摘要:

J. Chem. Soc., Faraday Trans. 2, 1989, 85(1), 1-10 Dynamics of the Li +Li, +Li, +Li Isoergic Exchange Reaction A Comparative Study on Two Potential-energy Surfaces Victor M. F. Moraist and Antonio J. C. Varandas* Departamento de Quimica, Universidade de Coirnbra, 3049 Coimbra Codex, Portugal The trajectory calculations of the alkali-metal atom +alkali-metal dimer reactions initiated in a previous work have been extended to the Li + Liz system using two different potential-cnergy surfaces for the Li, trimer. The results agree well with each other and with previous results by other authors, suggesting a statistical mechanism for this exchange reaction. Recently’ we have investigated whether the M’+ M2+M’M +M (M’= Li, Na; M = Na, K) alkali-metal exchange reactions wzre of the direct or indirect type by carrying out a detailed quasiclassical trajectory study of those reactions on recently reported’ modified LEPS functions.Somewhat surprisingly, the answer turned out to depend on the dynamical attribute one was looking at, e.g. we observed that the vibrational distributions of the products were non-thermal and yet the lifetime distributions for the complexes were of the statistical type. The question remains though of how much influence the potential-energy surface has on the final outcome. In this work, we carried out a comparative dynamics study of the title reaction on two recently reported potential-energy surfaces for the Li3 system. One of these surfaces is based on the semiempirical modified LEPS approach of Varandas and Morais3 and thus has a form similar to that employed in ref.(1) for the LiNa, and NaK, systems. The other Lij potential-energy surface used in the current work is due to Thompson et d4This potential-energy surface was obtained from a direct fit to reported a6 initio energies using the functional form suggested by Thompson et aL5 Lig Potential-energy Surfaces Since the potential-energy surfaces used in the present work have been described in detail we focus here on their major features. Table 1 compares the properties of the stationary points of the Varandas-Morais and Thompson et al. potential-energy functions. Despite the distinct sources of the input data used for their calibration (accounting for the considerable differences in the depth of the well associated to the equilibrium triatomic geometry), the two potential-energy surfaces show a close similarity regarding the relative positioning of the most relevant topographical features.Note, however, that the symmetrical collinear (’E:) saddle point on the potential-energy surface of Thompson etal. has a somewhat higher energy (in relation to the bottom of the Li3 well) than in our own potential-energy surface. Note also that in both potential- energy surfaces the C2vacute structures (’A,) correspond to saddle points which have one imaginary frequency. Furthermore, on both potential-energy surfaces the C2vobtuse structures (*B2) are the ones corresponding to the equilibrium geometry of Li,. t Permanent address: Instituto de Ciihcias BiomCdicas Abel Salazar, Universidade do Porto, 4000 Porto, Portugal.Dynamics of Isoergic Exchange Table 1. A comparison of the main topographical features of the potential-energy surfaces used in this work between themselves and with those of the Whitehead-Grice potential (for the linear symmetrical geometry) wavenumber state A E / kJ mol-' "asym %end ref. 2z; 5.2 180 57.8 370 40i 225 3 5.1 180 24.6 364 75i 206 4 5.3 180 34.7 307 18 205 11 2Al 5.7 52.0 69.2 162i 236 365 3 5.7 52.5 44.9 1OOi 252 367 4 *B2 5.2 74.0 70.7 140 210 345 3 5.3 70.1 45.4 130 190 349 4 2E' 5-4 60 64.8 ---3 5.4 60 40.2 ---4 R is the characteristic bond length, a is the angle and AE is the binding energy with respect to the atom-diatom asymptote and i is a.Fig. 1 shows energy contours for the two Li3 potential-energy surfaces used in the current work as a function of the two Li-Li stretching coordinates, keeping the angle fixed at the corresponding equilibrium value. The notorious difference is the larger well depth [this was chosen in ref. (3) to mimick the experimental atomization energy6 of Li3] of the minima associated to the equilibrium Li, structures in the Varandas-Morais potential-energy surface. Also apparent is a small energy barrier that separates a local minimum occurring for large atom-diatom separations from that associated with the equilibrium Li, species. Note, however, that this barrier lies below the atom-diatom dissociation energy.Thus, it is expected to have no significant dynamical implications. Fig. 2 shows another view of those two potential-energy surfaces in the form of a relaxed triangular plot.7 To obtain plots (a) and (6) of this figure the perimeter of the triangle formed by the three atoms has been relaxed so as to give the lowest potential energy at each value of the geometry defined by (@, 9:). A total of 500 perimeters (which were obtained by varying P between 1 and 60 a, at intervals of 0.13 a,) have been sampled. For simplicity, we do not give the associated optimum perimeters since the corresponding triangular equiperimeter contour plots show a strong similarity with those reported in ref. (7) for the H3 system. Note that all relevant physically accessible space is encompassed by these relaxed triangular plots.As a result, they are most convenient for visualizing the reaction dynamics;8 see also the next section. Trajectory Calculations The quasiclassical trajectory method as applied to atom-diatom collisions is well docu- mented in the literature' and hence no details