 9 10 65440000001?01000 223mmm6 9 11 95350000101110010 224mmm6 9 11 77350100002121000 225mmm6 9 11 65650000001211000 233mmm6 9 11 10 5 2 5 00 0 0 1 0 1 0 0 1 0 1 0 235mmm6 9 10 86430001000020100 244mmm6 9 11 87250100002012000 334mmm6 9 11 11515 0 0 0 0 2 0 1 0 1 1 0 1 0 33ee5 9 10 126042000000004000 223mme5 9 11 10 7 0 5 1 10 0 2 0 2 0 2 0 0 1 0 234mem5 9 10 10 8 0 3 1 1 0 6 0 0 0 0 1 0 2 0 0 2233mmmm5 9 13 12 3 0 8 0 0 00 0110 010 0 1 2234mmmm5 9 12 1060 6 0 1 0 3 2 0 2 0 0 0 1 1 0 2244mmmm5 9 13 6 9 0 8 0 0 1 0 0 0 6 0 0 2 0 0 0 2334mmmmS 9 12 1 2 4 0 6 0 0 0 0 4 0 0 0 0 0 0 2 0 10 10 8 76500000000000000 2m9 10 9 76510000000010000 5m9 10 9 8 7 6 1 0 0 0 0 0 0 0 0 2 0 0 0 0 335mmm7 10 12 108550100002122000 2233mmmm6 10 14 13 6 3 8 0 0 0 0 0 1 2 1 0 10 0 1 2255mmmm6 10 14 7 6 9 8 0 0 0 0 0 0 2 6 0 2 0 0 0 11 11 9 87600000000000000 2m10 11 10 87610000000010000 2255mmmm7 11 15 10 710 8 0 0 0 0 0 0 2 6 0 3 0 0 0 3355mmmm7 11 15 1211 6 8 0 0 10 0 0 6 2 0 4 0 0 0 22445mmrnmm6 11 16 1211 6 9 0 0 10 10 6 2 0 2 0 10 12 12 10 98700000000000000 3366mmmm8 12 16 13 811 8 0 0 0 0 0 0 2 6 0 4 0 0 0 22446mmmmm7 12 17 11 16 5 9 0 1 1 0 0 0 8 11 3 0 0 0 22466mmmmm7 12 17 1013 6 9 0 2 0 0 0 0 4 2 2 2 0 0 0 4466mmmm9 13 17 1417 8 8 0 0 10 0 0 8 2 0 4 0 0 0 3355meme7 13 17 181512 8 2 0 10 0 0 6 4 0 6 0 0 0 2233556(7m)7 14 22 21141513 0 0 10 11 7 8 0 2 0 11 G.R. SOMAYAJULU AND B. J. ZWOLINSKI 2223 TABLE5.-contd. n W2 W3 W4 WS YI QO 82 Q3 Q33 034 Q44 W34 W44 n23 n2.4 n33 n34 n44 5577mmmmll 15 19 16 19 14 8 0 0 1 0 0 0 8 4 0 4 0 0 0 4466meme9 15 19 20 21 16 8 2 0 1 0 0 0 8 4 0 6 0 0 0 16 1614131211 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2m15 1615131211 1 0 0 0 0 0 0 0 0 10 0 0 0 18 1816151413 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5b22 2625252525 1 1 0 0 0 0 0 0 0 3 0 0 0 0 1 1 b22 2625252525 1 1 0 0 0 0 0 0 0 3 0 0 0 0 1 ld21 3130303030 1 1 0 0 0 0 0 0 0 3 0 0 0 0 32 3230292827 0 0 0 0 0 0 0 0 0 0 0 0 0 0 TABLE6.-COMPARISON OF ENTHALPY OF ISOMERIZATION AT 298.15 K OBTAINED FROM EQUILIBRIUM DATA WITH VALUES OBTAINED FROM EXPERIMENTAL AND CALCULATED ENTHALPIES OF FORMATION AH, = AH1 b AH1 C equilibrium /kcal mol-1 /kcal mol-1 /kcal mol-1 n-butane = 2-methylpropane -2.12kO.05 -2.04 -2.18 n-pentane = 2-methylbutane -1.68k0.20 -1.65 -1.59 n-hexane = 2-methylpentane -1.7050.10 -1.86 -1.67 n-hexane = 3-methylpentane -0.96+0.10 -1.22 -1.09 n-hexane = 2,2-dimethylbutane -4.055 0.10 -4.55 -4.08 n-hexane = 2,3-dimethylbutane -2.27+ 0.10 -2.70 -2.11 2,4-dimethylpentane = n-heptane 3.3150.15 3.35 3.41 2,4-dimethylpentane = 2-methylhexane 1.6850.15 1.66 1.74 2,4-dimethylpent ane = 3 -met hylpent ane 2.36k0.15 2.47 2.25 2,4-dimethylpentane = 2,3-dimethylpen tane 1.9250.15 1.92 1.80 2,4-dimet h ylpen tane = 3,3 -dime t h ylpen t ane 0.495 0.15 0.49 0.47 2,4-dimethylpentane = 2,2,3-trimethylbutane -0.53k0.15 -0.66 -0.29 2-met hylhept ane = 4-met hylheptane 0.66k0.15 0.81 0.43 2,5-dimethylhexane = 2,4-dimethylhexane 0.475 0.15 0.78 0.43 2,5-dimethylhexane = 3,4-dimethylhexane 2.475 0.15 2.47 2.23 a Taken from ref.(2). b Calculated from the experimental enthalpies of formation. C Calculated from the estimated enthalpies of formation. d Adjusted values. Several of the alkanes such as 3,4-dimethylhexane, 3,4-dimethylheptane, etc., exhibit diastereoisomerism and it is possible that the various diastereoisomers of a particular alkane may have differing enthalpies of formation. These differences, however, may not be so significant as to make diastereoisomerism an important property from the standpoint of the enthalpies of formation, and we have therefore disregarded it in this study.This study also emphasizes the importance of studying molecular shifts and the enthalpies of formation on the same lines. The three new parameters ko, dS4, and 844 borrowed from the treatment of the molecular shift appear to be important in the treatment of the enthalpies of formation, and other properties. We thank Mrs. Annie Lin Risinger and other members of the Thermodynamics Research Center for help with the preparation of the manuscript. We also thank Mr. C. 0. Reed, Jr., for help with the computations. The study was supported in part by the Thermodynamics Research Center and the Texas Engineering Experiment Station. G. R. Somayajulu and B. J. Zwolinski, J.C.S. Furaduy ZI, 1972, 68, 1971 ; 1974, 70, 967; 1974, 70, 973.D. W. Scott, J. Chem. Phys., 1974, 60, 3144. T. L. Cottrell, J. Chem. Soc., 1948, 1448. GENERALIZED TREATMENT OF ALKANES G. R. Somayajulu and B. J. Zwolinski, Report of Investigation of American Petroleum Institute Research Project 44, Thermodynamics Research Center, Texas A&M University, April 15, 1975. J. D. Cox and G. Pilcher, Thermochemistry of Organic and Organometailic Conipounds (Academic Press, London and New York, 1970). D. A. Pittam and G.Pilcher, J.C.S. Faraday I, 1972, 68, 2224. W. D. Good, J. Chern. Thermodynamics, 1970, 2,237. W. D. Good, J. Chem, Thermodynamics, 1972, 4,709. W. D. Good, J. Chem. Eng. Data, 1969, 14,231. lo P. D. Desai, Dissertation (Texas A&M University, 1968). A. L. Seifer, E. A. Smolenskii and L. V. Kocharova, Thernzophysical Properties of Gases aid Liquids, ed. V. A. Rabinovich (trans. edn., U.S. Dept. of Commerce and National Science Foundation, Washington, D.C., 1970), pp. 173-185. l2 Selected Values of Properties of Hydrocarbons and Related Substances, ed. B. J. Zwolinski, (American Petroleum Institute Research Project 44, Thermodynamics Research Center, Texas A&M University, 1975). ERDA Energy Research Center, Bartlesville, Oklahoma. E. Morawetz, J. Chem. Thermodynamics, 1972, 4, 139, 145. (PAPER 5/949)

ISSN:0300-9238    

DOI:10.1039/F29767202213

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

He1 Photoelectron Spectrum of the P2(X1Cl)Molecule BY DENISK. BULGIN, JOHN M. DYKE*AND ALANMORRIS Department of Chemistry, The University, Southampton SO9 5NH, Hampshire Received 15th March, 1976 The He1 photoelectron spectrum of the P2(X'C;) molecule has been recorded and interpreted with the aid of ab initiu and semi-empirical molecular orbital calculations. Three ionic states of the diphosphorus molecule are found to be accessible with He1 radiation. Comparison is made between the properties of these states and the corresponding well established ionic states of nitrogen. The main objective of this work was to use photoelectron spectroscopy (pees.) to identify and characterize the low lying electronic states of P2f obtained from photoionization of P2 by He1 radiation.This was done in order to make a direct comparison between the low-lying ionic states of P2 and N2 and to compare the characteristics of these Pi states with information derived from other techniques. A number of states of P2 and P2f have already been characterized by optical In these studies the usual method for production of P2 is pyrolysis 59or electrical discharge 39 of P4vapour. Some theoretical studies have also been made on the P, molecule but no similar calculations appear to have been carried '9 out on the ground or any of the low-lying states of Pi. The p.e. spectrum of P, produced by pyrolysis of P4has been studied previously in the 9.0-1 1.0eV regio11.~ In this work, because the pyrolysis of P, was incomplete, the bands attributable to P, were roughly the same intensity as those from the parent P4.However, two bands were observed with vertical ionization potentials equal to 10.65 and 10.84 eV which were associated with ionization from the 2nu and 5ag P2 molecular orbitals respectively. Also, the far ultraviolet absorption spectrum of P2has recently been reported by Carroll and MitchelLG They were able to identify nine Rydberg series in their spectra. Four of these converge to the ground state of PZ, the X'lJ, state arising from the configuration .................................. (4~~)2(4a,,)2(5a,)2(271u)3, foul- to the low-lying A2X,f state arising from the configuration (415,)2(4a,) (sag)1 (271~~ on the basis of the measured quantum defect associated with the Rydberg series.However, the possibility that the series limit corresponds to the 'EC,+ state of Pt arising from the configuration _._.-___-------_-___-~-..----.----(40,) '(4%) '(5%) (27L)4 does not seem to have been considered. Comparison of data derived from this work with the information obtained from the initial p.e.s. study shows that a correction of -0.03 eV should be applicd to the pholoelectron data. 2225 P.E. SPECTRUM OF P2(x1xz) A related study has recently been made of the photoelectron spectrum of PN.IO Although the instrumental resolution was low, two bands were identified in the He1 region corresponding to ionization to the X2Z+ and A211 ionic states of PN with vertical ionization potentials of 11.85 and 12.52 eV respectively.EXPERIMENTAL AND COMPUTATIONALDETAILS The photoelectron spectrometer used in this study was an electrostatic analyser type and has been described previously.' ' Under the operating conditions the usual resolution was 20-25 meV as measured (full width at half maximum) for argon ionized by He1 radiation. Unless otherwise stated the i.p. values are quoted to an estimated accuracy of +O.Ol eV and the vibrational spacings to & 30 cm-'. I 2 0.0 15.0 10.0 ionization potential/eV 300 A2Zi -, 2a0 15.0 I0.0 ionization potential /eV FIG.1.-Helium I photoelectron spectrum of (a) P4and (6) P2. The diphosphorus molecule was produced in this investigation by heating a stream of P4vapour in a radiofrequency induction furnace at -1300K, 4 cm away from the ionization region.The P4vapour was introduced into the furnace by passing an inert gas (usually helium) through a U-tube containing small pieces of elemental white phosphorus (at -310 K). D. K. BULGIN, J. M. DYKE AND A. MORRIS Spectra were recorded using a chart recorder in the normal way or by signal averaging over many spectra using a multichannel analyser. Calibration was achieved using argon, nitrogen, water and benzene. The ionization potential region 17.0-21.O eV was investigated using a pre-accelerating grid biased to a potential of -3 volts. For P2, the ground electronic configuration can be written as For the ground state of P2 and the states arising from the (27ql)-l, (50,)-', (4a,)-' and (4ag)-l ionizations, wavefunctions and total energies were calculated in the matrix Hartree- Fock approximation using the open-shell method of Roothan and Bagus l2 with the ALCHEMY ~r0gramme.l~ This was done for all these states for at least five values of equilibrium bond length in order to check that these potential energy curves are bound.These were the only one-electron ionization processes considered, as previous calculations on P2 79 indicate that orbitals other than the 40,, 40,, 50, and 2n, orbitals are much too low-lying to be accessible with He1 radiation. The atomic basis set used for phosphorus in these calculations was taken from ref. (14). From the computed total energies, vertical ionization potentials were estimated by the ASCF method.These calculations ignore a number of important factors (i.e.,correlation energy differences, near-degeneracy effects and relativistic energy differences) which determine the exact order of the ionic states of the diphosphorus molecule.15 However, it is anticipated that these calculations when combined with the experimental observations should lead to a correct prediction of the ionic state ordering in P2+. The energies of the electronic states of PZ were also calculated using the same INDO semi-empirical method used for S; .I1 Phosphorus 3d orbitals were excluded from the initial basis set. In these calculations, vertical ionization potentials were calculated, as before,ll relative to the observed value for the first vertical i.p.according to the equation (i.p.)i = AEi(ion)+ (i.p.)o (1) where AEi is the excitation energy of the ith state and (i.p.)o is the first vertical ionization potential. 1.-CALCULATEDTABLE AND OBSERVED VERTICAL IONIZATION POTENTIALS OF THE P2(x1cl)MOLECULE vertical ionization potentials predicted ASCF observed using Koopmans' theorem ab initio orbital vertical nB initio nb initio ionic calculations INDO-CI symmetry I.P./eV this work ref. (7) state this work calculations 271, 10.62 10.09 10.26 'IIu 9.42 10.62 a 50, 10.81 11.05 11.13 "cg' 10.39 10.87 4aLl 15.52 16.46 16.38 "c,+ 16.00 16.21 4% -24.54 24.79 'Cg' 23.32 23.69 a fitted value ; b all calculations have been performed at an experimental (P-P) bond length of 1.8937 8, except for the calculations in ref.(7), where a bond length of 1.8507A has been used. This is the computed SCF value of re with the basis set adopted in ref. (7). RESULTS AND DISCUSSION The helium I photoelectron spectrum of the P4 molecule is shown in fig. l(a). This is in good agreement with previously reported photoelectron spectra.l6. l7 Pyrolysis of the P4 molecuie to produce P2 could be readily achieved and it was found that the P2 : P4ratio could be controlled by varying the temperature of the furnace. No peaks attributable to atomic phosphorus were seen although, under our experi-mental conditions, no measurable amounts of mono-atomic phosphorus would be expected.18 At about 1300 K, the contribution to the observed photoelectron P.E.SPECTRUM OF P2(x1x,') spectrum by P4 is very small and a spectrum that we attribute almost completely to P2 is shown in fig. l(b). However, because the overall count rates were rather low (typically 300 counts/s on the most intense peak) the spectrum shown in this figure was recorded many times and averaged using a multichannel analyser. On the basis of the calculations shown in table 1, three bands corresponding to one-electron ionization from the three highest valence orbitals would be expected in the He1 photoelectron spectrum of P2(X1XS+). Also, our INDO-CI calculations indicate that only simple one-electron ionizations need to be considered in the He1 region. The corresponding ionic states produced by one-electron ionization are, in order of increasing energy, the 211u,"C,.and 2Z: states. In fig. l(b), the first two bands arising from ionization of P, can be seen in the ionization potential region 9.0-12.0eV. An expanded version of this region is given in fig. 2(a). As can be Cfl LI a ionization potential lev ionization potential/eV FIG.2.