will be given here. This method has been used to calculate total reactive cross-sections for the title reaction using the two potential- energy surfaces described above. A total of 5000 trajectories were run at a collision energy of 3.5 kcal mol-'. As in ref. (l), the diatomic molecule was initially set at the ground vibrational state (u=0) and rotational quantum number J = 10 since these correspond approximately to those observed in supersonic molecular beams," and they have also been adopted in previous quasiclassical trajectory studies. ',"J* All calculations were carried out using a modified version of Muckerman'~'~ program.The step size for the trajectory numerical integration (based on a combination of a fourth-order Runge- Kutta and an eleventh-order Adams-Moulton method) has been chosen from the K M. F. Morais and A. J. C. Varandas CU 0 oq!l!lH Dynamics of Isoergic Exchange $001 -s2. N-.N c -. 0 c L'. 0 I tu-N I * x 51s V. M. F. Morais and A. J. C. Varandas Table 2. Summary of the trajectory calculations potential E N N' bmax Ur Varandas-Morais3 3.5 2500 943 8.0 75.8f1.9 4.30 Thompson et aL4 3.5 2500 808 7.5 57.1 f1.7 2.13 Whitehead14 4.0" 1000 25 1 7.5 44.4f2.4 1.09 ~ The units of energy, length and time used in this table are kcal mol-', A and ps, respectively." For data referring to other collisional energies see the original work. requirement that both the total energy and total angular momentum were conserved to four or more digits. Table 2 lists some of the relevant information from these calculations, while providing a comparison with the previous results of Whitehead" using the Li3 Whitehead-Gri~e'~ LEPS potential-energy surface. In table 2, E is the collisional energy, N is the number of compruted trajectories and N' is the number of reactive trajectories. Moreover, a' and Ad are, respectively, the reaction cross-section and associated 68% error limit calculated from a'( E) = Tbiax(N'/ N) and Aa'(E) = d[(N-N')/N'N]1'2 where b,,, is the maximum impact parameter that leads to reaction.The last column of table 2 shows the Li,* complex lifetime defined as the time during which the three Li atoms can be circumscribed within a circle of radius equal to 3.25 A. Of the three Li3 potential-energy functions, ours predicts the largest reactivity: it gives reaction cross-sections ca. 33% larger than those based on the potential-energy surface of Thompson et al. and ca. 71 O/O larger than those for the Whitehead-Grice potential-energy surface. Unfortunately, no comparison with experiment is possible at present to assess the reliability of the various potential-energy surfaces. However, it is interesting to note that there is an approximate linear relationship between the computed reactive cross- sections and the well depth of the corresponding Li3 potential-energy surface.This may provide a criterion to calibrate the potential-energy function when accurate estimates of the absolute total reactive cross-section become available. Since our own potential- energy function shows the largest well depth, it is perhaps fair to say that the correspond- ing cross-sections should provide a close upper bound to the true results. This expectation is also corroborated from the fact that our potential-energy surface is somewhat too attractive at large atom-diatom separations [this is partly due to the neglect of three-body dispersion effects in the semiempirical valence-bond formulation of ref.(l)]. Fig. 3 compares the opacity function for the Li +Liz isoergic exchange reaction on the Varandas-Morais and Thompson et al. potential-energy surfaces. Despite some differences at small and large impact parameters, there is a great similarity between the two sets of results. Also shown in fig. 3(c)-(f) is the dependence of the reaction probability on impact parameter considering separately the reactive trajectories that live less than 1 ps and those that have a larger lifetime. In comparison with the results reported elsewhere' for Li +Na, and Na+ K2, we note the larger percentage of trajec- tories living longer than 1 ps and which are therefore catalogued as statistical.Fig. 4 compares the Li+ Li, differential cross-sections for the same two potential- energy surfaces. As found previously by Whitehead, the angular distribution is nearly symmetrical around 6= 90" with sharp forward and backward peaks. This behaviour is to be expected at low collisional energies and in systems for which the maximum Dynamics of Isoergic Exchange 3llOL 0.2 0.0 I h? OL ni [jL02 ja 1 0.4 0.2 0.4 0.6 0.8 1.0 reduced impact parameter Fig. 3. Opacity functions showing the dependence of the reaction probability P( 6) on the reduced impact parameter (b/b,,,) calculated with the Varandas-Morais (a)and the Thompson et al. (d) potential-energy surfaces. Shown in the remaining plots of this figure is the dependence of the reaction probability on impact parameter, considering separately the reactive trajectories that live more than 1 ps [respectively, (b) and (e)] and those that have a shorter lifetime [respectively, (c) and (5)l.30.0-20.8-c .-G 22.5-15.6--2 v) 15.0-10.4-d r.-* $ 7.5-5.2-m % 7) 0.0--scattering angle/" Fig. 4. Centre-of-mass differential cross-sections for the Li + Liz reaction obtained with the Varandas-Morais (a) and Thompson et al. (b) potential-energy surfaces. V. M. F. Morais and A. J. C. Varandas 2.04. 0.82 -0.41 Ym -1.63. -2.86 -4.M -3 4 -262 -0.71 071 21 2 3. 4 0.0 0.0 1.L 2.8 4.2 5.6 7. Fig. 5. (a) Relaxed triangular plot of a long-lived reactive trajectory on the Varandas-Morais potential-energy surface.(b) Bond distance uersus time plot of the same trajectory. For the coordinates of plot (a),see fig. 2. Note that in (b)each line refers to a specific Li-Li bond distance. orbital angular momentum is much larger than the internal angular momentum (J= 10A). Moreover, the shape of the distribution in this osculating regime can be obtained from the expression relating the lifetime of the complex to its rotational period: 7=274I/L) (3) where I is the moment of inertia of the complex and L its orbital angular momentum. Using this expression we estimate (based on the equilibrium geometries predicted from the two potential-energy surfaces used in the current work) a rotational period for the Li; complex of ca.0.4 ps. This reinforces our belief that most Li +Liz reactive trajectories (living longer than 1 ps) are of the statistical type. One such trajectory is shown in fig. 5 using the relaxed triangular plot already discussed above. For comparison we- also show in this figure the corresponding conventional bond distance versus time plot. It Dynamics of Isoergic Exchange complex lifetime/ps Fig. 6. Histograms showing the complex lifetimes for the LiT complex on the Varandas-Morais (a) and Thompson et al. (b) potential-energy surfaces. I 1(dl 0.0 0.2 0.L 0.6 fractional energy (T) fractional energy (R) fractional energy (V) Fig. 7. Translational (T), rotational (R) and vibrational (V) product-energy distributions obtained by the trajectory calculations on the Varandas-Morais [(a)-(c)] and Thompson et al.[(d)-(f)] potential-energy surfaces. Shown for comparison are the predictions of a statistical model (+++). V. M. F. Morais and A. J. C. Varandas Table 3. Average product energy disposal for the Li +Liz reaction Varandas-Morais3 23.8 26.2 50.0 Thompson et aL4 23.6 24.8 51.6 Whitehead-Grice14a 26.3 25.3 48.5 a Interpolated from the data reported in the original work. LO-, 0 i 2 3 0 i 2 3 vibrational quantum no. Fig. 8. Vibrational product quantum-state distributions obtained with the Varandas-Morais (a) and Thompson et al. (b)potential-energy surfaces. Also shown in all plots are the Boltzmannian curves (+++) assuming thermal equilibrium at T = 300 K.is seen that the trajectory wanders around the three equivalent wells for equilibrium Li3 before escaping to the product channel. Also seen from this specific trajectory is the rotational motion of the product diatomic molecule, which is shown in the relaxed triangular plot as the lines on the upper right-hand corner of the physical triangle (these lines are nearly parallel to one of the sides of this traingle, with the vibrational motion being displayed through the small oscillations). The nearly statistical nature of the Li +Liq dynamics is further stressed by the exponential-type decay shown by the his- togram representations of the complex lifetimes in fig. 6. From this figure, one obtains values for the average complex lifetime of 4.3 and 2.1 ps for the Varandas-Morais and Thompson etal.potential-energy surfaces, respectively. These are ca. 10 and 5 times larger than the corresponding rotational periods. It appears, therefore, from the three reactions already studied (Li+Li, from this work and’ Li+Na, and Na+K,), that Li + Liz shows the more marked statistical behaviour. We take the opportunity to note that the values of T reported in our previous work’ are in error. The correct values should read 1.24 and 2.04 ps for LiNa, and NaK,, respectively. However, this result does not affect any of the conclusions stated in that reference. Fig. 7 shows the energy distributions obtained from the current trajectory calculations. In contrast to the results reported previously’ for the Li + Na, and Na+ K2 reactions, we observe now a remarkable similarity between the trajectory data and the curves calculated on the assumption of a statistical The average values of these energy distributions for the Varandas-Morais and Thompson et al.potential-energy surfaces are compared in table 3 with those from Whitehead.” It is seen that the data Dynamics of Isoergic Exchange are in good agreement, although they reflect also to a certain extent the small sensitivity of these quantities to the topographical details of the potential-energy surface. Fig. 8 compares the vibrational-state distributions for the product Liz molecules obtained from the trajectory calculations with the corresponding Maxwell-Boltzmann distribution assuming a vibrational temperature of 300 K.It is seen that the trajectory data are well described by a vibrational temperature, and in any case much better described than for Li +Na, and Na +K2. Conclusions The trajectory calculations from the present work support and extend the findings from previous work in the sense that the major conclusions then extracted should remain valid also for other realistic surfaces for the heteronuclear alkali-metal trimers. They also show that of the three alkali-metal atom-alkali-metal dimer reactions so far studied, the ordering concerning the highest degree of statistical behaviour is Li +Li, > Li +Na, > Na+K,. We thank the Instituto Nacional de Investigasgo Cientifica (INIC), Lisbon, for financial support.The allocation of computer time at the University of Oporto is also gratefully acknowledged. References 1 V. M. F. Morais and A. J. C. Varandas, J. Chem. Soc., Faraday Trans. 2, 1987, 83, 2247. 2 A. J. C. Varandas, V. M. F. Morais and A. A. C. C. Pais, Mol. Phys., 1986, 58, 285. 3 A. J. C. Varandas and V. M. F. Morais, Mol. Phys., 1982, 47, 1241. 4 T. C. Thompson, G. Izmirlian Jr, S. J. Lemon, D. G. Truhlar and C. A. Mead, J. Chem. Phys., 1985, 82, 5597. 