-Helium I photoelectron spectrum of (a)the first two i.p.'s of P2 and (b) the third i.p. of P2. seen from this diagram, the first band exhibits well-resolved vibrational fine structure with a measured vibrational separation of 670 cm-1 compared with the free molecule value of 780~m-l.~ This is, as expected, consistent with removal of a bonding electron. Also, the overall band shape is similar to the analogous band associated with ionization to the A2rII,state of N2+found in the p.e.spectrum of N2.19 Fig. 2(a) D. IS. BULGIN, J. M. DYKE AND A. MORRIS also shows that each vibrational peak of this first band is split into two components. This arises from spin-orbit splitting of each vibrational level of the ionic state and is further evidence that the ground state of P2f is a ’flu state. Our measured value for the spin-orbit splitting in this band is (1 SO+ 30) cm-l, in good agreement with the value of 150 cm-l determined from the emission spectrum of P2f but in poor agreement with the value proposed by Carroll and Mitchell on the basis of a study carried out by Brion et aL20 on the C2ngt X211, spectrum of P2f. The experimentally determined ionization potential to the v’ = 0 state of X2n, is 10.53 eV and to the v‘ = 0 state of X211+ is 10.55 eV.The value estimated by Carroll and Mitchell for the latter ionization process is (10.567f0.002) eV? The discrepancy of 17meV between the two techniques is outside the error of our measurements. However, we have checked the position of the X211+ component many times and consistently reproduced a value of (10.55k0.01) eV. The expsrimentally determined vertical ionization potentials of this band are estimated to be 10.61 eV for the X2fl, component and 10.63 eV for the X2n+component. For computational purposes in the INDO-CI calculations, the vertical i.p. is taken to be 10.62 eV. The second band in the P, spectrum arises from ionization of a 50, electron. The experimentally measured adiabatic and vertical ionization potentials coincide at 10.81 eV, in good agreement with the value of (10.808f0.002) eV determined by Carroll and Mitchell.6 As can be seen from fig.2(a),this band consists of a single peak without any associated structure and is very similar to the band associated with ionization to the X2X; band of N; in the He1 spectrum of nitrogen.lg The Franck- Condon envelope of this band was predicted, using the method adopted previously,l’ assuming vibrational frequencies and bond lengths for the ion and molecule obtained from previous investigations.’ The intensity ratio of the o’ = 0 t v’’ = 0 ionization to the v’ = 1 +-0’’ = 0 ionization is predicted to be 1 to 1 x and hence it is entirely consistent that only one vibrational component is observed experimentally.The calculations shown in table 1, predict that a band attributable to the 40; ionization should occur in the region 15.0-17.0 eV. We have denoted the ionic state produced by this ionization as B2C: by analogy with nitrogen. Fig. l(h) shows no intense bands in this area. A band was, however, observed only when this region was investigated in detail by averaging rnany spectra [see fig. 2(b)]. At first sight, the most obvious assignment of this band is that it arises from a nitrogen impurity. However, by adding controlled amounts of nitrogen it was shown to occur in a slightly different position and, moreover, the intensity of this band varied linearly with those of the other P2 bands.For this band, the experimentally measured adiabatic and vertical i.y.’s coincide at 15.52 eV. Also, the relative intensities of the two vibrational components and the value of the vibrational separation were measured as 1.0 :(0.33+0.14) and (820+60) cm-’ respectively where the errors quoted are twice the overall standard deviations. The experimental errors associated with these measurements are greater than those normally quoted in p.e.s. and reflect the very low signal-to-noise ratio associated with the third band. However this band has been reproduced in many spectra and there is little doubt that it is associated with an ionization of the P2 molecule. In addition, its position and measured vibrational separation are in good agreement with those recently determined from optical spectroscopy.G We have assigned the ionic state associated with this band as arising from the configuration l-l--.--__-.____(4a,)2(40,)1(50g)2(2nu)4, i.e., a ’Z: state.However, Carroll and Mitchell propose the 2E: state arising from the configuration ---------__________-____-___:4CQ2 (4%) ,(50,) (2%) (2%) 2230 P.E. SPECTRUM OF p,(X1~~) The latter configuration cannot be obtained from the ground state of P2 by a one- electron ionization and hence states arising from this configuration would not normally be observed in photoelectron spectroscopy. Our INDO-CI calculations indicated that the 2Z: state of Carroll and Mitchell corresponds to an ionization potential of 15.80 eV and is predicted to be very much weaker than the band corresponding to the 4a;l ionization predicted at 16.21 eV.Hence there is little doubt that the third band in the P2 spectrum arises from the 40; ionization. On comparison of the He1 spectra of P, and N,, there appears to be no reason why the third P, band should be so weak relative to the other two. However, this can be rationalised if the differential photoionization cross sections of the valence orbitals of P,, as a function of incident photon energy, are similar to those of nitrogen. These functions for nitrogen rise sharply near the ionization threshold, go through a maximum and then decrease slowly as the photon energy increases. For the photo- ionization cross-sections calculated as a function of photon energy for N2 by Rabalais et aZ.,21we would expect the maximum for the (5a,)-' and (2nJ-l ionizations of P2 to be 5-10 eV lower in energy than the maximum for the (40,)-' ionization.Hence if the differential photoionization cross-section curves for the three highest valence orbitals of P2 are approximately parallel in the threshold region as in N2,the bands arising from the 5a; and 2n; ionizations will be considerably more intense than the band arising from the 40; ionization. Although careful investigation of the ionization potential region 15.0-21.O eV was performed, no further evidence for any other bands could be found. TABLE2.-cOMPARISON OF PHYSICAL CONSTANTS FOR Ni AND Pi dissociation equilibrium vibrational energy bond length wave number state DdeV re IA G,/cm-l X1Z:N2 9.760+0.005 a 1.0977 a 2358.0 a X1ZS+P2 5.03+0.01 b 1.8937 a 780.9a A211,N2+ 7.7c 1.174a 1902.8 a X211,P,+ 4.97+ 0.05 1.9903 670 X2Z,fN; 8.7c 1.116 a 2207.2 a A2C,fPi 4.70+ 0.05 1.8926 732.9 B2Z:Ni 5.7c 1.075 a 2419.8 a B2Z;P; -e 1.854 0.01 820+ 60 a ref.(1) ; b ref. (22) and (23) ; Cref. (24) ; d ref. (2) ; e this value could not be estimated from fig. 3 because the dissociation products of the B2X;state of P: are uncertain. The peak that appears at a vertical ionization potential of 10.44eV, displaced by N 780cm-l from the first vibrational component of the first band, could not be associated with P4and does not appear to be a true member of the vibrational series in the first band.The intensity of this band did not vary linearly in intensity with the bands associated with P2and it could be removed by decreasing either the tempera- ture of the furnace or the rate of helium flowing through the furnace. On the basis of this evidence, it is assigned to ionization of vibrationally excited P2 in the vff = 1 level of the XlZ; state to the uf = 0 level of the X2nUstate of P2+. In accordance with this assignment, Franck-Condon calculations have been performed for ioniza- tions from the v" = 0-4 levels in P2X1EB+to the u' = 0-4 levels in P;X2nU. It was found from these calculations that the uf = 0 t vn = 1 transition is the only one of D. K. BULGIN, J. M. DYKE AND A. MORRIS 2231 sufficient intensity to be observed experimentally and from the observed intensity the maximum vibrational temperature of P2is estimated as 900 K.Also, our Franck- Condon calculations predict that no evidence for vibrational excitation of the neutral molecule would be expected associated with the second and third bands. We were also able to reproduce the vibrational envelope of the first band with a value of the equilibrium bond length for the Pi X2n, state of 1.9903 A determined from optical spectroscopy.2 Although the exyerimefitally determined relative intensities of the components of the third band were less accurately determined than those of the first band, it was possible to estimate the equilibrium bond length for the corresponding P2f state (denoted in this work as the B2C: state).Assuming a value of CO, of 820 cm-l for this P2+ state, the Franck-Condon envelopes were computed at various equilibrium bond lengths and from these predictions the ionic equilibrium bond length was estimated as (1.85 +O.Ol) A. The increased value of CO, and the decreased equilibrium bond length for this P2+ state compared with the corresponding parameters for the X1C; state of P, are entirely consistent with removal of an electron from the anti- bonding 40, orbital of P2. 24 I \ 20*i( /-I 1.0 1.5 2.0 2.5 bond length/A FIG.3.-Potential energy diagram for the X2HI,,AZC:and B2C:states of P:. The ionic state parameters of Pz determined both in this study and in other investigations have been used to construct the potential energy diagram shown in fig.3. The method adopted is the same as that used previously for S;.' In drawing this diagram, values of the dissociation energy of P,X1X; and the first i.p. of the phosphorus atom were taken as (5.03 kO.01) eV 22* 23 and 10.484 eV 25 respectively. P.E. SPECTRUM OF Pz(xl'cl) The values of the dissociation energies of the ionic states of P, observed in this study derived from fig. 3 are shown in table 2. In this table, the comparison of the physical constants for N2+ and P2+can be clearly seen. As expected ionization from the 27r, orbital in P2 (a bonding orbital analogous to the In, orbital in N,) produces a fairly large decrease in vibrational frequency and a reasonably large increase in bond length. Ionization from the 50, and 40, orbitals (analogous to the 30, and 20, orbitals in N,) produces, as anticipated, only small changes in vibrational frequencies and equilibrium bond lengths.The authors gratefully acknowledge the advice of Prof. N. Jonathan and Prof. P. K. Carroll during the course of this work. One of us (D. K. B.) thanks the S.R.C. for the award of a Studentship. B. Rosen, International Tables of Selected Constants ; Data Relatiue to Diatotnic Molecules (Pergamon, London, 1970). N. A. Narasimham, Canad. J. Phys., 1957, 35, 1242. F. Creutzberg, Canad.J. Phys., 1966, 44, 1583. A. Jakowlewa, 2.Phys., 1931,69,548. J. R. van Wazer, Phosphorus and its Compounds (Interscience, N.Y. 1958). P. K. Carroll and P. I. Mitchell, Proc. Roy.SOC.A, 1975, 342, 93. R. S. Mulliken and B. Liu, J. Amer. Chem. Soc., 1971, 93, 6738. * D. B. Boyd and W. N. Lipscomb, J. Cheni. Phys., 1967,46,910. A. W. Potts, K. G. Glenn and W. C. Price, Faraday Disc. Chem. Soc., 1972, 54, 65. lo M. Wu and T. P. Fehlner, Chem. Phys. Letters, 1975, 36, 114. l1 J. M. Dyke, L. Golob, N. Jonathan and A. Morris, J.C.S. Faraday ZZ, 1975, 71, 1026. l2 C. C. J. Roothan and P. S. Bagus, Methods in Computational Physics (Academic Press, New York, 1963), vol. 2. l3 P. S. Bagus, Alchemy Studies of Small h.lolecules, Proc. Seminar Selected Topics in Mol. Phys., Ludwigsburg, (IBM, Germany, 1971). l4 P. A. G. O'Hare and A. C. Wahl, J. Chem. Phys., 1971, 54,4563. l5 G. Verhaegen, W. G. Richards and C. M. Moser, J.Chem. Phys., 1967, 47, 2595. l6 S. Evans, P. J. Joachim, A. F. Orchard and D. W. Turner, Znt. .I.Mass. Spec. Zon Ph~s., 1972, 9,41. l7 C. R. Brundle, N. A. Kuebler, M. B. Robin and H. Basch, Inotp. Chem., 1972, 11, 20. la K. A. Gingerich, J. Chem. Phys., 1966, 44, 1717. l9 J. M. Dyke, N. Jonathan, A. Morris and T. J. Sears, J.C.S. Faraday ZI, 1975, 72, 597. 2o J. Brion, J. Malicet and H. Guenebaut, Cornpt. rend,, 1973, 276, 471. 21 J. W. Rabalais, T. P. Debies, J. L. Berkosky, J. T. J. Huang and F. 0. Ellison, J. Chem. Phys., 1974, 61, 516. 22 B. Rai, J. Singh and D. K. Rai, J. Chem. Israel, 1971, 9, 563. 23 A. G. Gaydon, Dissociation Energies and Spectra of Diatomic Molecrtles (Chapman and Hall, London, 1968). 24 F. R. Gilmore, J. Quantum Spectr. Rad. Transfer, 1965, 5, 369. 25 W. C. Martin, J. Opt. SOC.Amer., 1959, 49, 1071. (PAPER 6/500)