5 T. C. Thompson, D. G. Truhlar and C. A. Mead, J. Chem. Phys., 1985,82, 2392; T. C. Thompson and C. A. Mead, J. Chem. Phys., 1985,82, 2408. 6 C. H. Wu, J. Chem. Phys., 1976, 65, 3181. 7 A. J. C. Varandas, Chem. Phys. Lett., 1987, 138, 455. 8 A.J. C. Varandas, 1. Mol. Srrucr. (Theochem.),1988,166,59;A. J. C. Varandas, Faraday Discuss. Chem. SOC.,1987, 84, in press. 9 D. G. Truhlar and J. T. Muckermann, in Atomic- Molecular Collision Theory, ed. R. B. Bernstein (Plenum Press, New York, 1981), p. 475. 10 M. P. Sinha, A. Schultz and R. N. Zare, J. Chem. Phys., 1973, 58, 549. 11 J. C. Whitehead, Mol. Phys., 1975, 29, 177. 12 J. C. Whitehead, Mol. Phys., 1976, 31, 549. 13 J. T. Muckermann, Quantum Chemistry Program Exchange, no. 229 (Indiana University, Bloomington, Indiana, 1973). 14 J. C. Whitehead and R. Grice, Mol. Phys., 1973, 26, 267. 15 S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Lett., 1972, 12, 564. 16 P. J. Dagdigian, H. W. Cruse, A. Shultz and R. N. Zare, J. Chem. Phys., 1974, 61, 4450. Paper 8/01756E; Received 4th May, 1988

ISSN:0300-9238    

DOI:10.1039/F29898500001

出版商:RSC    

年代:1989

数据来源: RSC

ISSN:0300-9238    

DOI:10.1039/F298985BX003

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chern. SOC.,Faraday Trans. 2, 1989, 85(1), 11-28 Analysis of the Infrared Absorption Spectra of Solutions of Water in Some Organic Solvents Part 1.-Resolution of Overlapping Absorption Bands Sylvia 0.Paul?' and Thomas A. Ford*$ Department of Chemistry, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa An efficient approach to the resolution of infrared band envelopes into their component bands is described. The procedure involves first determining the number of component bands, using the factor analysis technique of Bulmer and Shurvell. The bands are then resolved by the methods of Pitha and Jones, and values for the wavenumbers, half-widths and intensities of the component bands extracted. The method is illustrated by the analysis of the spectra of water at high dilution in some ketone and ether solutions.The component bands are assigned to the vibrations of the hydrogen-bonded complexes present in these solutions, and the spectroscopic properties are rationalized in terms of the nature of the hydrogen-bonded interactions. For some years we have been engaged in a study of the infrared spectra of water dissolved in organic bases. The objective of this study has been to develop a model for the structures and energetics of the hydrogen-bonded complexes formed by water in such binary mixtures. Thus we have reported the spectra of H20 in some ketones' and ethers,2 in the OH stretching region and the HOH bending regi~n,~ and of HDO in the OH stretching regi~n.~ We have also investigated the effect of temperature on the appearance of the OH stretching bands of H20,' and have correlated the wavenumber shifts, half-widths and band intensities with some of the physical properties of the solvents studied.6 These experimental investigations have been augmented by a series of semiempirical molecular-orbital calculations, at the CND0/2 and MIND0/3 levels, of the structures, hydrogen-bond energies and other electronic properties of the 1 :1 and 2 :1 hydrogen-bonded complexes postulated to exist in these Two problems were encountered in our attempts to analyse and interpret the observed infrared spectra: the resolution of the band envelopes in the OH stretching region into the appropriate number of component bands, and the determination of the total OH stretching band intensity and of the individual component band intensities.This paper addresses the first of these problems; the second will be the subject of a forthcoming publication. lo The spectra Spectra were recorded for nine ketone and seven ether ~olvents.*-~~~ of water in acetone, ethyl methyl ketone, diethyl ketone, methyl n-propyl ketone, cyclopentanone and cyclohexanone had the appearance of two broad, overlapping bands centred around 3600 and 3500 cm-I. In solutions with di-n-propyl ketone, di-isopropyl ketone or di-n-butyl ketone as solvents, the spectra showed an additional, narrow band in the region of 3680 cm-' [ref. (l)]. This band was also evident in the spectra of the ?Present address: Department of Chemistry, University of South Africa, P.O.Box 392, Pretoria 0001, South Africa. $Present address: Mail Stop C345, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, U.S.A. 11 Resolution of Overlapping Absorption Bands ether-water solutions with di-n-propyl ether, di-isopropyl ether, di-n-butyl ether and di-n-amyl ether as solvents.* The spectra of water in tetrahydrofuran, tetrahydropyran and 1,4-dioxane seemed to indicate a high-wavenumber shoulder on the broad higher- wavenumber band.2 Thus it appeared that two kinds of spectra were observed; one with only two constituent bands in the envelope, the other with more than two bands. The interpretation of the first kind of spectrum presents no difficulty: the water molecule is presumed to be hydrogen bonded in a complex in which it retains its CZv symmetry. The two broad, overlapping bands may then be regarded as being due to the antisymmetric (v,) and symmetric (v,) stretching vibrations of water molecules hydrogen bonded in 2 :1 solvent-water complexes.The presence of another single band is not so readily explained. In whatever way the water molecule is pictured, either two bands (for only one kind of hydrogen-bonded water molecule) or four bands (for two kinds of hydrogen-bonded water molecules) should be observed in the OH stretching region. The analysis and interpretation of the spectra clearly depend upon the accurate determination of the number of component bands and the measurement of their spectro- scopic parameters. These are discussed below.Experimental The spectrophotometers used, and the solvent purification and solution-handling tech- niques have been described.'