ISSN:0300-9238    

DOI:10.1039/F29767202225

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Applications of a Simple Molecular Wavefuiiction Part 16.-Bond Angles and Orbitals of Singlet CH, BY LEOKPECKTAN"AND THE LATE JOHNW. LINNETT Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EP Received 30th March, 1976 The simple Floating Spherical Gaussian Orbital method gives low bond angles when lone pair electrons are present in the molecule on the atom participating in the two bonds. A way of modifying the lone pair orbital to correct this by using a linear combination of gaussian functions is described. The non-orthogonal orbitals have been transformed to orthogonal orbitals using the Lowdin procedure. Changes in the component energies are examined and the reason for the improvement in the calculated bond angle discussed.Calculations by Frost et a2.l' have shown that the simple Floating Spherical Gaussian Orbital (FSGO) method gives very good values for the shapes of hydro-carbon molecules but predicts poor bond angles for molecules like CH2, NH3 and OH2 which contain lone pairs of electron^.^ In a previous c~mmunication,~ we have shown for NH3 and CH2, that a more satisfactory bond angle is predicted when the lone pair orbital is described by a linear coinbination of floating spherical gaussian functions with single gaussian descriptions being retained for the other orbitals. Y is the electronic radial coordinate, a,.and R, are the exponent and vector positions respectively of the ith gaussian function ; N is the normalisation constant and the ci linear coefficients which can be positive or negative.In particular, the "best " lone pair orbital description, which employs a pair of axial gaussians (one positive and one negative resembling a "p type " orbital) together with a set of off-axial gaussians placed eclipsed to the bonds, predicted a bond angle of 106.3" for NH3 (simple FSGO 87.9"; experiment 106.7') and an angle of 183.5' for CH2(simple FSGO 91.5" ; experiment 102.4"). This paper presents an analysis of the results obtained for CH2 (the analysis holds equally for NH3,the results being very similar) in an attempt to understand the reasons for the failure of the simple FSGO method and the success of the particular ''difference " lone pair orbital modification in predicting accurate bond angles for molecules with unshared electron pairs.CALCULATIONS AND RESULTS Fig. 1 depicts (schematically) the simple FSGO model and the three ''difference '' lone pair orbital modifications A, B and C studied for CH, and the corresponding results obtained are listed in table 1. The simple FSGO model predicts too small a * present address : School of Chemical Sciences, Universiti Sains Malaysia, Penang, Malaysia. 2233 2234 APPLICATIONS OF A SIMPLE MOLECULAR WAVEFUNCTION bond angle of 91.5', which improves with an increasing number of positive gaussion functions in the "difference " lone pair orbital description until with three positive and one negative gaussian functions distributed as in C, a good bond angle of 103.5' is obtained. The calculated CH bond length remained close to the experimental value in all four models.'._I '*-H Asimple2 FSGO H H H z model A2-H H H H 7L L model B model C FIG.1.-The description (schematic) on the lone pair orbital in the various FSGO modifications investigated for singlet CH2. (The broken circles on the simple FGSO model are the inner-shell and bonding orbitals which are described by single floating spherical gaussian functions ; they are omitted in models A, B and C for clarity). In the FSGO method, the basis orbitals {4i}are not orthogonal to one another. Interpretation would be simplified in a number of ways if the non-orthogonal orbitals be transformed into a set of orthogonal orbitals. The Lowdin symmetric orthogonal- isation procedure is given, in matrix notation, by X= aT-5.where X and @ are the row vectors of the orthogonal and non-orthogonal orbitals respectively X = (XI ~2 * * -Xn). = (41 42. 4n>* Tis the inverse overlap matrix T = S-l where Sij = s 4'4jdz. Frost and Afzal 'have shown that these "Lowdin " orthogonalised orbitals, which have acquired negative contributions to obtain orthogonality, are still clearly identifiable as inner-shell, bonding, and lone pair orbitals. This is not surprising as it has been proved 8that the Lowdin symmetric orthogonalisation procedure produces the set of orthogonal functions that differ least, in a least squares sense, from the non-orthogonal basis functions. The non-orthogonal " local " lone pair orbital functions and the corresponding Lswdin orthogonalised lone pair functions of the simple FSGO model and model C are shown in fig.2(a)and 2(b)respectively. As regards the non-orthogonal lone pair L. P. TAN AND J. W. LTNNETT orbital functions, the introduction of a gaussian function with a negative coefficient into the linear combination does not produce a node in that orbital function. It only serves to decrease the value of the function in the interbond region. On the other hand, the Lowdin orthogonal lone pair functions show a much more definite change in form as the description is improved with the use of more gaussians. In the simple FSGO model, the orthogonal lone pair function has acquired a negative region inside the orbital (to achieve orthogonality with the inner-shell orbital) and the resulting function over a large volume resembles a "2s-type" orbital.In contrast, the orthogonal lone pair function in C resembles more an " sp2 " hybrid orbital, whilst that in A shows intermediate behaviour. TABLETHE VARIOUS FSGO CALCULATIONS FOR SINGLET CH2 model simple FSGO A B C energy/a.u.bond angle (102.4")bond length/a.u. (2.10) -32.966 91.5" 2.17 -33.046 94.9" 2.15 -33.053 98.9" 2.14 -33.165 103.5" 2.14 inner-shell orbital parameters a 9.3781 9.3676 9.3635 9.3395 Z 0.0009 0.0012 0.0011 0.0021 bonding orbital parameters a 0.3368 0.3416 0.3427 0.3325 d 1.26 1.26 1.26 1.26 e 91So 93.9" 100.0" 104.2" lone pair orbital parameters 0.2958 0.3305 1.4370 -0.311 1 -0.3228 -0.2407 1.o 0.5842 0.3427 -+0.4683 0.2797 &0.6331 -0.3077 -0.3193 1.o 1.o 2.4780 2.5270 1.9680 0.4657 0.4639 0.2422 -0.1009 -0.1857 -0.5010 The figures in brackets are the experimental value^.^ dis the distance (am.) of the bonding orbital from the carbon atom.0 is the angle subtended by the centres of the two bonding gaussian functions at the carbon atom. Another change in the orbital is that its maximum value is greater with model C than with the simple FSGO model, and the slope of the orbital value from the maximum towards the nucleus is also much greater [see fig. 2(b)]. A similar change was observed by Suthers and Linnett who investigated the use of one, two and three pairs of guassian functions to represent p-orbitals in atoms.It appears that a single gaussian function cannot achieve a correct representation of both the extent of the orbital and its maximum value. If only one is used, then it satisfies primarily the extent; the outer contours in fig. 2(6) for the orbitals for the simple FSGO model and for model C are very similar. With more than one gaussian for the positive lobe, the achievement of both becomes more possible. 2236 APPLICATIONS OF A SIMPLE MOLECULAR WAVEFUNCTION ----. F1~.!2(u).-The normalised "local " non-orthogonal lone pair orbital function for (i) the simple FSGO model and (ii) model C. (b)The normalised Lowdin orthogonal lone pair orbital function for (i) the simple FSGO model and (ii) model C.(ii) FIG.3.-The normalised Lowdin orthogonal bonding orbital function for (i) the simple FSGO model and (ii) model C. Fig. 3 shows the Lowdin orthogonal bond orbitals for the simple FSGO treatment and for model C. It is clear that they are not greatly changed in their overall form, much less than the lone pair orbital. DISCUSSION These results offer a simple qualitative explanation for the poor value obtained for the bond angle for singlet CH, by the simple FSGO model; and in particular, that the angle obtained is N 90". In the simple FSGO model, the lone pair electrons occupy an orbital which resembles, mure than anything else, a 2s orbital of the carbon L. P, TAN AND J.W. LINNETT atom. This causes the orbitals for the bonding pairs to approach pure p-character as regards the contribution of the carbon atom. This would lead to a bond angle near to 90". The 2s orbital is lower energetically than the 2p orbital and the very nature of the spherical description of the lone pair orbital, imposed by the simple FSGO model, cannot accommodate more p-character in such a way that there is a sufficient gain in electronic energy to compensate for the s-p promotion energy that is required. This prevents the bond orbitals from acquiring the sp2 hybrid character which would produce an increase in the interbond angle. TABLE2.-BOND ANGLES CALCULATED USING THE SIMPLE FSGO METHOD molecule CH,' NH3 H3O+ NH; Hz0 H2F+ PH3 H2S calculated 39 l1 87.5" 87.9" 90.2" 86.4" 88.4" 92.2" 90.9" 87.7" observed 106.7' 104.5" 93.2" 92.2" -0.6 -0.4 0.2-0.0 ---0.2 2 4 -0.4-d --0.6 -0.8 --1.0-FIG.4.-Graph showing the variations in the different energy contributions to the total energy in the different models for CH2 ; (a) electron repulsion, (6) kinetic energy, (c) nuclear repulsion, (d)total energy, (e) nuclear attraction.This analysis therefore suggests that the simple FSGO model will tend to restrict the bond orbitals to predominantlyp-type as far as the carbon atom is concerned so that angles of 90" will be obtained in molecules with lone pairs. Table 2 lists the bond angles of some hydrides of atoms in the first and second row which possess lone pairs as calculated using the simple FSGO model.These results support the explanation given above since the bond angles are not only calculated to be much smaller than the observed values, but they are indeed all in the region of 90". However to obtain a inore quantitative appreciation of the electronic and nuclear interactions, the variations in the different energy contributions to the total molecular energy for the different models used have been studied. Fig. 4 shows the variations 2238 APPLICATIONS OF A SIMPLE MOLECULAR WAVEFUNCTION in the kinetic energy, the electron-electron repulsion and the electron-nuclear attrac- tion energies and the nuclear-nuclear repulsion energy for the four models. The most notable feature is the very large increase in the electron-nuclear attraction energy, which more than compensates for the increase in the kinetic and electron- electron repulsion energies as the lone pair function is improved and the bond angle increases.Frost and Mia1 studied the various energy changes in H20as a function of bond angle using the simple FSGO model. Calculations were performed for different bond angles. All the orbital exponents remained fixed, the bond orbitals were held at the same distance along the OH bonds and the lone pair orbitals were kept at a fixed distance above and below the molecular plane. As the bond angle was increased from the calculated equilibrium value near go", both the electron-electron and nuclear-nuclear repulsion terms decreased, but there was a loss in the nuclear- electron attraction energy by an almost equal amount.These results imply that any tendency for the HOH angle to increase as a result of a decrease in electron-electron and nuclear-nuclear repulsions will be off-set by the fact that, as the orbitals and nuclei move apart, their mutual attractions decrease by approximately the same amount. This occurs because the lone pair orbital is represented by a single spherical charge density which cannot adjust adequately to the attractive forces of all the nuclei without encountering the repulsion of the electrons in the bonding orbitals. When a difference orbital is used, electron density is removed from the region between the bonding pairs.With the addition of off-axis gaussians (as in the most successful model C) the lone pair orbital is now able to spread spatially to be nearer to all the nuclei, including the protons, and yet not come too close to the bonding pairs for repulsion to increase, and off-set completely the gain in attraction energy. It can be said therefore that the lone pair orbital in model C experiences the attractive forces of all three positive centres, and thus has some bonding effect ; more than the lone pair does in the simple FSGOmodel where it remains predominantly in the field of the heavy nucleus only and is essentially non-bonding. A further analysis has been carried out in which the various energy terms are divided into the electronic contributions from the different orbitals. In order to avoid the appearance of the three- and four-centred electron interaction terms, which are inevitable when non-orthogonal orbitals are used and which are difficult to interpret, the integrals in terms of the Lowdin orthogonal orbitals have been used.The energy terms then reduce to the one-centred kinetic energy and nuclear-electron attraction terms, the one-centred Coulomb repulsion integrals and the two-centred Coulomb and Exchange integrals. The figures in table 3 confirm that it is indeed the gain in nuclear attraction of the electrons in the lone pair orbital that contributes most to the total increase in the nuclear attraction energy shown in the graph in fig. 4. The bonding electrons also experience a similar, though smaller, increase in the nuclear attraction energy.The inner shell orbital has lost some attraction energy as the models increase in complexity from the simple FSGO model to model C. The Lowdin orbital energies for the inner shell, bonding and lone pair orbitals are listed in table 4 for the different models. They refer to a pair of electrons in the orbital and have been calculated in the following way. The kinetic energy, the nuclear attraction energy, and the intra- and inter-orbital electron4ectron repulsion energy are summed for each orbital. The electron-electron repulsion energy between electrons in two orbitals is the sum of the appropriate Coulomb and Exchange integrals and is shared equally between the two orbitals.The sum of the Lowdin orbitaI energies is therefore equal to the electronic energy of the molecule. Table 3 shows that the Lowdin orbital energy for the lone pair is lower than that for the bonding L. P. TAN AND J. W. LINNETT orbital (larger negative number). This is perhaps a consequence of the fact that the lone pair orbital has more carbon 2s character than does the bonding orbital. The lone pair orbital energy does not change greatly for the different models though the component parts of that energy do change considerably. A possible explanation of the constancy of this orbital energy may be that, in the simple FSGO model, the lone pair orbital acquires the lowest energy by remaining as essentially the more stable TABLE3.-INDIVIDUAL INTEGRALS (IN i3.U.) FOR THE OTHOGONAL LOWDIN ORBITALS FOR THE DIFFERENT MODELS FOR CH2 model simple FSGO A B C one electron integrals KE (bib) 0.656 0.670 0.676 0.672 NA (bib) -4.622 -4.677 -4.724 -4.754 KE (klk) 14.480 14.403 14.396 14.358 NA (klk) -30.302 -30.290 -30.279 -30.239 KE (111) 0.692 0.780 0.779 0.878 NA (41) -5.146 -5.262 -5.259 -5.432 two electron integrals (i) one centre Coulomb (bbIbb) 0.675 0.680 0.682 0.674 (kklkk) 3.443 3.445 3.441 3.437 (11I10 0.638 0.676 0.671 0.695 (ii) two centre Coulomb and exchange (bblb’b’) 0.400 0.404 0.403 0.403 (bb’l b’b) 0.017 0.01 8 0.018 0.020 2(bbl b’b’)-(bb’l b’b) 0.783 0.789 0.787 0.787 (bblkk) 0.563 0.575 0.580 0.589 (bklkb) 0.004 0.005 0.005 0.005 2(bbl kk)-(bklkb) 1.121 1.146 1.155 1.174 (bbI w 0.407 0.414 0.420 0.41 8 (blI w 0.020 0.019 0.021 0.01 8 2(bblll)-(blllb) 0.795 0.810 0.818 0.818 (kkI w 0.737 0.755 0.752 0.782 (klI lk) 0.008 0.007 0.007 0.009 2(kk Ill)-(kl Ilk) 1.466 1.503 1.498 1.555 b, k and I refer to the orthogonal bonding, inner-shell and lone pair orbitals respectively.2s orbital on the carbon atom. With increasing flexibility in the lone pair description, the lone pair orbital can acquire increasing p-type character to form a hybridised orbital which is able to “spread” more widely over the molecule. This would explain the increase in the nuclear attraction energy experienced by the lone pair orbital. It appears that this effect is about sufficient to offset the loss in energy due to a decrease in s-character.Though these changes have not produced a lowering cifthe lone pair orbital energy, they have produced a lowering of the bonding orbital energy and this could be due to their assuming more carbon 2s-character. The changes in the inner-shell orbital energy are regular and not easy to interpret, Because these orbitals do not possess a cusp at the nucleus it is probable that these changes are not of any real significance. 2240 APPLICATIONS OF A SIMPLE MOLECULAR WAVEFUNCTION So far the results have been considered in terms of localised valence bond type orbitals. Alternatively, these can be transformed into the molecular orbitals which reflect the symmetry of the whole molecule. An analysis can be carried out within this formulation.The energies of the lal, 2al, lb, and 3al molecular orbitals are shown in table 5. The energy of the lowest, lal, molecular orbital rises as more gaussians are introduced to represent the lone pair orbital. The energy of the highest occupied orbital, 3al, falls in the same sequence. Of the other two, the 2al orbital rises slightly in energy while the lb, falls slightly. The lal orbital is primarily the TABLE4.-LOWDIN ORBITAL ENERGIES/a.U. model simple FSGO A B C total energy bond angle -32.965 91.5' -33.046 94.9" -33.053 98.9' -33.164 103.5" inner-shell orbital nuclear at traction -60.603 -60.580 -60.557 -60.478 kinetic energy electron repulsion intra-orbital 28.960 7.150 3.443 28.805 7.240 3.445 28.792 7.250 3.441 28.716 7.338 3.437 inter-orbital 3.707 3.795 3.809 3.901 orbital energy -24.493 -24.535 -24.515 -24.424 bonding orbital nuclear at traction -9.245 -9.395 -9.448 -9.509 kinetic energy electron repulsion intra-orbital 1.312 3.374 0.675 1.340 3.426 0.680 1.351 3.443 0.682 1.344 3.452 0.674 inter-orbital 2.699 2.746 2.761 2.778 orbital energy -4.559 -4.629 -4.654 -4.713 lone pair orbital nuclear at traction -10.293 -10.523 -10.518 -10.864 kinetic energy electron repulsion intra-orbital 1.384 3.693 0.638 1.560 3.800 0.676 1.559 3.806 0.671 1.756 3.885 0.695 inter-orbital 3.055 3.124 3.135 3.190 orbital energy -5.215 -5.164 -5.153 -5.223 nuclear repulsion 5.861 5.911 5.923 5.909 1s orbital on the carbon atom and, in all these models, lacks the cusp it should have at the nucleus.Consequently the changes in energy may not correspond to reality. The 2al orbital consists in part of the two bonding and the lone pair orbitals. The carbon contribution to this will be largely 2s. The 3alorbital will be largely 2p as far as the contribution of the carbon atom is concerned (this being the 2p orbital which is symmetric about the molecular symmetry axis). It is this 2p orbital that has been improved by the addition of more gaussian functions and so it is hardly surprising that the energy of this orbital is lower for model C than for the FSGO model. The lbz orbital change in energy is much less. It involves the other carbon 2p orbital and the description of this has not changed as a result of the additional gaussian functions added to the FSGO model.Estimates of the first ionisation potential of singlet CH2 can be obtained from the energy of the highest occupied orbital using Koopmans' theorem.1° The simple L. P. TAN AND J. W. LINNETT 2241 FSGO model predicted an ionisation potential of 7.3eV which is too low (observed 10.40 eV 5). As the lone pair orbital is improved by the addition of more gaussian functions the ionisation potential is improved. For model C it becomes 9.26 eV. TABLE5.-MOLECULAR ORBITAL ENERGIES FOR CH, (IN a.U.) model simple FSGO A B C 1a1 -9.164 -9.073 -9.063 -8.973 2a 1 -0.793 -0.768 -0.765 -0.753 1b2 -0.391 -0.385 -0.393 -0.408 3a1 -0.270 -0.302 -0.296 -0.340 I.P./eV (expt 10.4) 7.3 8.2 8.1 9.3 This improvement is to be expected as the modifications that have been made go to improve the carbon 2p-component part of this orbital (see above).CONCLUSION The inadequate description of the lone pair orbital in the simple FSGO model is shown to be responsible for the poor bond angles predicted for CH2 and NH,.4 The lone pair orbitals in these molecules can be modified to produce satisfactory bond angles by using a pair of axial gaussian functions combined with opposite sign to give p-character and a set of off-axial gaussians located eclipsed to the CH or NH bonds. Adopting the concept of hybridisation of atomic orbitals it appears that the simple FSGO model predicts low bond angles because the lone pair orbital (by virtue of its single gaussian representation which is therefore spherical) remains essentially 2s in character.As a result the bonding orbitals are essentially pure p Nin character so that bond angles of 90" are obtained. The increased flexibility allows the lone pair orbital to accommodate some p-character, so that the bonding orbitals gain some s-character to form hybridised orbitals which give more accurate bond angles. One of us (L. P. T.) wishes to thank the Commonwealth Scholarship Commission and the Universiti Sains Malaysia for financial assistance. A. A. Frost, J. Chem. Phys., 1967, 47, 3707, 3714. A. A. Frost and R. A. Rouse, J. Amer. Chem. Soc., 1968, 90,1965. A. A. Frost, J. Chem. Phys., 1968, 72, 1289. L. P. Tan and J. W. Linnett, J.C.S. Chem. Comm., 1973, 736. G. Herzberg, Electronic Spectra of Polyatomic Molecules (Van Nostrand, Princeton, 1966). P. 0. Lowdin, J. Chem. Phys., 1950, 18, 365.'M. Afzal and A. A. Frost, Int. J. Quantum Chem., 1973, 7,51. B. C. Carlson and J. M. Keller, Phys. Rev., 1957, 105, 102. R. A. Suthers and J. W. Linnett, Chem. Phys. Letters, 1974, 29, 589. loT. A. Koopmans, Physica, 1933, 1, 104. S. Y. Chu and A. A. Frost, J. Chem. Phys., 1971, 54,760. (PAPER 6/612) 11-71