-5 The spectra were digitized manually at 4 cm-' intervals, generally in the range 3720-3420 cm-' for the ketone-water solutions and 3720- 3380 cm-' for the ether-water solutions. Although visual evidence seemed sufficient to deduce whether there were two or more component bands in the envelope observed for a given solvent-water system, a statistical method based on the algebraic factor-analysis te~hnique'l-'~ was employed to compute the true number of bands constituting the band envelope. Determination of the Number of Bands in a Band Envelope using the Factor-analysis Technique The method of factor analysis, developed and adapted for computers by Bulmer and Sh~rvell,"-'~was used to determine the number of overlapping components in the observed band envelope; this number was determined by analysing the digitized spectra of a number of solutions at various concentrations and was independent of the component bandshapes.The factor analysis, or matrix rank analysis, of digitized infrared bands is based on a number of algebraic definitions and theorems, viz. the maximum number of linearly independent rows (or columns) of a matrix is called its rank;14 the rank of a matrix of absorbance measurements is related to the number of independently varying components in the and the rank of a matrix which can be written as the product of two matrices is equal to the rank of the smaller of the two matrices.'' If the number of wavenumber values at which the absorbances of a spectrum are determined is n,, and the number of solutions of different concentrations whose spectra are analysea n,, then an n, x n, absorbance matrix, A, may be generated.The number of independent vectors, n,, in this matrix is equal to the number of component bands in the spectral envelope (see above). The integer n, may be equated to the rank of matrix A (see above), if the Beer-Lambert law is taken into consideration, i.e. A=EC (1) where the absorbance matrix A is normalised to unit pathlength, E is the n, x n, molar absorptivity matrix and C is the n,x n, concentration matrix.If both n, and n, are greater than n,, the integer to be determined, this integer is the rank of matrix A S. 0.Paul and T. A. Ford according to the third theorem given above. However, under some conditions the rank of matrix A may be less than nC,l8viz. when either the spectrum of one of the components is linearly dependent on the spectra of the other components, or the concentration of one of the components is a linear combination of the concentrations of the other components. Provided that these two conditions are avoided, the determination of the rank of matrix A yields n,, the number of overlapping bands in the spectrum. In order to determine the rank of matrix A, the real symmetric matrix Q, where Q = A~A (2) is constructed, where AT is the transpose of A.The fact that a matrix and its transpose have the same rank,19 in consideration of the third theorem above, leads to the conclusion that Q has the same rank as A. Since each real symmetric matrix may be expressed in terms of its eigenvalues and eigenvector~,~~ the rank of Q is found by computing the number of non-zero eigenvalues of Q; this number equals the rank of the matrix.'6-18 Since Q is real and symmetric, it may be transformed to a real diagonal matrix by an orthogonal transf~rmation'~ D = S'QS where S is an orthogonal matrix. An orthogonal transformation is simultaneously a similarity transformation. l9 Two matrices related by a similarity transformation have the same eigenvalues, and the eigenvalues of a diagonal matrix are its diagonal elements.20 The eigenvalues of matrix Q are therefore identical with the diagonal elements of matrix D.A detailed description of the use of the factor-analysis computer program CHISQ"-'~ in analysing the spectra of water in diethyl ketone solutions has been presented.' The validity of applying the factor-analysis method to the spectra of the overlapping OH stretching bands of water was considered in the light of the two conditions discussed above. Care was taken to ensure that the concentrations of the solutions whose spectra were used for the computations were not linearly dependent.16 However, there was a possibility that the number of antisymmetric vibrations and the number of symmetric vibrations of the molecules determined during a spectral scan were interrelated over the concentration ranges considered.This would be equivalent to the second condition above, i.e. the ratio of the 'concentrations' of the antisymmetrically and symmetrically vibrating OH groups would be constant. Assuming that one kind of associated water molecule only is present in a solution, then the spectrum would consist of two OH stretching bands, whereas the OH stretching band envelope should consist of four overlapping components if two different kinds of hydrogen-bonded water molecules were present in the solution. Results from the factor analysis would indicate a smaller number of bands if the intensities of the constituent bands were linearly dependent. Application of the factor-analysis technique revealed the numbers of component bands in the spectra for each solvent indicated in table 1.Resolution of the band Envelopes