ISSN:0300-9238    

DOI:10.1039/F29767202233

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

B3n(O+)States of IF, IC1 and IBr Part 1.-Calculation of the RKR Turning Points and Franck-Condon Factors for the B-X Systems BY MICHAEL AND I. STUARTA. A. CLYNE* MCDERMID Department of Chemistry, Queen Mary College, University of London, Mile End Road, London El 4NS Received 6th Maj), 1976 Values of the spectroscopic constants for the B3rI(O+)-X'Z+ systems of IF, IC1 and IBr have been evaluated and used to determine the RKR turning points for the B311(O+)and X'C+ states of the iodine monohalides. The RKR potential functions have been used to calculate r-centroids and Franck-Condon factors for the B-X systems. Accurate potential energy curves for the B31T(O+)and XIE+ states of the iodine monohalides do not appear to be available ; nor are Franck-Condon factors available for the corresponding B-X band systems of IC1 and IBr.Since this information is important, e.g. when interpreting a spectroscopic study by laser induced fluorescence, we have calculated the RKR turning points and Franck-Condon factors as a preface to such a study.' The Franck-Condon factor is defined by eqn (1) and the r-centroid by eqn (2) F,,,,,. = 1)~~1c/~~~dr/lm1c/,,m,buIp 1:dr 0 where and are the vibrational wavefunctions, or solutions of the radial Schrodinger equation, for levels v' and v" of the excited and ground states respectively. Coxon's programs,2 and the University of London CDC 6600 computer, were used. RESULTS AND DISCUSSION SPECTROSCOPIC CONSTANTS FOR IF, 135~1AND 179~r In order to calculate the RKR turning points and the Franck-Condon factors for the B311(O+)-XIX+ systems of the iodine monohalides, a critical assessment of the existing spectroscopic data was made.The preferred values for the relevant constants are shown in table 1. The major uncertainties are in the dissociation energies of both states of IF, and in the values of Be and wefor the excited states of IC1 and IBr. Selin's * extrapolations (from v' = 2) for IBr B 'rI(O+) were used to find Bd and a;. The excited B state of ICl is even more strongly perturbed than that of IBr, and this very shallow state shows large variation (with v') in both B;, and in the spacing of the vibrational levels. The present work gives the first data on the level v' = 0, now enabling reliable values of a;and Bd to be obtained (table 1).Eqn (3) and (4) were 2242 M.A. A. CLYNE AND I. S. MCDERMID 2243 The values for the constants were derived from Hulthh (v’ = 1-3) and from our work ’ (u‘ = 0) ; they are given in Part 2.’ TABLE SPECTROSCOPIC CONSTANTS1.-EVALUATED IF I35C1 179~r quantity X‘Z+ B3/1(0+)a X’Z. b PIr(O+)bod xlZ+c ~311(0+) units We 610.03 e 406.51 384.293 204.5 268.71 142 cni-* Wexe 3.10e 1.30 1.501 2.595 0.83 2.6 cm-WeYe -0.004 95 e -0.198 -0.937 --0.1 cm-’ Be 0.2799 a 0.2272 0.114 154 0.087 05 0.056 788 0.0132 cm-’ Ee 0.001 S87a 0.001 398 0.000 533 6 0.002 00 0.000 199 0.0005 cm-I Ye -0.000 00s -0.000 082 0.000 001 2 0.000 43 im-l1.9089 a 2.1189 2.318 68 2.657 2.4699 2.83 -19 054 -17 375.4 -16 165 cni-‘ De 22 99s d 11 544d 17 557.5 1063.8 14793e 2314 cm-’ a D~rie,~h HulthCn et a1 ;6y12 C Selin :’9 l3 d this work (Part 2 l) ; e COXO~.~ Whilst the vibrational constants for the ground XIX+ states of IC1 and IBr l3 are well-known, short extrapolations (see above) were necessary to find w: for both ICl and IBr. The uncertainty in co; values is quite small.For IF, Coxon’s reinterpreted values of a;,O”X; and airy; from Durie’s work have been adopted in preference to those given by Durie him~elf.~ This enables a reliable extrapolation to be made of the ground state vibrational levels up to u” = 15. For the B ”n(O+) state of IF, Durie’s vibrational constants were sufficiently accurate to represent the vibrational energy levels n(k < 10 cm-’) up to U’ = 11. Larger errors than 10cm-l would be introduced into the potential energy functions of IF by residual uncertainty in D:.The dissociation energies of the interhalogens have been the subjects of much discussion. The upper B311(O+)states are perturbed by interactions with repulsive ‘ diabatic Of It is, therefore, not possible to place any reliance on a Birge- Sponer extrapolation of the B state, unless B-X bands (u’, u”) are observed to v’ levels above the crossing region and with v” ground state vibrational numbering determined unequivocally. Unfortunately this is not so for the iodine monohalides. However, in the case that the A311(l)-X1Z+ system, which dissociates to two ground state ’P3atoms, is observed, the convergence limit of the ground state can be obtained from a Birge-Sponer extrapolation of the A state levels.With the recent observation of an emission spectrum assigned to the A311(l) state of IF by Birks, Gabelnick and John~ton,~ this information is now available for all three iodine monohalides. The results on the A-X system indicate that the B311(O+)state of IF should correlate diabatically with I’P+ +F’P+ and not with 12P++ F2P, as originally suggested by D~rie.~ Unfortunately, for the A311(l) state of IF, a long extrapolation of the vibrational levels is needed to find 0:.However, the ground state dissociation energy, D:,can nevertheless be estimated usefully in this way. Coxon considered that Durie’s predissociation at 23 341 cm-1 and extrapolation of Birks’ data on the A311(l)-X1C emission spectrum, fixed the dissociation energy, D;,between the values 23 100 < D,(IF) < 23 341 cm-’ ; and that the dissociation energy D; obtained by taking the mean of these values is, therefore, (23 520+ 120) cm-’. 2244 ~3n(0+)STATES OF INTERHALOGENS Results of a laser fluorescence study of IF (described in Part 2 I) indicate that predissociation of the B state commences at an energy of (22 998 20) cm-1 above the potential minimum of the ground state.This result will be discussed in detail in Part 2. We summarize the conclusions of that work by stating that the preferred value for D; of IF is 22 998 cm-l, and that this value is not inconsistent with the extrapolation of the A3n(1) state vibrational levels.The dissociation energies of ground state IC1 and IBr are known much more precisely (to within a few wavenumbers) from short extrapolations of their A311(l)-X'C+ absorption systerns.l2* I3 To determine the dissociation energies, DL of the excited B31T(O+)states, the following relationship was used, Dd = DI+E-Te where E is the spin orbit atomic excitation energy of the relevant halogen, E(2P,-'P+)(F = 404 cm-l, C1 = 881 cm-l, Br = 3685 cm-l, I = 7598 cm-' 14). Since T, can be determined from T, = voo -G'(0) +G"(0) and G(0) = 42 -oex,/4+ w,j1,/8, DL for the B311(O+)states can be found. 30 25 2c r( IE .2 15n W s 10 5 0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 rlA FIG.1.-Morse curves for IF; (a)1 'P++F2P+ (b)I 'Pt +F2P+ The values given for 0:in table 1 are the dissociation energies of B311(O+)states unperturbed by avoided crossing with the O+ repulsive states.The value of Db for ICI reported recently by Birks et aL5 (799 cm-') appears to be a misprint. M. A. A. CLYNE AND I. S. MCDERMID POTENTIAL ENERGY FUNCTIONS Tables 2, 3 and 4 summarize the vibrational energies and RKR turning points calculated for the B and X states of IF, IC1 and IBr. Near the potential minima, the corresponding Morse functions (see below) agree closely with the RKR functions. In order to summarize the entire range of the potential curves, including the limited energy ranges where enough data to calculate RKR curves were available, the Morse functions were evaluated, as shown in fig.1, 2 and 3 : U(r)= De{l-exp [-P(r-re>])’+Te; fl = 1.2177x lo7.ue(p/De)*. 22 20 18 16 14-k 12 m E: 13 10 b 8 6 4 I2 0 2.0 3.0 4.0 5.O 6.O rlA FIG.2.-Morse curves for 13W; (a)12P++CI2P+; (b)12Q+C12P+. The avoided crossings of the B states of IF, IC1 and IBr with the 0’ repulsive states are shown schematically in fig. 1, 2 and 3. The energies of the crossing points are based on the present results (part 2 l) for IFand ICl, and on the work of Selin 7* for IBr. There is uncertainty about the exact locations and nature of the interactions, and it is one of the aims of the present study to investigate them further. FRAN cK-C 0NDON FACTORS The results of the Franck-Condon factor computations for rotationless states, using the RKR potential energy functions, are listed in tables 5, 6 and 7.The range 20 18 16 14 Ti 123 22 10 22,3 8 6 4 2 0 2.0 3.0 4.0 5.0 6.O rlA FIG.3.-Morse curves for 179Br; (a) 12Ps+Br2P+; (6) l2P9+Br2P+. TABLE2.-RKR TURNING POINTS FOR IF ---_ X1Z'- __-- ~3n(0+)- 0 C(o) rrnin rmax G(u) rmin rmax 0 304.3 1.8542 1.9701 203.O 2.0514 2.1934 1 908.1 1.8173 2.0190 606.3 2.0063 2.2530 2 1505.7 1.7936 2.0550 1005.2 1.9773 2.2973 3 2097.0 1.7753 2.0860 1398.5 1.9550 2.3360 4 2682.0 1.7601 2.1140 1785.1 1.9367 2.3717 5 3260.8 1.7470 2.1400 2163.7 1.9210 2.4060 6 3833.1 1.7355 2.1647 2533.1 1.9072 2.4397 7 4399.1 1.7252 2.1884 2892.3 1.8949 2.4733 8 4958.6 1.7158 2.21 12 3239.9 1.8836 2.5072 9 551 1.7 1.7072 2.2335 3574.9 1.8729 2.5422 10 6058.3 1.6994 2.2553 3895.9 1.8630 2.5783 11 6598.4 1.6920 2.2767 4201.9 1.8534 2.6158 12 7132.0 1.6851 2.2978 13 7659.0 1.6788 2.3 187 14 8179.5 1.6728 2.3394 15 8693.3 1.6672 2.3600 M.A. A. CLYNE AND I. S. MCDERMID of u” is 11 u” >, 0 for IF, representing the energy range where the vibrational and rotational constants have been experimentally determined.4 No accurate data for the higher v” levels of the XIX+states of ICl and IBr are available; but the extra- polations of the constants up to v” = 11 (ICl) and v” = 7 (IBr) should be reliable.TABLE3.-RKR TURNINGPOINTS FOR 13Tl XlZ+ ~317(0+) 2, G(u) rmin rmax G(u) rmin rmax 0 191.77 2.26680 2.38012 101.5 2.5902 2.7484 1 573.06 2.22973 2.42666 297.8 2.5482 2.8261 2 951.35 2.20591 2.46099 480.4 2.5225 2.8918 3 1326.6 2.1871 2.4900 643.9 2.5050 2.9629 4 1698.9 2.1713 2.5158 5 2068.2 2.1574 2.5396 6 2434.5 2.1453 2.5622 7 2797.8 2.1343 2.5837 8 3158.0 2.1241 2.6041 9 3515.3 2.1147 2.6239 10 3869.6 2.1058 2.6430 11 4220.9 2.0975 2.6617 12 4569.1 2.0897 2.6800 13 4914.4 2.0822 2.6979 14 5256.7 2.0751 2.7155 15 5595.9 2.0684 2.7328 16 5932.2 2.0619 2.7500 17 6265.5 2.0557 2.7669 18 6595.7 2.0497 2.7837 19 6923.0 2.0440 2.8003 20 7247.2 2.0384 2.8169 TABLE4.-RKR TURNING POINTS FOR XIZ+ ~3n(0+) 0 C(4 rmin rmax C(u> rmin rmX 0 134.14 2.42112 2.52281 70.6 2.7684 2.9089 1 401.19 2.38760 2.5641 9 207.8 2.7281 2.9756 2 666.58 2.36554 2.5941 1 338.3 2.7026 3.0291 3 930.31 2.3481 9 2.61935 462.4 2.6831 3.0778 4 1192.4 2.3335 2.641 8 579.0 2.6671 3.1263 5 1452.8 2.3208 2.6625 679.5 2.6476 3.1853 6 1711.5 2.3095 2.6820 7 1968.6 2.2991 2.7002 The agreement of the FC factors for IF B-X with those reported (for u’ < 8) by Birks et aL5 is good for bands possessing high Franck-Condon factors.Even for bands with low Franck-Condon factors, agreement is generally within a factor of two. This suggests that the computations are not sensitive to the precise values of the spectroscopic constants used, since presumably Birks et al.used the data of Durie rather than the later values of C~xon.~ The present results for the FC factors of the B-X systems of IF, ICI and IBr will be discussed in relation to experimental studies of laser fluorescence in these molecules. TABLEs.-cALCULATED BAND ORIGINS/VaC Cm-’, FRANCK-CONDONFACTORS (qvt,orr) AND U-CENTROIDSIAFOR THE B3lI(O+)-XICf SYSTEM OF l2’Il9F, J’ = J” = 0 V‘/VII 0 1 2 3 4 5 0 18 954.20 18 351.15 17 753.57 17 161.79 16 576.14 15 996.96 0.004 82 0.029 32 0.085 23 0.156 79 0.204 45 0.200 57 2.0067 2.0306 2.0550 2.0798 2.1052 2.13 13 1 19 357.46 18 754.41 18 156.83 17 565.05 16 979.40 16 400.22 0.022 20 0.089 27 0.149 15 0.120 36 0.033 02 0.002 13 1.9908 2.0142 2.0378 2.0615 2.0845 2.1270 2 19 756.35 19 153.30 18 555.72 17 963.94 17 378.29 16 799.11 0.053 48 0.132 00 0.099 39 0.008 60 0.028 59 0.096 83 1.9753 1.9981 2.0208 2.0404 2.0728 2.0955 3 20 149.66 19 546.61 18 949.03 18 357.25 17 771.60 17 192.42 0.089 97 0.121 29 0.019 28 0.0246 8 0.085 12 0.028 85 1.9602 1.9826 2.003 1 2.0320 2.0534 2.0749 4 20 536.22 19 933.17 19 335.59 18 743.81 18 158.16 17 578.98 0.119 23 0.071 50 0.002 91 0.073 85 0.030 74 0.010 46 1.9456 1.9675 1.9987 2.0144 2.0350 2.0669 5 20 914.83 20 311.78 19 714.20 19 122.42 18 536.77 17 957.59 0.133 21 0.022 34 0.038 28 0.055 91 0.001 02 0.059 88 1.9315 1.9526 1.9780 1.9982 2.0393 2.0462 6 21 284.30 20 681.25 20 083.67 19 491.89 18 906.24 18 327.06 0.130 92 0.000 56 0.066 63 0.011 78 0.035 50 0.038 64 1.9178 1.9353 1.9631 1.9311 2.0094 2.0287 7 21 643.46 21 040.41 20.442 83 19 851.05 19 265.40 18 686.22 0.116 60 0.007 83 0.060 50 0.001 55 0.054 05 0.001 63 1.9046 1.9268 1.9494 1.9821 1.9938 2.0012 8 21 991.10 21 388.05 20 790.47 20 198.69 19 613 04 19 033.86 0.095 95 0.030 78 0.032 78 0.023 80 0.030 80 0.012 83 1.8918 1.9132 1.9367 1.9604 1.9791 2.0074 v‘lv” 0 1 2 3 4 5 9 22 289.05 21 686.00 21 088.42 20 496.64 19 910.99 19 331.81 0.074 05 0.054 47 0.008 04 0.044 94 0.004 17 0.038 10 1.8793 1.NO5 1.9263 1.9469 1.9629 1.9912 10 22 647.11 22 044.06 21 446.48 20 854.70 20 269.05 19 689.87 0.054 22 0.069 83 0.000 03 0.045 29 0.002 63 0.036 73 1.8673 1.8883 1 A433 1.9349 1.961 1 1.9778 11 22 953.10 22 350.05 21 752.47 21 160.69 20 575.04 19 995.86 0.037 93 0.074 38 0.008 18 0.029 09 0.019 24 0.015 73 1.8554 1.8767 1.8940 1.9243 1.9457 1.9653 M.A. A. CLYNE AND I. S. MCDERMID 2249 TABLE5 .-contd. UI/d’ 6 7 8 9 10 11 0 15 424.59 14 859.37 14 301.63 13 751.70 13 209.92 12 676.63 0.153 28 0.093 36 0.045 88 0.018 31 0.005 98 0.001 60 2.1581 2.1860 2.2150 2.2454 2.2774 2.3 112 1 15 827.85 15 262.63 14 704.89 14 154.96 13 613.18 13 079.89 0.063 43 0.140 02 0.157 75 0.118 29 0.065 02 0.027 38 2.1417 2.1676 2.1952 2.2241 2.2545 2.2865 2 16 226.74 15 661.52 15 103.78 14 553.85 14 012.07 13 478.78 0.068 12 0.004 11 0.027 92 0.109 42 0.147 87 0.1 19 01 2.1192 2.1342 2.1802 2.2052 2.2335 2.2638 3 16 620.05 16 054.83 15 497.09 14 947.16 14 405.38 13 872.09 0.007 77 0.075 23 0.068 92 0.006 05 0.024 84 0.106 28 2.1110 2.1300 2.1538 2.1699 2.21 87 2.2438 4 17 006.61 16 441.39 15 883.65 15 333.72 14 791.94 14 258.65 0.070 40 0.027 56 0.007 49 0.071 71 0.058 85 0.002 04 2.0863 2.1073 2.1473 2.1649 2.1889 2.1926 5 17 385.22 16 820.00 16 262.26 15 712.33 15 170.55 14 637.26 0.023 20 0.013 31 0.064 42 0.016 40 0.015 69 0.074 82 2.0662 2.1000 2.1194 2.1385 2.1801 2.2005 6 17 754.69 17 189.47 16 631.73 16 081.80 15 540.02 15 006.73 0.004 74 0.055 83 0.010 10 0.024 86 0.056 89 0.004 11 2.0626 2.0781 2.0954 2.1324 2.1528 2.1626 7 18 113.85 17 548.63 16 990.89 16 440.96 15 899.18 15 365.89 0.042 87 0.019 41 0.016 20 0.479 7 0.000 66 0.041 40 2.0402 2.0587 2.0914 2.1104 2.0986 2.1656 8 18 461.49 17 896.27 17 338.53 16 788.60 16 246.82 15 713.53 0.039 29 0.001 93 0.045 59 0.003 47 0.033 10 0.030 45 2.0238 2.0628 2.0715 2.0832 2.1232 2.1423 9 18 759.44 18 194.22 17 636.48 17 086.55 16 544.77 16 011.48 0.007 45 0.029 89 0.017 62 0.015 90 0.034 56 0.001 29 2.0051 2.0363 2.0531 2.0853 2.1033 2.1 556 10 19 117.50 18 552.28 17 994.54 17 444.61 16 902.83 16 369.54 0.002 38 0.036 32 0.000 35 0.037 60 0.001 49 0.032 85 2.01 23 2.0209 2.0822 2.0670 2.0718 2.1168 11 19 423.49 18 858.27 18 300.53 17 750.60 17 208.82 16.675.53 0.021 24 0.013 78 0.019 11 0.017 62 0.013 02 0.026 37 1.9909 2.0055 2.0351 2.0500 2.0821 2,0984 2250 ~3n(0+)STATES OF INTERHALOGENS 6.-BAND ORIGINS/VaC Cm-l, FRANCK-CONDONTABLE FACTORS (qui,utf)AND !‘-CENTROIDS/A FOR THE B311(O+)-XIZ+ SYSTEM OF 127135Cl,J’ = J” -0-v’lv” 0 1 2 3 4 5 0 17 283.57 16 902.28 16 523.99 16 148.70 15 776.42 15 407.13 8 .exp-7 2.4724 0.000 01 2.4882 o.oO0 12 2.5040 0.000 63 2.5199 0.002 47 2.5359 0.007 48 2.5522 1 17 479.87 17 098.58 16 720.29 16 345.00 15 972.72 15 603.43 6 .exp-6 2.4643 0.000 09 2.4800 0.000 67 2.4957 0.003 09 2.51 14 0.010 14 2.5273 0.025 07 2.5432 2 17 662.47 17 281.18 16 902.89 16 527.60 16 155.32 15 786.03 0.000 02 0.000 32 0.002 05 0.008 12 0.022 15 0.043 97 2.4568 2.4724 2.4880 2.5036 2.5192 2.5349 3 17 825.97 17 444.68 17 066.39 16 691.10 16 318.82 15 949.53 O.OO006 0.000 75 0.004 17 0.014 15 0.032 12 0.050 56 2.4500 2.4656 2.48 1 1 2 A966 2.5121 2.5276 u’lv’* 6 7 8 9 10 11 0 15 040.85 14 677.57 14 317.30 13 960.02 13 605.75 13 254.48 0.018 32 0.037 11 0.063 15 0.091 98 0.116 85 0.130 87 2.5687 2.5855 2.6027 2.6203 2.6382 2.6563 1 15 237.15 14 873.87 14 513.60 14 156.32 13 802.05 13 450.78 0.048 26 0.072 98 0.086 01 0.077 06 0.048 79 0.016 85 2.5594 2.5759 2.5928 2.6099 2.6273 2.6444 2 15 419.75 15 056.47 14 696.20 14 338.92 13 984.65 13 633.38 0.064 23 0.067 13 0.045 48 0.014 20 0.000 08 0.014 99 2.5508 2.5669 2.5831 2.5990 2.7139 2.6384 3 15 583.25 15 219.97 14 859.70 14 502.42 14 148.15 13 796.88 0.053 78 0.033 90 0.007 17 0.001 58 0.022 20 0.04238 2.5431 2.5585 2.5726 2.6007 2.61 18 2.6284 TABLE7.-BAND ORIGINS/VaCCII1-l , FRANCK-CONDON AND Y-CENTROIDS/bi FOR THE(gut,t)ff) SYSTEM OF 127179~~~~3r1(0+)-X~X+ J’ = J” = 0 d/u’* 0 1 2 3 4 5 6 7 0 16 101.55 15 834.50 15 569.11 15 305.38 15 043.31 14 782.90 14 524.15 14 267.06 7.exp-9 1 .exp-7 1 .exp-6 0.000 01 0.000 05 0.000 22 O.OO0 76 0.002 29 2.6166 2.6320 2.6468 2.6613 2.6754 2.6893 2.7030 2.7168 1 16 238.73 15 971.68 15 706.29 15442.56 15 180.49 14 920.08 14 661.33 14 404.24 9.exp-8 2.exp-6 0.000 01 0.000 09 0.000 39 0.001 39 0.004 16 0.010 53 2.6088 2.6243 2.6393 2.6539 2.6682 2.6820 2.6957 2.7092 2 16 369.23 16 102.18 15 836.79 15 573.06 15 310.99 15 050.38 14 791.85 14 534.74 6.exp-7 0.000 01 0.000 07 0.000 40 0.001 56 0.004 79 0.012 04 0.025 14 2.6012 2.6169 2.6321 2.6469 2.6612 2.6752 2.6888 2.7021 3 16 493.27 16 226.22 15 960.83 15 697.10 15 435.03 15.174.62 14 915.87 14 658.78 3.exp-6 0.000 04 0.000 30 0.001 34 0.004 46 0.011 58 0.024 17 0.040 71 2.5939 2.6098 2.6252 2.6402 2.6547 2.6687 2.6824 2.6956 4 16 609.87 16 342.82 16 077.43 15 813.70 15 551.63 15 291.22 15032.47 14 775.38 0.000 01 O.OO0 15 0.000 89 0.003 48 0.009 89 0.021 48 0.036 50 0.047 95 2.5871 2.6031 2.6187 2.6338 2.6485 2.6627 2.6765 2.6897 5 16 710.41 16 443.36 16 177.97 15914.24 15 652.17 15 391.76 15 133.01 14 875.92 O.OO0 04 0.000 41 0.002 13 0.007 16 0.017 25 0.031 04 0.042 06 0.041 14 2.5805 2.5971 2.6128 2.6281 2.6429 2.6574 2.6713 2.6845 M.A. A. CLYNE AND I. S. MCDERMID 2251 M. A. A. Clyne and I. S. McDermid, Part 2. J.C.S. Faraday 11, 1976, 72,2252. ’J. A. Coxon, J. Quant. Spectr. Rad. Trans., 1971, 11,443. J. A. Coxon, Chent. Phys. Letters, 1975, 33, 136. R. A. Durie, Canad. J. Phys., 1966, 44, 337. J. W. Birks, S. D. Gabelnick and H. S. Johnston, J. Mol. Spectr., 1975, 57, 23. E. HulthCn, N. Jarlsater and L. Koffman, Arkiv Fysik, 1960, 18,479. ’L. E. Selin and B. Soderborg, Arkiv Fysik, 1962, 21, 515. L. E. Selin, Arkiu Fysik,1962, 21, 529. W. G. Brown and G. E. Gibson, Phys. Rev., 1932, 40, 529. lo M. A. A. Clyne and J. A. Coxon, Proc. Roy. SOC.A, 1967,298,403. l1 M. S. Child and R. B. Bernstein, J. Chem. Phys., 1973, 59, 5916; M. S. Child, Mol. Phys., 1976, in press. l2 E. Hulthh, N. Johansson and U. Pilsater, Arkiu Fysik, 1958, 14, 31. l3 L. E. Selin, Arkiv Fysik, 1962, 21,479. l4 C. E. Moore, Atomic Energy Leuel Tables (Nat. Bur. Stand. Circular 467, 1958). (PAPER 6/860)

ISSN:0300-9238    

DOI:10.1039/F29767202242

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

B311(Of)States of IF, IC1 and IBr Part 2.-Observation and Analysis of the Excitation Spectra of IF and ICl BY MICHAEL A. A. CLYNE* AND I. STUART MCDERMID Department of Chemistry, Queen Mary College, University of London, Mile End Road, London El 4NS Received 6th May, 1976 Narrow band tunable radiation from a nitrogen pumped dye laser has been used to excite fluorescence in the B311(O+)-X1C+systems of IF (430 to 500nm) and of ICl (568 to 650nm). The kinetically labile IF molecules were produced in a fast flow system by the rapid elementary reaction F+ICl+ IF+Cl. No laser excitation or absorption spectrum of IF has been described previously. Onset of pre-dissociation has been observed at J’ = 12, v’ = 10of IF B3n(O+),and a new value for the dissociation energy of IF, Dg (IF) < (22 700t 15) cm-’, is reported.Criteria for the commencement of pre-dissociation in IF spectra are discussed. The mechanism of formation of the B and A states of IF in F2+I2 systems is considered to arise from initial production of IIF, in the elementary step, I2+F2+IIF+ F. Laser fluorescence of IC1 from the excited B3H(O+)state (v’ = 0, 1, 2) has been observed. The 0-2 band of the B-X system of 135Cl has been analysed, providing the first spectro- scopic constants for the level v‘ = 0 of the B state. A complete evaluation of constants for this shallow, weakly-bound state, has thus been possible. The onset of predissociation in ICl B3rj(O+) near J’ = 70 of v‘ = 2 is discussed in the light of linewidth measurements of other workers.The spectroscopy of the ground and low lying states of the diatomic halogens and interhalogens is well established. This should facilitate detailed lifetime studies of these excited states, as a function of quantum state. However, of the possible molecules, detailed lifetime measurements have been reported only for the excited B311(0,f)state of 12,2aand very recently, for Br2.26 Recombination of halogen atoms leads to formation of low lying excited molecular states of halogens (Br2, Cl,) and interhalogens (BrCl, ICl, IBr), which emit chenii- luminescence. Knowledge of predissociative, radiative and collisional lifetimes 9 of these states is essential to the understanding of these prototype recombination reactions. The extensive photochemistry of the halogens and interhalogens is another area in which excited state studies are required.One example of this is the scheme of Datta, Anderson and Zare for laser separation of chlorine isotopes using ICl(A-X). The present series of studies on iodine monohalides, whose spectra have comparatively simple isotopic structure, is intended to provide systematic data on their excited states. In this part of the work, we report the first observation of laser excitation fluorescence spectra of the B-X transitions of IF and IC1. New spectro- scopic data on the B311(O+)state of IC1 are reported, and predissociations in the B states of ICl and IF are studied in detail. In a succeeding paper,6 we shall report quantitative lifetime data for the excited B state molecules.The diatomic halogen and interhalogen molecules, except F2, all possess discrete spectra in the visible region, corresponding to transitions between the XIE+ ground states and the B311(O+)or A311(l) excited states. The excited states approximate to Hund’s case (c), and the energy splitting between the A and B states increases with 2252 M. A. A. CLYNE AND I. S. MCDERMID molecular weight. The lower lying A state is unperturbed and dissociates to two ground state 'P+halogen atoms. Bands of the A-X system are readily identifiable in that they each contain one P, Q and R bran~h.~The observed B-X absorption bands are either overlapped by A-X bands (as for ICl), or lie at appreciably shorter wavelengths than the A-X bands (as for 12). The B-X bands show a simple PR struct~re.~ The excited B3TZ(O+)states of the interhalogens correlate diabatically to one 'P+ atom and one excited 'P, atom.For all the B states except that of ClF, it is definitely known which halogen atom is excited : IF (12P,+F2P&;8* BrF(Br2P,+F2P+) ;', lo ICl(12P++C12P+) ;l1, l2BrCl (Br2P3+C12P+) 42and IBr (12Ps+Br2P,).13* l4 Strong interaction of the B311(O+)state with a repulsive Of state (correlating to 'P++'P% atoms) leads to an avoided crossing.' This forces the B state to dissociate to 'P3+ 'P3 atoms, in some cases via a potential maximum. The relevant potential energy curves have been given elsewhere, for example, fig. 1-3 in Part 1 l6 for IF, IC1 and IBr. The result of this interaction is that the B states are all more or less unstable.The most extreme case is ICl, where the vibrational level v' = 0 of the B state lies a mere 80 cm-l below the dissociation limit (to 'P++ 'P+ atoms) of the ground state. In the case of IC1, the present work shows, somewhat surprisingly, that the levels v' = 0, 1 and 2 are all stable to predissociation, and there is a small potential energy maximum (N 600 cm-l) between the B state levels and the 'P++ "P2 energy limit. The most stable B state is that of IF, in which some eleven vibrational levels are stable, with a difference of -3750 cm-l between v' = 0 and the 'P3+ 2P,dissociation limit. EXPERIMENTAL The experimental system comprised a pulsed, nitrogen laser (Molectron UV 300) which pumped a dye laser (Molectron DL400), interfaced to a fast flow system.It has been described previously.17* l8 Improvements have since been made in the reduction of scattered laser light, which limited the smallest detectable fluorescence signal in that work.17* The improved interface to the flow-tube is shown in fig. 1 and comprised two side arms, each 500 mm long, provided with 50 internal disc baffles. Each disc had a central hole 5 mm in diameter, and was treated with a black Teflon coat to provide a matt and inert surface. Light scattered from the Brewster-angled windows was barely perceptible using these baffles, and a standard blocking filter, at the excitation wavelength. The minimum detectable fluorescence signal was limited by photomultiplier noise, using an EM1 9558B photo-multiplier. The continuous scanning capabilities of the dye laser were greatly improved by the replacement of the synchronous motors, described previo~sly,'~ by stepping motors con- trolled by computer logic circuits (Molectron DL040A+ DL040B).The computer scan control evaluates a tracking function, eqn (11), and it continuously adjusts the relative rates of tilt of the two tuning elements-the echelle grating and the solid etalon. Eqn (I) relates the wavelength change transmitted by the etalon to its tilt angle, 8, away from the normal d;! = -Ivo8. dO/n ?id, (1) where iz is the refractive index and nd is the dispersive index of fused silica at wavelength &,, and Lo is the wavelength at 8 = 0.The tracking function, which relates the rate of the etalon motor, Re, to that of the grating motor, R,, is given by eqn (11) ~Re = -5 lo5KR,/NG (11) where Re is the etalon motor rate (ccd8/dt), R, is the grating motor rate (ccdlL/dt),N is the first order laser wavelength, G is the etalon display counter reading (scaled etalon angle, proportional to 8) and K is a preset constant derived from eqn (111) : K = lo6. Cln nd/C$, (111) B311(O+)STATES OF IF, IC1 AND IBr where C1 is the grating motor constant (0.0025 nmstep-'), and C2 is the etalon motor constant (2.92 pad step-'). When only a few etalon modes are to be scanned repetitively, as in this work, n and nd are the refractive and dispersive indices of quartz at the centre wavelength for the particular order of the grating being used. In operation, the etalon rotates from its starting angle near the normal Oo, where it is synchronised manually to the grating, to a designated stopping point, Of.Of is chosen to be laser lxis -=z. Filters or rJ Photomultiplier Sampling System 21@ Elec!ranmultiplier Flight Tubec&/rlrpI4 -u Magnet ? Resoiving Slits FIG.1.-The flow system. (a) front view, (b)side view. M. A. A. CLYNE AND I. S. MCDERMID an integral number of etalon modes (3 to 5 modes in this work, each of about 0.02-0.04 nm) from the starting angle. When the etalon reaches Of, the grating stops and the etalon retraces to 8, ; and the cycle restarts. Using this control unit, high resolution scans, i.e., with laser bandwidth < 0.001nm, were possible over a range of 5 nm or more before resynchronisation was necessary.(This should be compared with the maximum range of < 0.1 nm which was possible previously.)17 The mean tracking error over a 2nm scan near 605 nm was determined to be 0.01 nm, or 0.5 %. This scan consisted of approximately 15 cycles each of three etalon modes. (The free spectral range of the etalon was 1 cm-l.) The original flowing dye cell was replaced by a magnetically stirred cuvette dye cell. This offered several advantages; much less dye solution (3 cm3 instead of 125 cm3) was required; use of two simple cuvettes meant that dyes could be changed instantly; the cuvettes were much easier to clean and the contamination of dye solutions was reduced thus extending their useful life. It was also noted, in contrast to ref.(18) that the bandwidth was not degraded when the dyes were interchanged, the condition for minimum bandwidth being very similar to that for maximum power. For the experiments on IF near the predissociation limit of the B state around 440 nm, the 1 cm-1 free spectral range of the intracavity etalon used was equivalent to only -0.02nm, compared with 0.04 nm at 600 nm. Therefore, it was necessary to use great care to minimise the bandwidth of the laser before installing the etalon in order to prevent more than one etalon mode lasing simultaneously. DYES A number of dyes were needed to cover the wide range of wavelengths spanned by the absorption spectra of the iodine monohalides.For IF, where the region of interest lies in the blue and green regions of the visible spectrum, three dyes were used. These were coumarin-120+ ethanol (420-457nm), 7-dimethylamino-4-methylcoumarin+ethanol (440-480 nm) and 7-dimethylamino-4-trifluoromethylcoumarin+dioxan (465-520 nm). ICl B-X absorption bands (from u'' > 2)lie in the red region of the spectrum, and the dyes used were Rhodamine-6G+ ethanol (568-605 nm), and Rhodamine-B+ ethanol (600-640 nm). For the far red absorptions of ICl and IBr, equimolar mixtures of Rhodamine-B or Rhodamine-6G with cresyl violet perchlorate (A < 657nm) were used. REAGENTS IC1 (98 %) and IBr (97 %) were obtained from B.D.H. Impurity 1, severely obscured the excitation spectra and, therefore, had to be reduced or removed.Because of the continuous disproportionation of these compounds to 12, C12 and Br,, it is not possible to remove all the 12; but sufficient can be removed in the case of ICl that the I2 spectrum is much less TABLE1.-THERMAL POPULATION DISTRIBUTION Of: THE X'c* GROUND STATE VIBRATIONAL LEVELS AT 295 K L' " IF I35CI 179~r 0 94.73 84.40 72.71 1 4.9s 13.10 19.72 2 0.27 2.08 5.45 3 0.015 0.34 1.54 4 0.0009 0.054 0.42 5 0.00005 0.009 0.12 6 0.0015 0.034 7 0.0095 intense than that of IC1 (< 0.1). In the case of IBr, even the small residual amount of I, was sufficient totally to obscure any IBr laser excitation spectrum. This is not surprising, since TBr B-X has a lower transition moment and the B-X bands with the greatest Franck- Condon factors l6 have low ground state vibrational populations (table 1).Contrary to B311(O+)STATES OF IF, ICl AND IBr expectation, the best way of purifying ICl, as determined by the absence of I2 bands in the excitation spectrum, was by warming it until sufficient for the experimental run had liquefied. This was then decanted leaving the solid behind. Fluorine was obtained as a 5 mol % mixture with helium (B.O.C.Special Gasesj. The mixture was used without any further purification. Fluorine atoms were produced by a microwave discharge (2.45 GHz, 75 W) in this mixture. The typical degree of dissociation of F2was 60 to 90 %. RESULTS PRODUCTION OF IF Iodine monofluoride was produced in the flow system, in the presence of a large flow of helium car:-ier gas, by the rapid reaction (1) of F2Patoms with iodine niono- chloride, F+ICl-+ IF+C1; (1) the rate constant k:98 is equal to (5k2) x lo-" cm3 molecule-' s-l." The reaction (2) of fluorine atoms with iodine, F+I2 + IF+I (2) s-'1 l9 is also fast and produces IF.There-= (4.3f1.1) x cm3 m~lecule-~ fore, the impurity I2 in the IC1, which might otherwise interfere in the excitation spectrum at wavelengths longer than 500nm, is rapidly removed and repeated purifications of the ICl are unnecessary. The alternative reaction of F atoms with iodine monochloride to form CIF, F+ICl -+ ClF+I, (14 has been shown by Appelman and Clyne '' to be a minor channel (-20 %).This is expected according to Dixon, Parrish and Herschbach,22 since the central atom in the triatomic collision complex from F+ICl should be I and not Cl. In fact, no evidence for C1F was noticed in any of the excitation spectra, probably due to the weakness of the B-X transition of ClF.23 In their study of reactions (1) and (2), Appelman and Clyne '' found that both IF and IF, were produced, even after a reaction time of 2 ms ; however, no evidence was found for IF3 as a product. The ratio [IF,]/[IF] was reported to increase with reaction time, and was favoured by an excess of F atoms. Low or nil yields of IF, were correlated with the reverse stoichiometric conditions, i.e., with unreacted IC1.The reason, they concluded, that IF had never been isolated as stable molecule was that it is kinetically unstable with respect to wall-catalysed disproportionation, and a half-life of only a few milliseconds in a 2.5 cm diameter vessel at 1 Torr pressure of helium was indicated. In order to produce the maximum [IF]/[IF,], a high linear flow velocity (15 to 20 m s-I), giving a maximum reaction time of -5 ms and a flow tube pressure of -1 Torr ; and a small excess concentration of ICl was used. Although no accurate measurements of the concentration of IF were made, it is estimated that [IF] in the fluorescence cell was < loi3 ~m-~. IF B-X EXCITATION SPECTRA The intensity of fluorescence from IF B311(Of)was at least an order of magnitude greater than that from BrF B31T(O+)'* under similar conditions.Although no absorption spectrum of IF has previously been reported, we had no difficulty in observing strong fluorescence [B311(O+)-X'Z+] arising from the absorption of laser M. A. A. CLYNE AND I. S. MCDERMID radiation by X’C+ ground state IF molecules. Low resolution laser wavelength scans were carried out between 430 and 500nm. For most bands, the P and R branches were totally resolved, except very close to the band head, even at low resolution (0.01 nm bandwidth). Since there are only single natural isotopes of I and F, the IF spectrum appeared as a set of regular PR doublets. The absence of a Q branch confirms the assignment of the transition as 31T(O+) -PZ+, rather than 311(1)-XIZ+.The bands were easily assigned using Durie’s band head measurements 2o for IF emission spectra from the I2+F2flame. Since the room temperature (295 K) popu-lation of the level v” = 1 is -5%, and that of v” = 2 is only -0.3% (table l), little overlapping of bands from different ground state vibrational levels occurred. Weak bands from v” = 1 were seen for v’ = 8,9, 10,for which transitions the Franck- Condon factors l6 are most favourable. No bands from v” = 2 were seen. Table 2 lists the bands assigned at wavelengths shorter than 500nm. No experiments were carried out at longer wavelengths, since no additional information on the B311(O+) state was thereby available. TABLE2.-wAVELENGTHS,a &jr/rlrn, FOR THE OGSERVED BANDHEADS OF IF B-X v~lv” 0 1 3 496.125 4 486.817 5 478.028 6 469.736 7 461.931 8 454.600 467.455 9 447.762 460.207 10 441.446 453.538 11 435.754 a Durie [ref.(20)] ; b not observed in laser fluorescence. 4ilD 413.1 1135 4799 480.0 h/nm FIG.2.--Head of the 5-0 band of the IF B-X system, at low resolution (0.01 nm). A search for additional bands was made, using the maximum sensitivity of the detection system, to wavelengths shorter than the observed predissociation limit near 443 nm. No fluorescence was detected, which suggests that there are no stable vibrational levels above the crossing; or less probably that the new levels which could be formed by the crossing have a much larger r-centroid value, thus leading to exceptionally low Franck-Condon factors for these transitions (cf.IBr) ; or a combination of both these explanations. B311(O+)STATES OF IF, IC1 AND IBr Fig. 2 shows part of the 5-0 band near the band head, recorded at 0.10 nm resolu- tion. For this band, using a laser bandwidth of 0.01 nm, the P and R branches are overlapped, which gave the spectrum a very simple appearance. According to the table of Franck-Condon factors,’ this band has the highest transition probability for laser excitation. Rotational transitions up to J’ > 70 are seen before they are obscured by the 4-0 band head. High resolution scans (bandwidth -0.001 nm) were carried out on selected bands and parts of bands. The whole of the 9-0 and 10-0 bands were recorded. Fig.3 shows the entire 10-0 band. The rotational levels were assigned by the method of combination differences, i.e., using R(J) -P(J) = 4BL(J+ i), R(J+ 1) -P(J-1) = 4B:(J+3) with Durie’s values for the rotational constants B,, and neglect of centrifugal stretching. r I I -r-------------1 4420 4 4 1.5 X/nm FIG. 3.--The entire 10-0 band of the IF B-X system, at high resolution (0.001nm) showing the predissociation. PREDISSOCIATION IN IF ~3n(0+) A total breaking-off of fluorescence from rotational levels with J’ > 32 can clearly be seen in the 10-0 band. The value of J’ corresponding to onset of predissociation was determined. The line intensities, i.e., the mean of the P and R lines with the same J’, have been compared with those calculated from the Boltzmann distribution which accurately predicts the intensities in bands from levels far from the crossing point, e.g.,in the 5-0 band.Because of the selection rule J’-J” = 1, the intensities of the pairs of lines with the same J’ depend on the ground state populations in the levels (J”-1) and (J”+ I). The mean ground state Boltzmann population Nl;has M. A. A. CLYNE AND I. S. MCDERMID therefore been calculated using the approximate expression Fig. 4 shows the comparison of the measured line intensities with those predicted from the Boltzmann population “Jff.It can be seen that the onset of predissociation occurs near J’ = 12, and at an energy of 25 cm-l above the energy of J’ = 0 in the vibrational level v’ = 10. The implications of this result for the dissociation energy of IF will be discussed below. Comparison of the relative intensities of 9-0 and 10-1 bands near their band heads, which occur in the same wavelength range, was made.Within a factor of two, the relative intensities were in accordance with the relevant Franck-Condon factors and ground state vibrational populations (table 1). This result indicates that the lowest few rotational levels (J’ < 12) of the vibrational state v’ = 10 are not appreciably predissociated. A similar conclusion is reached from the observation of satisfactory fit of rotational line intensities to the Boltzmann distribution for J’ < 12 of u‘ = 10 in the 10-0 band (fig. 4). 0, 0, I I I . I 0, I 1 I r 0 m 20 30 40 0 100 200 300 400 J B’J’ (J’+ l)/cm-‘.FIG.4.-Rotational line intensities and predissociation in the 10-0 band of IF B-X. -, Boltzmann at 295 K ; .-.-.experimental. Icl EXCITATION SPECTRA Preliminary excitation spectra of unpurified ICl (-0.1 Torr in 2 Torr of helium) were recorded using laser wavelengths in the range 600-620 nm and a bandwidth of 0.01 nm. In this spectral region, the A311(l) f-X’Zf absorption bands are intense, and therefore we expected to see fluorescence from theA311(l)state. In fact, the appear- ance of the spectrum was very complex and obviously due to many overlapped bands. Preliminary analysis showed that some of these bands were due to the A311(I) -XIC+ system of IC1 and others were due to the B3rl[(0,+)-X’Zf system of Iz, but several strong bands remained unassigned.Therefore, high resolution scans of these bands were run. In the course of these experiments, it was noticed that the intensities of fluorescence, particularly from the A3lI(l) state of ICl and also from the B311(0,f) state of 12,were sensitively decreased by increase in the ICl pressure, but that the yet unassigned bands were barely affected at pressures up to 5 Torr. Thus, it was found that by working at a pressure of 5Torr of ICl, unwanted fluorescence from the A B311(O+)STATES OF IF, IC1 AND IBr state of IC1 and I, could be almost totally quenched out. This immediately shows that the collision-free lifetime of the fluorescing state, later shown to be ICl B311(O+), must be short (< 1 ,us).High resolution spectra (0.001 nm) were recorded, at 5 Torr pressure of ICI, in the region 568 to 650 nm. The spectra showed a series of doublets, overlapped with a similar series of lower intensity due to the 37Cl isotope. These sets of PR doublets and the absence of a Q branch show that the transition is IC1 3rl(O+) -XIE+. Data from Hulthh l2 on the 1-0, 2-0 and 3-0 bands of the B311(O+)-XIC+transition, and our own data on the 0-2 band (see below), were used to calculate the band origins for V” = 0 to 4 and v‘” = 0 to 3. These results are summarised in table 3. A more detailed explanation of the band assignments can be found in the section on the 0-2 band. It was possible to verify the vibrational numbering of the B311(O+)state from the magnitude of the isotopic shift, ~G(v,u’) = (p-l)[(v” + +)CO;-(v” + 3)0:3 where p is the square root of the ratio of the reduced masses, p/p’.A complete rotational analysis of one band with v” = 1, the 1-3, and one with V” = 2, the 2-3, was carried out for 13Wusing the method of combination differences and the B, values from Hulthdn and co-workers.12 Also the 1-3 band of 137Cl was analysed in the same way. Fig. 5 and 6 show parts of these bands recorded at high resolution. TABLE3 .-WAVELENGTHS, &/nrn, FOR Ic1 B-x ,;’\dt 0 1 2 3 4 0 578.373 591.420 604.956 619.015 633.622 1 571.879 584.632 597.856 a 611.583 a 625.835 2 565.964 578.451 591.397 a 604.825 a 618.760 3 560.777 573.034 585.733 598.902 612.565 a band observed ; b band searched for but not observed.THE 0-2 BAND OF 135~1B-x Only the vibrational levels v“ = 1, 2, 3 of the excited B3n(O+)state of ICl have been observed previously in absorption. Brown and Gibson l1 observed the 3-1, 2-0 and 3-0 bands of the B-Xsystem, which lie between 560 and 575 nm. The longer wavelength bands originating from v” > 0 have much higher Franck-Condon factors [see table 6 of ref. (16)]. However, these strong bands are heavily overlapped by even more intense IC1 A-X absorption bands, as well as by I, B-X impurity bands. Also, the Boltzmann populations of the X state levels with v”’ > 1 are low (table 1). The failure to observe bands from v“ = 0 may thus readily be understood, particularly in light of the very low Franck-Condon factors for transitions to v” = 0 from the lowest few vibrational levels of the ground state.As explained above, fluorescence of the A-X system of ICl could be suppressed by quenching out the long lived A311(l) excited state under conditions where the short lived B31t(O+) state is not greatly affected. Hence, the intense 1-3, 1-4, 2-3 and 2-4 red bands of ICl B-X were readily identified, free of overlapping A-X bands (fig. 5 and 6). The calculated Franck-Condon factors for the 2-3 and the 0-2 bands,16 which are expected to be overlapped, indicated that the 0-2 band at 295 K should be in the order of one-tenth the intensity of that of the 2-3 band in the laser excitation spectrum. With this prediction, it has proved possible to identify the 0-2 band.About 33 lines in all, including three overlapped lines, could be picked out. M. A. A. CLYNE AND I. S. MCDERMID 226 1 Measurements of line wavelengths was carried out approximately from the dye laser counter. A much more accurate approach that eliminates tracking error and zero error was to use the frequencies of unblended lines of the overlapped 2-3 band to calibrate the wavelength scale. Hulthh, Jarlsater and Koffman l2 have deter- mined accurate values for the band origin of the 2-0 band of P5CI (17 664.04 cm-'), I $7 36 I $1, -__--1 ---7---I-----T---~___611 9 011 x h' OII b X/nm FIG.5.