and Bandshape Analysis The band envelopes of the observed spectra in the OH stretching region were resolved into the appropriate number of components, as listed in table 1. The additional band at the high-wavenumber end of those spectra with more than two components was assumed to be due to weak interactions of the non-bonded OH groups of 1:1 solvent-water complexes with the bulky alkyl groups of the solvents. The interaction was considered to be weak because the band at the high-wavenumber end exhibited the smallest wavenumber shifts from the OH stretching bands of water vapour.Resolution of Overlapping Absorption Bands Table 1. The number of component bands in the spectra of the solvent-water complexes, deduced from the factor-analysis computations no. of component solvent bands present acetone 2 ethyl methyl ketone 2 diethyl ketone 2 methyl n-propyl ketone 2 cyclopentanone 2 cyclohexanone 2 di-n-propyl ketone 4 di-isopropyl ketone 4 di-n-butyl ketone 4 di-n-propyl ether 4 di-isopropyl ether 4 di-n-butyl ether 4 di-n-amyl ether 4 tetrahydro furan 4 tetrahydropyran 4 1,4-dioxane 4 The band of the 1:1 complexes due to OH groups bonded to the carbonyl groups of the ketones, or to the ether oxygen atoms, was then envisaged to be strongly overlapped with one or more of the bands of the 2: 1 complexes. This assumption was verified by observations made during the variable-temperature experiments.’ The shapes of bands in gas-phase spectra are determined by collision broadening and thus exhibit Lorentzian band Most research workers concerned with infrared bandshapes of condensed-phase systems have assumed that there was an analogy between the bandshapes in the spectra of gases and those of condensed-phase systems.23 This assumption has been verified by several experimental measurement^.,^^-^' but for most infrared spectral determinations it was found that the bands measured had a profile of mixed character; some bands exhibited considerable Gaussian character in their band shape^,^^-^' while others did so to a far lesser Only in some isolated cases have bands of pure Gaussian shape been analy~ed.”,~~ The departure from a bandshape described by a pure Lorentzian function was considered to be due to a Gaussian perturbation, caused by the convolution of the solution band with a Gaussian slit error f~nction,~’or by specific solute-solvent of the solute molecules whose bands were being investigated.The spectra in the present study were not corrected for slit di~tortion,~~ since the component bands in the envelopes were broad (with bandwidths at half maximum height of the order of 100 cm-’), compared with the spectral slit widths (<4cm-I), and the absorbance values at the maxima of the bands, at the concentrations employed, were in the region of 0.1. The corrections listed for quantities of these magnitudes in ref.(24) (tables 1 and 2) are negligibly small. Moreover, the wavenumber encoding interval chosen (4 cm-’) was of the same order of magnitude as the spectral slit width and was thus too large for successful deconvolution of the measured ~pectra.~~,~~ The slit width would also have to have been approximated, because it varied automatically during a scan. Band envelopes were arbitrarily chosen for resolution from the large number of spectra available. Six band envelopes of the two-band systems, and eight to ten of the four-band systems were resolved into their components for the evaluation of the average S. 0.Paul and T. A. Ford values, and their standard deviations, of the wavenumber positions of the band centres, fimax, the half-band widths, Afi1,2, and the intensities of the individual bands. Two programs were used in the band-resolution procedure, GSAN~~?~'and PJRES.~''~~ Both programs fit component bands to the observed spectral band envelopes, the individual bands having shapes described by either Gaussian or Lorentzian functions, or by combinations of the two.The program GSAN is based on a non-linear least-squares adjustment of parameters; the squares of the residuals, which are conveniently expressed in the form of a truncated Taylor series, are minimised. The program is operated via an interactive teletype computer terminal, so that the user can terminate the iteration procedure at any stage, e.g. when the parameter values and/or the sum of the squared residuals remain constant.The program GSAN is available for the resolution of envelopes into bands with pure Gaussian shapes only, although it could readily be changed to solve for the parameters of bands having Lorentzian shapes by changing the equations for the partial derivatives of the bandshape function. If the program had been altered to accommodate Gaussian/ Lorentzian product or sum functions, a further iterative step would have been necessary to calculate the half-widths of the component bands. Addition of such a sub-program would have resulted in excessive waiting times on the interactive terminal. Two further limitations of GSAN were that no baseline parameter was included, and that no damping factor was provided in the minimisation function.The program PJRES was a slightly modified combination of two programs published by Pitha and Jones.41742 In the first program4' the bands were resolved, while in the second42 band parameters such as half-widths and shape ratios were .evaluated. If the band envelope consists of n, component bands, there are 3n,+ 1 parameters to be optimised for the Gaussian and Lorentzian functions, 4n,+l for the product function and 5nC+1 for the sum function. In order to fit a curve of n, bands