-Head of the 1-3 band of the 13W B-Xsystem, at high resolution. 4 35 30 L.----,--(l I----A-7------r-------45 40 1 I 1 1 ,607 0 9 8 7 .6 606.5 4 3 2 I IT----,-7-L-7--I._ < 606 0 9 u 1 6 bO5 5 4 3 2 I 6050 hlnm FIG.6.-Part of the 2-3 band of the 135ClB-X system, at high resolution.Bi (0.082 95 cm-l), and D$ (1.05 x cm-l), based on extremely careful high resolution spectrometry with interferometric wavelength calibrations. The same group have reported ground state rotational energies F:(J) for the vibrational levels = 0, 1 and 2 using the same mefhod.l2 The rotational energies Fi(J) for the 21'' level v" = 3 may be readily calculated using Bi = 0.112 281 cm-l, determined from B311(O+)STATES OF IF, IC1 AND IBr the expression,12 B; = 0.1 14 1544-0.000 535,(u”+5). The very short extrapolation of one vibrational level (to u” = 3), and the small magnitude of a,”, ensure that the calculated Fi(J) term values will be sufficiently reliable. The centrifugal stretching constants D;for the ground state levels (u” = 0, 1,2) contribute only slightly.The ground state vibrational energies G”(O), G”(1) and G”(2) have been deter- mined,12 and [G”(3) -G”(2)] may readily be determined using the well established relation, G”(u) = 384.293 (u+$)-1.501(~+4)~,which is expected to be accurate for extrapolation to d’= 3 of the XIE+ state. The origin of the 2-3 band of 13Tl was determined from these data to be 16 529.17 cm-l, with an estimated uncertainty of k0.05 cm-’. TABLE4.-THE 0-2 BAND* OF THE B3n(o+)-x’x+SYSTEM OF 135c1 J P(J)/cm-1 R(J)/cm-’ 26 16 502.20 27 500.56 28 498.861-29 97.15 30 95.39 31 93.49 32 91.55 33 89.62 16 501.16 34 87.577 499.48 35 85.53 97.75 36 83.39 95.97 37 81.22 94.187 38 79.02 92.25 39 76.71 90.27 40 74.37 88.29 41 72.00 86.25 42 16 469.56 84.13 43 81.98 44 79.77 45 77.49 46 75.18 47 72.80 48 16 470.37 Observed vacuum wavenumbers are listed.* band origin vo, = (16 525.5 50.2) cm-’. 7 over-lapped lines. The wavelengths of a number of rotational lines of the 2-3 band were then calculated, and the wavelengths of the lines of the weaker 0-2 band were determined by interpolation. Trial combination differences were formed, indicating that the lower state was v” = 2 of 13Tl XlXf, and the upper state was v’ = 0 of B3n(O+). The rotational numbering of the lines was uniquely determined.Table 4 shows the wavelengths and assignments of the 0-2 band lines. No 137Cl band could be seen, because of the low intensity of the main band. The main 13’Cl band could be followed from J” N 48 to J” 2: 26, i.e., through the range of the maximum Boltzmann population of the ground state at 295 K. The increasing density of lines in the 2-3 band, approaching the band head, precluded identification of 0-2 band lilies with J‘ < 26. The assignment of the 0-2 band was confirmed by determination of the molecular constants (table 5) ; thus, the position of the band origin was found to be (16 525.5 & hf. A. A. CLYNE AND I. S. MCDERMID 0.2) cm-l. This energy is close to that predicted by extrapolation of Hulthen's band origin data for the levels v' = 1, 2, 3.TABLE5.-sPECTROSCOPIC CONSTANTS FOR THE B3n(o+)STATE OF 13w a (a) measured data 0' vV',o AG'(cf $) B: D~X107 0 17 285.1 0.086 14 0.75 196.3 1 17 481.38 0.084 63 1.oo 182.7 2 17 664.04 0.082 95 1.05 163.4 3 17 827.46 0.080 41 2.01 (h)evaluated data G' G'(u) 0 101.5 1 297.8 2 480.4 3 643.9 G'(G)= 204.5(~+5)-2.595( u+-$)2 -0.937(~+3)BI(J)= 0.087 05-2.00~ 10-3(u+4)+4.32~ ~O-"(U++)~-1.15~10-4(u+$)3 Te = 17 375.4k0.5 Dd = 1063.8+0.5 0 all units cm-' ; b estimated value, see text. Table 5 shows a summary of the vibrational and rotational constants for the B state of 135Cl. Data for vr = 1, 2 and 3 are from HulthCn ;12 data for vr = 0 are from this work.The centrifugal stretching constants DL reported by Hulthtn l2 appear irregular. We estimated DL = 6.3 x 10-8 from the Dunham relation, D, = 4B,3/w?, and obtained Db = 7.5 x by interpolation between this value and Hulthtn's 0;value. On this basis, we determined 236 from our data to be 0.086 14 cm-l. The value of Bb is not sensitive to the assumed magnitude of Db because rotational lines with relatively low J (< 42) were used in our work to deter- mine the rotational constants. The derived Bb value would vary only from 0.085 98 if DL = 0.0, up to 0.086 22 if Db = 1.0 x lo-'. Only the lowest four vibrational levels of the B state of IC1 have any degree of stability. The Bh values for these levels were fitted to a third degree polynomial (table 2), giving Bd = 0.087 05 +0.0002 and rd = 2.657 A.It was clearly impossible to use Coxon's 21 five parameter method applicable to strongly perturbed states such as the B311(O+),because only four data points were available. The large variation in B, with v' is in accordance with expectation. A similar approach was used to obtain the vibrational constants. In this case, a second degree polynomial fit was necessary. The value obtained for wk was (204.5k0.5)cm-'. The large magnitude found for weye(-0.937) is what would be expected for a very shallow, strongly perturbed state. It is interesting to note that a Birge-Sponer extrapolation of AG'(u +$), using the second degree polynomial which fits the energy levels u' = 0-3 (table 5). gave a dissociation energy DL equal to 1003 cm-l in good agreement with the correct value of (1063.8k0.5)cm-'.Normally, such extrapolations based on polynomials give poor results. The good agreement for the B311(O+)STATES OF IF, IC1 AND 1Br B state of IC1 does serve as a confirmation that the diabatic dissociation products of IC1 B311(O+)are I 2P,+Cl "pt, on which fact the value DL = 1063.8 cm-l is based. PREDISSOCIATION IN ICLB~II(O+) A thorough search was made for fluorescence from v' = 3 but none was observed. In many cases the Franck-Condon (FC) factors for transitions to v' = 3 are much more favourable than those for bands which are observed. For example the 1-1 band, which was observed, has a FC factor of 0.000 09 and the 3-1 a FC factor of 0.000 75, nearly an order of magnitude greater.From these results it was concluded that the whole of the u' = 3 level was predissociated. The v' = 2 level was then examined carefully for signs of the onset of predissociation. It appears that it occurs near J' = 70 in this vibrational level but, because the Boltzmann population is also very low for J' = 70 at 295 K, unequivocal identification of the precise J' for the onset of predissociation was not possible. ATTEMPTED IBr EXCITATION SPECTRUM The IBr B3TZ(O+)-XIC+ band system has been photographed in absorption by Brown l3 and by Selin.14 The spectrum was found to have very iow intensity and, therefore, measurements were difficult, and the accuracy not as high as for ICl.However, the v' numbering was determined from the isotope shifts and the v" numbering was fixed with reference to the well-studied A3H(l)-XIZ+ system.14 Brown l3 noted that predissociation occurred at about 50 cm-l above the v' = 5 level but, because of the weakness of the spectrum, Selin l4 was unable to confirm this. We have tried, unsuccessfully, to observe fluorescence from IBr B311(O+). The excitation wavelength was scanned from 620 nm to the longest wavelength we could achieve, 657nm. The intensity of the laser in this long wavelength region was considerably reduced from that normally obtained at wavelengths shorter than 630 nm. The high sensitivity of the detection system is indicated by the successful observation of several bands originating from high v" of I2 impurity. These were the 4-4, 5-4, 6-4, 5-5, 6-5, 7-5 and 8-5 bands of the I, B-X system.The thermal population of v" = 5 of I, XIZ,+is 0.58 % at 295 K. From the Franck-Condon factors of IBr B-X,16 it can be seen that, from the levels with low v", the greatest transition probabilities to the B311(O+)state are to the energy region lying above the predissociation of the B state. Combining the Franck- Condon factors with the ground state vibrational populations, the strongest laser excitation bands are expected to be those with u' = 3 and 4 as indeed found by Brown l3 and Selin.14 Comparison with other species, e.g., ICl B311(O+)-X'X+ suggests that very weak fluorescence should be observable from IBr B311(O+).29 However, in our experiments fluorescence from the I, produced by decomposition of IBr was sufficient to totally obscure any emission from IBr.DISCUSSION We first consider the result of the present work that the onset of predissociation in IF occurs near J' = 12 of u' = 10 in the B311(O+)excited state. This corresponds to an energy of (22 700+ 15) cm-1 above the level U" = 0 of the ground XlV- state. The criterion for the onset of predissociation in our work is unequivocal. It was taken from the observation of significant diminution in fluorescence intensity below that expected for the 295 K Boltzmann population of IF absorbers (see fig. 3 and 4). M. A. A. CLYNE AND I. S. MCDERMID On the other hand, Durie,” in a conventional high-resolution study of IF emission spectra from I,+F, flames, reported onset of predissociation at J’ = 46 of v’ = 11 in the B state. The corresponding energy, 23 341 cm-l, is appreciably greater than that found by us.We are of the opinion that Durie’s ‘O value is a considerable over-estimate, as explained below. Durie ‘O identified the onset of predissociation from the commencement of detectable broadening of the rotational lines in the emission spectrum. He observed a number of diffuse lines definitely lying above Durie’s dissociation energy of IF XIE+, and at shorter wavelengths, a weak continuum.20* 24 On the basis that lines could be observed from J’ < 120, the equivalent Boltzmann temperature of his flame source is estimated as around 1000 K.At this temperature, the Bolzmann population [I 2Pt]/[I’P+]spin-orbit excited atoms is negligible (-1 x %) but that of F 2Ppt-excited atoms is appreciable (-22 %). This line of argument would suggest that IF B311(O+)could be formed in Durie’s atmospheric pressure I,+F2 flame 20* 24 by radiative recombination of I 2P3 atoms with F ‘P+or F ‘Pt atoms : F2,1, +M -+2F, 21+h/l, I 2~~ + F 2~+ v’, + M,+ M -+ IF ~3n(0+), I v4+F v,+ M -+ IF ~3n(0+),v’, + M. The last process would account for weak lines from excited states having energies 21 500 cm-1 above the dissociation limit for I ’P4+F 2P+,20since the F 2P+ atom has a spin-orbit energy of 404 cm-’. However, the failure to observe IF B-X emission in the I ’P++F ’P+experiments of Clyne, Coxon and To~nsend,’~ except with pumping by 0, ‘Ag, tends to rule out radiative recombination of I + F as the major mechanism for forming IF B311(O+).We suggest that in fact the mechanism for formation of IF B311(O+)in Durie’s flame 20* 24 is similar to that now also put forward by us for population of the B and A states of IF in the low pressure 12+F2chemiluminescence studies of Birks, Gabelnick and Johnston.’ In Durie’s system, the longer lived A state would be preferentially quenched, so that only emission from the short-lived B state would be actually observed. Birks et aL9 however saw both A-X and B-X emission, since quenching of the A state at reduced pressures was not complete. The work of Lee and co-workers 26 provides a satisfactory mechanism for forma- tion of the B or A states of IF from I2+ F2in the studies of both Durie ’O* 24 and Birks et a1.’ In a series of elegant crossed molecular beam studies, Lee 26 showed that I, reacts directly with F2 to form the triatomic species IIF : I,+F, + IIF+F.This reaction is slightly endoergic, and IIF has a dissociation energy (to I+IF) of about 17 kJ mo1-1.26 The reaction proceeds with an appreciable activation energy, and would, therefore, not be important in fast discharge-flow kinetic studies on systems such as F+I,, Ft-ICl.’’ However, in static systems or using high reagent concentrations, the rate of formation of IIF could be fast and could maintain flame propagation, as in Durie’s work.20 IF formation from IIF occurs via the exoergic reaction, F+IIF -+ IF+IF; AU&* 21 -257 kJ mol-l.One of the IF molecules formed can be electronically excited, either in the B or A state. The exoergicity of formation of IF in this reaction corresponds to 21 495 crn-l, or to emission from A or B states at wavelengths A 3 465 nm. This corresponds B3rI(Of)STATES OF IF, ICl AND IBr quite well with the short wavelength cut-offs in the A-X and B-X band systems seen by Birks et aL9 In the case of Durie's I2+F2flame, 2op 24 emission extends to some- what shorter wavelengths corresponding to some 23 000 cm-'. Thermal contribu- tions could be important here, however. Whatever the nature of the steps populating the B state in Durie's work,20* 24 considerations based on the Uncertainty Principle indicate that the diffuse rotational levels (J' N 55) belonging to 0' = 11 of this state are short-lived, with z E lo-'' s.Because of the continuous nature of the population process, it is possible for a finite pseudo-equilibrium concentration of these IF molecules to be established, and to emit radiation. As the rotational energy ladder is descended, the observed line width decreases,20 indicating a reduction in the strength of the non-radiative interaction and an increased lifetime. At a certain point, the line width determined by the excited state lifetime will equal the instrumental or Doppler linewidth. This will occur when z N 0.4 ns, corresponding to a line width of -2.5 GHz (0.08 cm-l). On the other hand, analogy with other B-X transitions of the (inter)halogens suggests that the purely radiative lifetime of the B state of IF is very unlikely to be less than 10011s.For instance, the radiative lifetime of I2 B3II(O;) is not less than about 70011s.~ The results presented above indicate that the lifetime would have to fall by at least a factor of 250 from the purely radiative lifetime, before noticeable line broadening could be seen. In fact, no doubt extensive quenching in Durie's work 2o would have reduced the lifetime of the stable level sof the B state to a value in the order of a few ns. Thus, the commencement of predissociation would lead to a negligible further depopulation of the B state. The predissociation would have to be sufficiently extensive for its lifetime to be less than a few hundred ps, before appreciable weakening of the B-Xemission could be observed in Durie's work.The conclusion of these arguments is that observation of diffuseness in the emission spectrum of IF B-X is a poor criterion for the onset of predissociation. The present value of the minimum predissociation energy may, therefore, be used to provide a reliable upper limit for the dissociation energy of IF; thus, DG (IF) < (22 700+ 15) cm-'. We may compare this value with estimates based on rather long extrapolations of the vibrational levels of the A state, which dissociates to I "P3+ F "P+ ground state atoms. Coxon * has described two different Birge-Sponer extrapolations, one based on a second degree polynomial and giving D: (IF) = 24 927 cm-l, and the other based on a similar third degree polynomial giving a value of 23 103 cm-l.It now appears that even the latter value is too high, and that a slightly more sigmoid [AG'(u+$),u'] function applies for IF A311(l) than that suggested by Coxon.8 The highest vibrational level of A311(l), the u' = 10 level, listed by Birks et a1.' is at 118 979 cm-' above the state X'Z+, 0'' = 0. An extrapola- tion of some 2700 cm-' is required to reach convergence of the A state, so that an error of 400 cm-I in the extrapolated convergence energy would not be surprising. The type of plot of AG(v++) against u' indicated for IF A311(l) would be consistent with the well known sigmoid shaped curves for other 3rI(l)states of the ha1ogens.l.l2,l4 The predissociation limit 22 700 cm-' for IF is an upper limit and it is probably close to the dissociation energy. The above discussion indicates that the true value is unlikely to be appreciably lower than 22 700 cm-'. The close limit value 06 (IF) = (22 700+ 15) cm-' leads to a new value for the excited state dissociation energy, Do (IF) = (11 345215)cm-'. THE EXCITED B~II(O+)STATE OF ICI All the stable vibrational levels of the B state of 13Tl are now known. Our observation and analysis of the 0-2 band provide the molecular constants for the M. A. A. CLYNE AND I. S. MCDERMID elusive lowest level, u’ = 0. Only the lowest three levels are stable to predissociation, onset of which occurs in the vicinity of J’ = 70 in the level v’ = 2.Sharp absorption transitions are however also found involving the next level, u’ = 3.119 l2 As expected for the very shallow and perturbed B state, both the rotational and vibrational constants show strong variations with u’ and the anliarmonic terms are very large (see table 5). The value of voo for the B state of 13Tl is 17285cm-l, compared with the dissociation energy of the ground state 0:which is 17 366 cm-l.’ The stability of even the lowest three levels of the B state, as manifested by the successful observation of laser-induced fluorescence, is. therefore, somewhat surprising. Predissociation of the B state evidently occurs over a relatively narrow raiige of energies. This predissociation can be considered further in the light of work by Olson and Inne~,’~who measured the absorption linewidths of a number of lines of the 3-1 band of the B-X system of 13W, using Fabry-Perot interferometry.These workers also obtained an estimate of the radiative lifetime (T~)of the B state (v’ = 3) from measurements of the absorption coefficient of several lines. These results gave zR = (0.98+O. 10) ps, which may be revised, using our Franck-Condon factor of 7.5 x l6 for the 3-1 band based on new spectroscopic data, to give an estimated value of 1.4 ps which could be in error by a factor of two or more and is consistent with the value of 500 ns found by us fop. the collision-free lifetime of IC1 B (u’ = 1, 2).6 [We note the large difference in lifetimes between the B state for the stable levels and the A state (100 PS).~~]The absence of strong quenching of B-X fluorescence, and the high intensity of such fluorescence in our work, are consistent with a lifetime of 500ns6 for the levels v’ = 0, 1 and 2 of the B state.According to our results on the breaking-off of the spectrum in fluorescence, strong predissociation evidently sets in at about J’ = 70 of u’ = 2, and is extensive for all rotational levels of v’ = 3 these levels were not observed in laser fluorescence. The results of Olson and Innes 27 are consistent with our data. They reported an overall lifetime z N 0.2ns for the lower rotational levels (J’ = 5 to 30) of the v’ = 3 state, and z decreasing from 0.211s to 0.0211s with J’ increasing from 35 to 42.These results are clearly indicative of strong predissociation in the v’ = 3 level. Our own results, based on the intensities of high J’ lines in the 2-3 and 2-4bands and the non-observa- tion of any v’ = 3 bands in fluorescence, indicate that the lifetime of the level v’ = 3 must be at least 50 times less than that of the level v’ = 2. If we accept the zR value of 1.14 ,us from Olson and Innes 27 for the lifetime of v’ = 2, the lifetime of all rotational levels of v’ = 3 would be < 28 ns. Clearly, valuable further information on the predissociation in the B state of 13W can be expected from direct lifetime measurements. We thank John Coxon for helpful discussions and Yuan Lee for a preprint, and are grateful to the S.R.C., the Royal Society and the British Gas Corporation for support.Partial support by the U.S. Air Force Office of Scientific Research is also gratefully acknowledged. See for review J. A. Coxon, Chenz. SOC.Spec. Report on Moiecular Spectroscopy (Chem. SOC., London, 1972), vol. I, chap. 4. (a)K. Sakurai, G.Capelle and H. P.Broida, J.Cizem.Phys., 1971,54,1220 ; G. Capelle and H. P. Broida, J. Chem. Phys., 1973, 58, 4212 ; J. A. Paisner and R. Wallenstein, J. Chem. Phys., 1974, 61,4317 ; (6) K. B. McAfee and R. S. Hozack, J. Chem. Phys., 1976, 64,2491. R. J. Browne and E. A. Ogryzlo, J. Chem. Phys., 1970, 52, 5774; M. A. A. Clyne and J. A. Coxon, J. hfol. Spectr., 1967, 23, 258 ; M. A. A. Clyne, J. A. Coxon and A. R. Woon-Fat, Faraday Disc.Chem. Soc., 1972, 53, 82. 2268 B3n(Of)STATES OF IF, Ic1AND IBr M. A. A. Clyne and J. A. Coxon, Proc. Roy. SOC.A, 1967, 298,424. S. Datta, R. W. Anderson and R. N. Zare, J. Chern. Phys., 1975, 63, 5503. M. A. A. Clyne and I. S. McDermid, to be published. R. S. Mulliken, Phys. Reu., 1930,36, 1440; R. S. Mulliken, J. Chem. Phys., 1971, 55, 288. J. A. Coxon, Chem. Phys. Letters, 1975, 33, 136. J. W. Birks, S. D. Gabelnick and H. S. Johnston, J. Mol. Spectr., 1975, 57, 23. lo P. H. Brodersen and J. E. Sicre, 2.Physik, 1955, 141, 515. l1 W. G. Brown and G. E. Gibson, Phys. Reu., 1932, 40, 529. l2 E. HulthCn, N. Johansson and U. Pilsater, Arkiv Fysik, 1958, 14, 31 ; E. HulthCn, N. Jarlsater and L. Koffman, Arkiv Fysik, 1960, 18,479. l3 W.G. Brown, Phys. Rev., 1932, 42, 355. l4 L. E. Selin, Arkiv Fysik, 1961, 21, 479; L. E. Selin and B. Soderborg, Arkiv Fysik, 1961, 21, 515 ; L. E. Selin, Arkiv Fysik, 1961, 21, 529. M. S. Child and R. B. Bernstein, J. Chem. Phys., 1973, 59, 5916. l6 M. A. A. Clyne and I. S. McDermid, Part 1, J.C.S. Faruday ZZ, 1976, 72,2242. l7 M. A. A. Clyne, I. S. McDermid and A. H. Curran, J. Photochem., 1976,5, 201. M. A. A. Clyne, A. H. Curran and J. A. Coxon, J. Mol. Spectr., 1976,63, 73. l9 E. H. Appelman and M. A. A. Clyne, J.C.S. Furuday I, 1975, 71,2072. 2o R. A. Durie, Cunud. J. Phys., 1966, 44, 337. 21 J. A. Coxon, J. Mol. Spectr., 1974, 50, 142. 22 D. A. Dixon, D. D. Parrish and D. R. Herschbach, Furaduy Disc.Chem. Soc., 1973, 55, 385. 23 W. Stricker and L. Gauss, Z. Nuturforsch., 1968, 23a, 1116. 24 R. A. Durie, Proc. Roy. SOC.A, 1951, 207, 388. 25 M. A. A. Clyne, J. A. Coxon and L. W. Townsend, J.C.S. Furaday ZZ, 1972, 68, 2134. 26 J. Valentini, M. J. Coggiola, J. M. Farrar and Y.T. Lee, Znt. J. Chem. Kinetics, 1976, in press. 27 C. D. Olson and K. K. Innes, J. Chem. Phys., 1976, 64, 2405. 28 G. W. Holleman and J. I. Steinfeld, Chem. Phys. Letters, 1971, 12,431. 29 Note added in proof. E. M. Weinstock, J. Mol. Spectr., 1976,61,395, has reported observa- tion of laser fluorescence using a C.W. dye laser to excite the higher B’(0’) state of IBr. (PAPER 6/861)

ISSN:0300-9238    

DOI:10.1039/F29767202252

出版商:RSC    

年代:1976

数据来源: RSC

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Molecular Motion in Solid K-n Molecular Complexes Part 3.-Pulse n.m.r. Measurements on Solid Charge-Transfer Complexes of Naphthalene and Pyrene BY COLIN A.FYFE*AND DUANEHAROLD-SMITH Guelph-Waterloo Centre for Graduate Work in Chemistry, Guelph Campus, Chemistry Department, University of Guelph, Guelph, Ontario, Canada N1 G 2W1 AND JOHN RIPMEESTER* Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6 Recehed 6th May, 1976 Pulse n.m.r. techniques have been used to measure the temperature dependence of TIand TIP for the proton resonances of the 7--rr molecular complexes of the donor molecules naphthalene and pyrene with the acceptor molecules tetracyanoethylene, tetracyanobenzene, and pyromelitic dianhy- dride in the solid state.The results confirm the existence of various molecular motions in these complexes and yield accurate activation parameters for them. Theoretical calculations of the energy barriers using semi-empirical non-bonded interatomic potential functions have also been made. Both sets of results are compared with the available literature data from wide-line n.m.r. and X-ray crystallographic investigations. There has been considerable interest for some time in the investigation of the structures of solid n--71 charge transfer complexes by X-ray crystallography. These solid state structures are of particular importance as the weakness of the bonding makes the investigation of their structures in solution or in the gas phase very difficult. Many of the X-ray structures of these complexes in the solid are characterized by very diffuse reflections, indicative of anomalously high thermal motion or possibly disorder.This situation was first discussed quantitatively by Herbstein IC* who has suggested that several structures should be re-interpreted in terms of a disordered model. In some cases, the situation is quite clear. Thus, for the complex of pyrene (PY) and pyromellitic dianhydride (PMDA), Herbstein and Snyman found two different sites (A and B) for the pyrene molecules at 110 K and an ordering along the stacking axis of ---PY(A)---PMDA---PY(B)---PMDA---PY(A)---. Near 200 K there was an order-disorder transition involving the halving of the c-axis dimension, and the high temperature structure was considered to have a random distribution of the pyrene molecules over the two possible orientations A,B giving a statistical 50 : 50 occupancy at each pyrene site ---PY(AV)---PMDA---PY(AV)---PMDA---PY(AV)---. However, it was not possible to distinguish clearly between this.and a model of a * Authors to whom enquiries should be addressed. 2269 MOLECULAR MOTION IN SOLID COMPLEXES single pyrene oriented midway between the two possible orientations with a very large in-plane thermal motion. This indicates that disorder effects may well go undetected, seriously affecting both the detailed molecular parameters or even the gross orienta- tions of the two components. Where the angle between the two possible orientations is large, the situation is quite clear: For example, in the naphthalene (N)--tetra- cyanobenzene (TCNB) complex at room temperature there is clearly a random distribution of the naphthalenes over two sites related by a 34" in-plane r~tation.~ For other complexes the situation is less clear, either large amplitude vibrations or disorder being possible models.A question which cannot be answered from X-ray diffraction measurements, even where disorder is clearly indicated, is whether this disorder is of a static or a dynamic nature involving motion of the molecules. Wide-line n.m.r. has been widely used for the detection and characterization of molecular motions in the solid state,4 and in the two previous papers in this series 5* was used to investigate the motions of the donor inolecules in the complexes of naphthalene and pyrene with the acceptor molecules t etracyanoethylene (TCNE), tetracyanobenzene (TCNB) and pyromelliticdianhydride (PMDA).It was found in all cases that the naphthalene and pyrene molecules under- went very large in-plane motions involving complete reorientation in their molecular planes. There was clear evidence for the naphthalene +TCNB complex that jumping over a small angle occurred first, followed at higher temperatures by jumping over the larger angle,5 and that in the pyrene+PMDA complex the two occurred almost simultaneously.' For some of the other complexes there was some motion still occurring at 77 K as the second moments had not reached their limiting " rigid-lattice "values, but since both large amplitude vibrations and jumping over two closely related sites will reduce the observed second moment values, it was not possible to distinguish between these two possibilities.The presence of molecular motions in the solid state also manifests itself in large temperature dependences of the relaxation times of the nuclei. These temperature dependences can be treated quantitatively and used to determine the activation ener- gies for the motions.' One purpose of the present work was, therefore, to investigate the temperature dependence of T1(the spin-lattice relaxation time) and TI, (the spin- lattice relaxation time in the rotating frame) * of the proton nuclei in these complexes to first confirm the existence of motion, and secondly to provide accurate values for the energy barriers involved. We have recently used semi-empirical non-bonded interatomic potential functions together with a simple model for the reorientation process to calculate theoretically the barriers to rotation in molecular solids.These calculations have been reasonably successful in the case of polycyclic ar~rnatics,~ cage-like aliphatic molecules lo and adamantane and hexamethylenetetramine,l including the phase transition and diffusion l2 of adamantane. As an extension of this work, we have attempted to perform such calculations for the motion of the naphthalene and pyrene molecules in these complexes in order to determine the importance of the lattice forces which do not involve charge-transfer to the energy barriers for motion and the possible occurrence of disorder in these systems.Calculations of this type have recently been performed by Schmueli and Goldberg l3 for the complexes of naphthalene with tetracyanobenzene and tetracyanoethylene, although they were restricted to molecular orientations close to the potential energy minima. These will be discussed in the text. EXPERIMENTAL Pulsed n.m.r. measurements were made at 25.3 MHz on a modified n.m.r. Specialities spectrometer and at 9.2 and 25.3 MHz using a Bruker SXP variable frequency instrument. C. A. FYFE, D. HAROLD-SMITH AND J. RIPMEESTER 227 I Measurement techniques and methods of temperature measurement and control have been described previously.l49 The complexes were prepared as previously described ’9 and had melting points in agreement with published values.Calculations were performed using Fortran IV programswritten by the authors for an IBM 360 computer. RESULTS AND DISCUSSION The effect of a single motional process characterized by a correlation time T,, upon the spin-lattice relaxation time (T,)of a nucleus in the system is described by eqn (1) where coo is the radio frequency of measurement and C is a constant which depends on the details of the motion. Usually it is convenient to equate C with 2/3y2ASM where y is the gyromagnetic ratio for the nucleus in question, and ASM is the change in the observable second moment produced by the motion.The temperature dependence of Tl may be related to an activation energy for the motional process if one assumes that the correlation times obey an Arrhenius-type temperature dependence, eqn (2) T, = zoexp(-E,/RT). Thus a plot of log TIagainst 1 /Tshould give a “ V ” shaped curved with a minimum where oo~, 4 1) and high = 9.62 and limiting low temperature slope (where oO~, temperature slope (where w0z, @ 1) equal to Ea/R and -Ea/R respectively. Spin-lattice relaxation times, then, are sensitive to motions with correlation times such that T, N l/oo,and under usual experimental conditions yield minima for 7, 10-8-10-9s. Lower frequency motions can be characterized by measuring Tlp,the relaxation time measured in the presence of a low amplitude rotating magnetic field H,, Typical magnitudes for H1 are 1-50 G and minima in Tlpare then observed for correlation times z, of -5 x to 1 x s.In the weak collision limit the expression for TlPis given by (3) where col = yH1. In practice, the Tlpminimum for low HI values occurs in about the same temperature region as the CW n.m.r. line narrowing transition. Further-more, there are common assumptions in the derivation of eqn (1) and (3) and the two measurements should yield self consistent data. Where there is more than one motional process possible, as is thought to be the case for several of the systems under study, the situation is more complex. On the assumption that two motional processes (a) and (b)can be separately characterized by correlation times z(a) and z(b)which are related to the Arrhenius activation energies E,(a) and E,(b)respectively, the combined effect of the two motions can be described by eqn (4) and (5) for Tland Tlprespectively.1 1 f-Tl(a) Tl(b) MOLECULAR MOTION IN SOLID COMPLEXES If Ea(a)and E,(b) are quite different, then plots of log Tl and log TIPagainst 1 /T will each show two minima (although in quite different temperature regions). If the two motional processes are similar and have very similar activation energies, it is possible for these two minima to coalesce to a single minimum in T1and TIP. The format of our previous calculations of energy barriers to rotation in molecular crystals has been described in detail and will only be briefly outlined here.It is assumed that the energy of interaction between a molecule and its surroundings can be described as the sum of the pairwise interactions between all of its atoms (i =I 1 to n) and all of the atoms in the surrounding lattice (j= 1 to a)eqn (6) The empirical functions used are of the "exp. 6 '' type [eqn (7)] and the coefficients were those obtained by Williams l6 uij= -A/~:+Bexp (-crij). (7) Where all of the molecules are in their positions of minimum potential as indicated by the X-ray structure, the energy of interaction of the test molecule with its surround- ings is equal to the sublimation energy. To determine the energy barrier for motion about a particular axis, the test molecule is rotated about this axis and the potential between it and the rest of the lattice evaluated as a function of the angle of rotation, all the other molecules being kept at their positions of minimum potential.The difference between the "zero-degree rotation ''energy and the maximum on this curve is equated to the activation energy for comparison with experiment. It should be noted that, in this very simple model, any correlated motions between the molecules are neglected. The only justification for such a simple model lies in its agreement with experiment. This does not necessarily imply that such cooperative motions do not occur, only that there is no need to postulate such motions at this One problem which may be anticipated in the application of these calculations to systems where disorder or large thermal motions are present (as in the present instance), is that these effects may have given rise to incorrect or at least inaccurate molecular structures, and uncertainties in the molecular structures will seriously limit the accuracy of the calculations.The application of these two approaches to the complexes studied has met with varying degrees of success, and the different cases will be discussed individually. The activation parameters and the assigned motions are collected together for all the complexes in table 1. TABLEl.-OBSERVED AND CALCULATED VALUES (kJ m01-l) OF THE BARRIERS TO ROTATION IN SOLID MOLECULAR COMPLEXES OF NAPHTHALENE AND PYRENE complex small barrier large barrier calc. obs. calc. obs.N+TCNB * 8.0 9.7 46.0 42.7 N+TCNE a 5.0 none to 77 K 40.0 53.0 N+PMDA -none -41.0 PY+TCNB none none to 77 K 65.0 57.0 PY+TCNE none none to 77 K 105.0 61.O PY +PMDA -none -57.0 a Naphthalene molecules oriented at 0". C. A. FYFE, D. HAROLD-SMITH AND J. RIPMEESTER N A P H T HALE NE-TE TR A C Y CA NOB EN Z E NE (TCNB) As suggested in the introduction, the X-ray structure indicated the statistical occupancy of two possible orientations for the naphthalene molecules in the complex related by a 34" in-plane rotation (fig. The previous broad-line n.m.r. measure- ments suggested that two motional processes were occurring, one with a very low activation energy which was still present (on an n.m.r. timescale) at 77 K. A qualita-tive energy profile for the complete reorientation of the naphthalene molecules in their molecular planes by jumping over both small and large barriers, is indicated in fig.2. FIG.1 .-Schematic representation of the relationship between the two possible disordered orier,ta- tions for a single naphthalene molecule found in the naphthalene+TCNB complex. FIG.2.-Schematic representation of the relationship of the potential energy profile for the motion of the naphthalene molecules in the naphthalene+TCNB complex to the two possible disordered orientations. Plots of log Tland log TI, against 1/Tare shown in fig. 3. Both plots are strongly temperature dependent, indicative of the presence of molecular motion. In fact, both the T1and Tlpplots show complete minima, the minimum in Tl occur-ring at a lower temperature range than that of Tlp.Since for a given motion the mini- mum in TImust lie to higher temperatures than the TIPminimum and the linewidth transition, these two minima must be due to two quite different motional processes. The TIminimum must refer to a low energy process and the TIPminimum to a much higher energy process. The dotted line in fig. 3 represents a theoretical plot of eqn (4) and (5) with the correlation times z(a) and 7(b) defined ils in eqn (8) and (9) z(a) = 8.33 x exp(9400/RT) ~(b)= 4.84 x exp(42 700/RT). * Where R is in units of J K-' mol-'. MOLECULAR MOTION IN SOLID COMPLEXES The pulsed n.m.r. measurements thus fully substantiate the conclusions of the wide-line n.m.r.investigation as illustrated in fig. 2, and the diagram is now made more quantitative by defining E,(a) = 9.4 kJ mol-l and E,(b) = 42.7 kJ mol-l. Below the low temperature TIminimum the datum points are markedly lower than the calculated TIcurve. Such behaviour is typical of systems where there is a distri- bution in correlation times. Such a distribution may reflect a variation in reorienta- tional barrier heights in going from one molecule to another. loo. -10. -1. --0.1 .01 -1 I”I 1 1 1 9.0 11.0 13.03.O 5.0 7.0 103 KIT FIG.3.-Plots of TIand TIPon a logarithmic scale against the reciprocal of absolute temperature for the proton resonance of the solid naphthalene+TCNB complex. One other piece of information that can be obtained from the relaxation time measurements is an estimate of the temperature at which the very low energy motional process occurs, even if it is below 77 K, the lowest temperature at which measurements were made.Thus the theoretical curve for TI,may be extended to lower temperatures and the minimum in this curve used to estimate the approximate temperature range of the linewidth transition. Such a procedure predicts a temperature range of 50-60 K for the onset of motion. The temperature of the linewidth transition may also be pre- dicted from the empirical Waugh estimate, eqn (lo)* E, = 155T (10) which relates the activation energy in joules to the temperature of the transition in K. Using the value of E, = 9400 J mol-l found from the Tl measurements, again pre- dicts a temperature range of 50-60 K.Thus, on the basis of the n.m.r. measurements and neglecting any possible effects of correlation time distributions it is predicted that the motion of the naphthalenes will begin at about 50-60 K, on a n.m.r. timescale. Either the disorder will freeze in, giving the crystal a residual zero-point entropy, or more probably, an ordering will occur, giving a specific heat anomaly of 3R In 2 and probably a doubling of the stacking axis in this temperature range. The spin-lattice * Eqn (11) was originally formulated as Ea = 37T where the activation energy was expressed in calories. C. A. FYFE, D. HAROLD-SMITH AND J. RIPMEESTER 2275 relaxation time measurements have shown that there is no evidence of a phase transi- tion down to 61 K.In the application of potential energy calculations, it was hoped that it might be possible not only to simulate the observed energy barriers, or at least calculate that part that results from lattice forces, but that it might be possible to determine the source of the disordering forces. The model used was as described previously, and the nitrogen atoms were incorporated into the calculations in the usual way. The potential for the rotation of a single naphthalene molecule in a lattice in which the surrounding naphthalenes are disordered at each site is shown in fig. 4. In fact, the exact potential will be a function of the local environment of a particular naphtha- lene, in many cases this is found to give a reasonable simulation of the situation. In the region of the zero rotation the potential shows the required " W " structure.The angle between the potential minima is 36", in excellent agreement with the value reported experimentally (34"). The behaviour of the potential in this region is similar to that reported recently by Schmueli and Goldberg who used a similar model with different potential functions; they also found a double minimum (36") with a low barrier (12.6 kJ mol-'). The barrier to rotation between the two disordered positions was calculated in the present work to be 8.0 kJ mol-l compared with 9.4 kJ mol-l from the n.m.r. measurements. A barrier of 46.1 kJ mol-l was calculated for the large angle and end-over-end rotation compared with 42.7 kJmol-l from the n.m.r.measure- ments. The agreement here is probably to some extent fortuitous as the model and -1o.l-rl CI I2 -20.