to the envelope, the parameters for each individual band must be optimised. This optimisation proved to be most succe~sfu1~~ when an iterative least-squares method described by Meir~n~~was employed. The most significant observations regarding the use of program PJRES were the following.The choice of a Lorentzian shape for the individual bands resulted in half-widths which were unrealistically large, and in large negative baseline constants a. The shape ratios determined were irreproducible even for bands obtained from envelopes measured during a single experimental run. Bad initial estimates of some of the parameters resulted in meaningless parameters such as negative values for the half- widths. The values recommended by Pitha and Jones for the input parameter^'*^^"^^ were also found to be suitable for the present investigations. The best fits were obtained when a Gaussian shape was chosen for the individual bands. When using program GSAN~~,~'it was found that the error values were smaller than those obtained when the PJRES program was used for band envelopes containing two bands.However, divergence of the root mean-square of the residuals resulted in most cases where the resolution of an envelope with four component bands was attempted. No convergence could be achieved in spite of starting with a number of different initial estimates for the parameters; this might have been due to the fact that two of the four component bands were often found to be closely overlapping. The results of resolving band envelopes of a solution into bands with either pure Gaussian or pure Lorentzian profiles are shown in table 2. When program PJRES was used and a Lorentzian bandshape was assumed, the sum of the areas of the individual bands, taking the baseline constant, a,into account, was much smaller than the originally determined area of the total band envelope.This is indicated by the value of the ratio a(env)/a(res) in table 2. The baseline constant was a large negative quantity, which in turn resulted in unrealistically large half-widths for the bands. This 'broadening effect' was also evident when program GSAN was used, although no baseline parameter was considered in this program. Table 2. Comparisons between band resolutions carried out using programs GSAN and PJRES, with pure Gaussian and pure Lorentzian klband profile functions (two-band systems) intensity/ 0 fimax/cm-' A fi,,2/ cm-' km mol-' 3 std. max. band band band % a (em)/ error error baseline 0solvent function a (res) cons tan t 1 2 1 2 1 2 33GSAN gacetone Gauss 0.99 4.52 3618 3526 86 120 97 138 5' @QLorentz 0.77 8.79 3610 3525 79 111 133 162 cyclohexanone Gauss 0.99 4.88 3603 3504 76 112 82 130 bFLorentz 0.75 8.03 3601 3506 60 117 90 191 0 PJRES $.acetone Gauss 0.99 6.00 13.55 -0.001 47 3617 3521 90 114 114 130 Lorentz 0.57 6.94 17.71 -0.02741 3615 3515 119 154 264 301 3 cyclohexanone Gauss 0.99 5.49 13.77 0.00256 3602 3505 72 109 77 121 23Lorentz 0.64 6.41 14.09 -0.01440 3602 3500 85 136 151 266 3 S.0.Paul and T. A. Ford Results Representative spectra of water in cyclopentanone, di-n-propyl ketone and di-n-propyl ether, together with their resolved component bands, may be seen in fig.1 and 2 of ref. (1) and fig, 1 of ref. (2), respectively. Resolutions were carried out assuming pure Gaussian and pure Lorentzian profiles and using Gaussian/ Lorentzian sum functions. Comparisons among the calculated band parameters are listed in tables 3 and 4, for the two-band systems acetone-water and cyclohexanone-water. As an example of a four- band system, the parameters for the di-n-propyl ketone-water solutions are gathered in table 5. The values of the parameters Fmax and Aij1,2 did not change significantly when the input shape ratios for the sum function using program PJRES were varied. Moreover, the calculated shape ratios did not appear to be sensitive to the concentrations of the solutions. Thus, although the component bands, except band 1 of the di-n-propyl ketone-water complexes, showed mixed Gaussian/ Lorentzian character (see table 5), the mean values of the band parameters determined using both the Gaussian and the sum functions did not differ substantially, and for consistency the discussion which follows is based on the results obtained using the pure Gaussian function.The bands at the highest wavenumbers in the four-band systems showed the lowest intensities of all the bands, and their wavenumber maxima Gmax varied very little. The large errors in the determinations of the positions of the two bands at the lowest wavenumbers indicated that these two bands were strongly overlapping, that they were not readily resolved, and that their parameters, especially their calculated intensities, were determined with relatively low precision.The area ratios of band 2 and band 1 for the two-band systems (tables 3 and 4) appeared to be somewhat more consistent than the ratios calculated for the four-band systems (table 5). Discussion Number of Component Bands and Band Assignments The following criteria may be used for the successful interpretation of the factor-analysis results: I inspection of eigenvalues, determination of residual standard deviations (RSD), estimation of the square root of the variance of each eigenvalue, regeneration of the absorbance matrix and estimation of its goodness of fit.' In the case of those systems whose spectra appeared visually to contain more than two components, some of these criteria indicated the presence of three, and some of four bands.According to Bulmer and Shurvell,13 the number of components should be