-25 -30.--40.--60.1 -180 -90 0 90 180 rotation angle/deg FIG.4.-The angular dependence of the potential energy for the in-plane rotation of a naphthalenemoleculein the naphthalene+TCNB complex with (inset) the contributions to the potential from the naphthalene-naphthalene and naphthalene-TCNB interactions. functions are certainly not exact, and the contribution from charge-transfer forces has not been included. This contribution is difficult to calculate for a " stack " of donor and acceptor molecules as is found in a crystal lattice, but its magnitude and angular dependence for the motion of one component may be estimated from the MOLECULAR MOTION IN SOLID COMPLEXES behaviour of an isolated donor-acceptor pair.Calculations of C.T. interaction energies by Mayoh and Prout l7 indicate that for this complex, the observed orienta- tion gives 95 % of the charge-transfer interaction energy for the symmetrical orienta- tion (naphthalene at 0" rotation). The overall effect would be to raise the minima with respect to the maximum between them, but the effect would be small. Multi-polar interactions between the complexes would also be expected to show a small orientation dependence. Another question is the origin of the disordering of the naphthalene molecules. Fig. 4 (inset) shows the napthalene potential in the region of the zero rotation broken down into the contributions from the naphthalene-naphthalene interactions and the naphthalene-TCNB interactions, for a structure in which all the naphthalenes are ordered at 0", i.e., midway between the two possible disorder orientations.As can be seen from the figure, the major contribution is the naphthalene-TCNB interactions, although the naphthalene-naphthalene interactions show the same tendency even when the surrounding naphthalenes are not at either of the disordered orientations. NAPHTHALENE + TETRACYANOETHYLENE The X-ray structure of this complex was first investigated by Williams and Wall- work '* who found large thermal parameters for the naphthalene carbons. Their data were reinterpreted by Herbstein and Synman who suggested on the basis of a difference synthesis, that there was a statistical disordering of the naphthalenes over two possible orientations as in the naphthalene +TCNB complex, although over a much smaller angle of 7.5".A qualitatively similar conclusion to that of Herbstein and Synman was arrived at by Schmueli and Goldberg from potential energy calcu- lations of the motion of the naphthalenes close to their positions of minimum potcntial. 1 ilII I I I 3.0 4.0 5.0 103KIT FIG.5.-Plot of Tl/son a logarithmic scale against the reciprocal of absolute temperature for the proton resonance of the naphthalene +TCNE complex. They, however, found an angle of 36" between the two disordered orientations and have recently found evidence for this value from a constrained refinement on this struct~re.~ Previous wide-line n.m.r.investigations indicated the presence of a high energy motional process involving the complete reorientation of the naphthalenes C. A. FYFE, D. HAROLD-SMITH AND J. RIPMEESTER and a very low energy process still occurring at 77 K on the n.m.r. timescale, but could not determine whether the latter involved a very large amplitude vibration or the jumping between two sites, although it did appear that the angle involved was less than that of the N+TCNB complex. 14N n.q.r. measurements 2o on this complex suggested a slight change in crystal structure between room temperature and 77 K. A plot of log T, against l/Tfor the proton resonance of this complex is shown in fig.5. The activation energy derived from this is 53 kJ mol-l, in rough agreement with that found for the other two naphthalene complexes for a similar motion of the naphthalene rings. Tlbecomes very long (TI= 520 s at 180 K), and any further motional process must involve very low activation energies. The results of potential energy calculations on this system are shown in fig. 6. As can be seen, there is first the appearance of a double minimum, suggesting the possible occurrence of disorder, and secondly a larger barrier of 29 kJ mol-1 to the complete reorientation of the molecule. This latter value is in qualitative agreement with the value obtained from the n.m.r. experiments -50 kJ mol-'.The behaviour of the potential in the region of zero rotation is in good qualitative agree- ment with the results obtained by Schmueli and G01dberg.l~ The barrier between the two is, however, much smaller in our case (-4.5 kJ mol-' cf. 16.6 kJ mol-'). The disordering force comes, as in the case of the N+TCNB complex from the acceptor molecules in the system although the neighbouring naphthalene molecules also con- tribute, even with artificially ordered at zero degree rotation (fig. 6, inset). -20.-L I- I I I -1 80 -90 0 90 180 rotation angle/deg FIG. 6.-Angular dependence of the potential for the in-plane rotation of a naphthalene molecule in the naphthalene+TCNE complex with (inset) the contributions to the total potential from the napht halene-napht halene and naph t halene-TCNE interactions .One possible reason why a motional process might not be detected by the relaxa- tion time measurements, although predicted by these calculations, is that the calcula- tions include non-bonding interactions only and neglect the charge transfer interactions between the two components. As indicated in the previous section, these are usually small and not very sensitive to the exact orientation of the two components."' 21 MOLECULAR MOTION IN SOLID COMPLEXES However, the calculated barrier in this case is very small, and even a small contribution from the charge-transfer interaction energy which tended to raise the energy of the minima relative to the barrier maximum might be very important.There is also evidence that the barrier calculations reported here and by Schmueli and Goldberg may not be for the stable low temperature structure. On the basis of 14N n.q.r. measurements, Kubo and co-workers 22 have suggested that a phase transition occurs between 77 and 200 K. At 77 K there are two inequivalent N atoms in the crystal whereas the room temperature X-ray results indicate that all N atoms are equivalent. NAPHTHALENE + PYROMELLITICDIANHYDRIDE A preliminary X-ray investigation of this complex indicated a high degree of appa- rent thermal motion,23 but no complete structure is yet available. Wide-line n.m.r. studies indicated a high energy reorientation process, corresponding to complete reorientation of the naphthalene molecules.At 77 K there was again some degree of motion, but it was not possible to distinguish between jumping between disorder sites or a large amplitude vibration/oscillation. 4, T1P lk1 I I 1 I I I 3.0 40 5.0 6.0 7.0 8.0 lo3KIT FIG.7.-Plots of Tl/sand Tlp/son a logarithmic scale against the reciprocal of absolute temperature for the proton resonance of the naphthalene+ PMDA complex. The relaxation times of the protons are strongly temperature dependent (fig. 7), confirming the presence of motion. There is a clear minimum in Tlpwhich has been used to calculate the theoretical curves for T,, Tlpindicated by the broken lines. These yield an activation energy for the process of 41 kJmol-l, in good agreement with the interpretation of the earlier wide-line observations in terms of a high energy process.There is, however, no evidence in the Tlmeasurements for a second relaxa- tion process down to 77 K, Tlat this temperature being 50 s and any process below this point must be of very low energy, as the second minimum for N +TCNB was very clearly observable with an activation energy of 9.4 kJ mol-l. The ASM value used for the calculated Tland T1,curves was 0.87 G2,much less than the value expected for complete reorientation of the naphthalene molecule. This implies that there is another motion at lower temperatures which partially averages the second moment C. A. FYFE, D. HAROLD-SMITH AND J. RIPMEESTER 2279 and/or that the motion takes place between inequivalent sites.The (second moment, temperature) behaviour excludes neither of these possibilities. It was not possible to perform potential energy calculations for this complex due to the lack of structural data, and also reliable oxygen parameters for the non-bonded interactions. PYRENE + TETRACYANOETHYLENE The room temperature crystal structure of this complex 24 shows ordered pyrene molecules with the tetracyanoethylene molecules oriented above and below the end rings of the donor molecule. A recent X-ray diffraction study on C2H8]pyrene TCNE at 77 K found a disorder in the TCNE molecules which consisted of the occupancy to about 7 % of an alternate site by a 90" in-plane rotation of the TCNE Wide-line n.m.r. investigations indicated that complete reorientation of the pyrene molecules was occurring above room temperature. A plot of log Tlagainst 1 /Tfor the proton resonance of this complex is shown in fig.8. The dotted line is that for an activation energy of 61 kJmol-l. TI becomes very long at lower temperatures and there is no evidence for further motions. looI -10 1-2.5 3.5 4.5 103 KIT FIG.8.-Plots of Tl/son a logarithmic scale against the reciprocal of absolute temperature for the proton resonances of the complexes of pyrene with 0 TCNE, 0TCNB and 0 PMDA. The calculated potential for reorientation shows the zero degree orientation to be the most stable for this complex, and a barrier to rotation of 105 kJmol-l? although this depends on one or two large interactions and may be lowered by slight movements of the pyrene out of its plane at the barrier maximum.The subminimum at 90" rotation would not be significantly populated as it is 33 kJ mol-1 higher than the position of minimum potential. PYRENE -k PYROMELLITICDIANHYDRIDE As discussed in the introduction, the crystal structure of this complex has been investigated at both room temperature and 110 K.2 The low temperature form is ordered and there is an order-disorder transition near 200 K, where there is a statistical disordering of the two pyrene molecules over the two possible sites (fig. 10) related as MOLECULAR MOTION IN SOLID COMPLEXES in the naphthalene +TCNB complex by an in-plane rotation. Wide-line n.m.r, measurements indicated that there was a rigid structure up to the phase transition and then complete reorientation of the pyrene molecules in their molecular plane^,^ the observed spectral changes being too large to be explicable in terms of just a jumping between the two disorder sites as the angle between them is only 16".I I I I -180 -90 0 90 180 rotation angle/deg FIG.9.-The angular dependence of the potential for the in-plane rotation of a pyrene-molecule in the pyrene+TCNE complex with (inset) the contributions to the total potential from the pyrene- pyrene and pyrene-TCNE interactions. \ FIG.10.-Schematic representation of the relationship between the two possible disordered orienta- tions for a single pyrene molecule. The results of the spin-lattice relaxation time measurements are shown in fig.8. There is clear evidence for a high energy motional process E, N 57 kJ mol-l and TI becomes very long as the temperature is lowered. From these data, it is not possible to deduce the activation energy for the jumping over the small angle between the two possible orientations. Since there is no motion before the phase transition, the Tl data will not show a minimum at lower temperatures, unlike the naphthalene +TCNB complex. Although structural data are available for this complex, it was unfortunately not possible to perforin potential energy calculations due to the lack of good para- meters involving the oxygen atoms in the PMDA molecule. C. A. FYFE, D. HAROLD-SMITH AND J. RIPMEESTER 228 1 PYRENE + TETRACYANOBENZENE lnvestigations of the X-ray structure of this complex at 178 K and 290 K have been made.25 The structure showed large thermal motion at both temperatures, but refinement in terms of a disordered structure was reported to give significantly worse agreement than refinement employing anisotropic rigid-body motion of the pyrenc molecules.N.m.r. measurements indicated a rigid lattice at 77 K and complete reorientation at room temperature. The tempxature dependence of TIfor the pro-ton resonance of this complex is shown in fig. 8. The activation energy for the high energy motion causing this change in T1is 2157 kJ inol-l. TI becomes large at lower temperatures, but it is not possible to say whether there is another low energy motion as a similar situation to the pyrene+PMDA complex might exist.Potential energy calculations indicate a large barrier to rotation (65 kJ mol-l) with no disorder orienta- t ions. CONCLUSIONS The spin-lattice relaxation time measurements have confirmed the existence of large in-plane motions for the naphthalene and pyrene molecules in all the complexes studied, as suggested by the previous wide-line n.1n.r. investigation~.~g In the cases of the naphthalene +TCNB, pyrene +TCNE and pyrene +PMDA, comparison of the data from X-ray diffraction, wide-line n.m.r., measurements of TI and potential energy calculations gives a reasonably complete description of the total dynamic structure of the solid complexes (table 1). In the case of the other complexes (naph- thalene +TCNE and +PMDA and pyrene +TCNB) the description is less complete.Thus, all show in-plane reorientation of the donor molecules, but it has not been possible to distinguish by any of these methods unambiguously between a jumping of the donor molecules between two closely related sites and a large amplitude in-plane vibrational motion of the donor molecules. The T1measurements indicate that the low energy barrier to a jumping between sites would probably have to be of the order of 4 kJ mol-' or less, and this distinction will be difficult to make. Although the changes in orientations are small, it is important that they be well understood, as they may be critical in determining the conductive and magnetic properties of these com- plexes, especially at low temperatures. One possible avenue which has not yet been explored is the use of low temperature heat capacity measurements.These could be carried out down to liquid helium temperatures and one would expect a residual zero point entropy of $R In 2 or an order-disorder transition with an associated entropy change of +R In 2 if there are indeed two distinct sites for the donor molecules. Although the entropy changes would be small, the fact that they would be at such low temperatures makes these experinients quite viabIe as the overall heat capacities would be small and contribu- tions from disordering would constitute a relatively large proportion of the total heat capacity. It is suggested that these measurements be made, first on the naphthalene + TCNB complex where a prediction of a disordering transition probably below 60 K has been made, and then on the naphthalene +TCNE and pyrene +PMDA complexes.The authors would like to thank the National Research Council of Canada for a grant in aid of research (C. A. F.) and Dr. H. S. Gutowsky for providing facilities for some of the measurements. (a) R. Foster, Organic Charge Transfer Complexes (Academic Press, London, 1969) ; (b) C. K. Prout in Molecitlar Complexes, ed. R. Foster (Logos, London, 1973), vol. VI ; (c) F. H. Herb-stein in Perspectires in Structural Cltcmistry, ed. J. D. Dunitz and J. A. 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ISSN:0300-9238    

DOI:10.1039/F29767202269

出版商:RSC    

年代:1976

数据来源: RSC