taken as the smallest number of eigenvectors with which the absorbance matrix is satisfactorily reproduced. The consistent result of observing only two analysed components for all the spectra in which only two bands are visually evident led to the conclusion that the bands due to the two stretching modes of the hydrogen-bonded water molecules are linearly independent at the various solution concentrations. When three bands were visible in a spectrum in the OH stretching region it was assumed that there were four bands present, but that two of those bands overlapped so strongly that they were not visually distinguishable.The fact that only three bands were analysed using program CHISQ may be accounted for by the fact that the equilibrium between the two different hydrogen-bonded species present causes a dependence which results in a reduction by one of the rank of the absorbance matrix. The assignments of bands in the two-band system were readily deduced: bands 1 and 2 were taken as the v3 and vl vibrational modes of the 2 :1 solvent-water complexes. Because of its relatively small wavenumber shift, the high-wavenumber band 1 of the four-band systems was regarded as being due to the vibration of the non-bonded OH Table 3. Comparison between resolutions using Gaussian functions and program GSAN, and using sum functions and program PJRES, CIfor bands of acetone-water solutions 00 std.max. ci/ 1o-' error error shape baseline Ymax AC,,21 intensity/ mol cmP2 a(env)/a(res) ratio constant /cm-' /cm-km mol-' a(2)/a(l)" Gaussian function (program GSAN) 3.4299 0.99 4.91 3620 84 89 1.57 353 1 126 141 4.2333 1.oo 3.19 3613 86 110 1.06 3521 108 117 R34.9749 0.99 4.52 3618 86 97 1.42 53526 120 138 5.8916 1.oo 3.66 3620 88 75 1.40 3 3522 116 105 6.2418 0.99 4.65 3619 84 93 1.37 3524 118 127 6.91 13 1.oo 2.7 1 3612 84 76 1.39 3516 114 106 means and standard deviations 3617 f4 85*2 90* 13 3523 f5 117*6 122* 15 sum function (program PJRES) 3.4299 0.92 5.22 17.65 0.03 -0.002 90 3617 88 105 1.62 0.46 3527 123 169 4.2333 1.32 10.38 89.34 0.58 -0.002 94 3613 69 115 0.67 0.56 3523 64 77 4.9749 0.97 6.09 13.85 0.14 -0.002 65 3618 90 118 1.17 0.04 3522 119 138 5.8916 0.88 3.70 14.26 0.63 -0.006 87 3617 96 122 0.94 0.21 3516 121 115 6.2418 0.93 7.69 21.29 0.38 -0.006 00 3619 91 126 1.10 0.11 3521 120 138 6.9113 0.87 3.71 8.71 0.02 -0.008 30 3613 91 86 1.83 0.60 3514 123 158 means and standard deviations 3616 f1 88*9 112* 15 3520f4 112f23 133*33 a a(2) stands for the area of band 2, a(1) that of band 1.Table 4. Comparison between resolutions using Gaussian functions and program GSAN, and using sum functions and program PJRES, for bands of cyclohexanone-water solutions std. max. -Afi,,21 intensity/~i/lo-' error error shape baseline Vmax mol cmP2 a(env)/a(res) ratio constant /cm-' /cm-km mol-' a(2)/a(l)" Gaussian function (program GSAN) 1.6583 0.98 6.44 3597 92 149 1.01 3495 90 151 4.089 1 0.99 2.1 1 3601 88 111 1.13 3497 102 126 4.1818 0.99 4.88 3603 76 82 1.59 3504 112 130 4.4805 0.98 2.22 3605 88 94 1.65 3506 126 154 P5.3045 1.oo 3.00 3600 90 116 1.13 3496 106 132 6.9300 1.oo 2.61 3615 94 67 2.09 3509 136 140 means and standard deviations 3604f6 88*6 103f29 3501 f6 112*17 138f12 sum function (program PJRES) 1.6583 0.94 3.76 9.89 0.09 -0.002 15 3596 104 183 0.93 0.29 349 1 89 169 4.089.1 0.94 2.37 6.65 0.42 -0.002 31 3600 93 142 0.88 0.05 3498 102 126 4.1818 0.93 5.55 13.81 0.48 -0.000 80 3603 74 101 1.29 0.07 3504 113 130 4.4805 0.9 1 26.16 146.14 0.98 -0.009 54 3610 77 146 1.07 0.08 3 503 123 157 5.3045 0.95 3.36 7.44 0.02 -0.002 03 3600 95 124 1.17 0.27 3495 104 145 6.9300 0.95 7.36 32.19 0.02 -0.000 11 3612 95 71 2.08 0.28 3 507 131 147 means and standard deviations 3603*7 89f 12 129f39 3500f7 llO* 15 146* 16 CI a(2) stands for the area of band 2, a(1) that of band 1.\o t4 0 Table 5. Comparison between resolutions using Gaussian functions and program PJRES, and using sum functions and program PJRES, for bands of di-n-propyl ketone-water solutions std. max. ci/ 1o-' error error shape baseline Vmax A F,,21 intensity a (2+ 3) mol cm-2 a(env)/a(res) ratio constant /cm-' /cm-/kmmol-' /a(1+4)" Gaussian function (program PJRES) 4.8513 0.96 2.49 6.61 0.001 24 3680 33 4 3.26 3614 67 36 3530 65 37 3468 184 18 4.9749 0.96 3.47 8.98 -0.002 58 3686 15 6 2.08 %3625 87 114 3535 70 60 9m 3494 147 78 i+4.9852 1.oo 3.05 9.63 0.002 51 3676 31 7 1.81 3622 63 45 S' 3544 76 27 oa 3507 99 33 br5.3354 1.01 3.17 9.46 0.001 50 3675 32 10 0.82 0 3619 55 37 $.3539 69 20 3521 131 61 3 5.5105 0.98 4.28 24.72 0.001 27 3685 23 8 1.77 F 3623 76 83 3 % 3537 67 50 3494 149 68 5.7680 0.97 3.47 12.59 -.O.OOO 88 3681 18 3 1.54 3624 83 45 3535 56 18 3500 123 38 6.0255 1.01 3.49 9.11 0.005 53 3683 18 2 1.76 3625 81 32 3544 57 14 3496 93 24 6.2521 0.99 2.93 11.12 0.002 95 3679 32 5 2.01 3622 71 38 3534 65 25 3508 132 27 6.4066 0.96 4.20 10.72 0.003 40 3678 27 6 1.42 3617 77 47 3530 63 30 3501 184 49 6.7774 0.9 1 3.80 14.37 -0.003 44 3685 15 4 1.32 363 1 88 57 3534 69 28 3498 200 61 means and standard deviations 3681 f5 24*7 5*2 3622f5 75* 11 53 f25 3536 f5 66f6 31 f14 3499 f14 144f36 46 f20 P sum function (program PJRES) 4.8513 0.93 2.5 1 5.97 0.00 0.001 72 3680 22 2 2.85 0.50 3613 70 42 0.68 3537 47 28 .Y 0.83 3506 60 23 44.9749 0.79 3.74 10.46 0.00 -0.007 80 3686 15 6 1.58 0.36 3627 87 120 0.61 3535 76 86 0.79 3498 177 1254.9852 0.90 3.08 10.00 0.00 0.000 6 1 3676 26 5 2.47 0.55 3622 70 62 0.63 3542 66 35 0.69 3499 81 355.3354 0.88 3.17 10.00 0.00 -0.000 69 3676 30 8 0.95 0.38 3619 58 46 0.73 3544 68 33 0.83 3513 112 745.5105 0.84 4.37 23.80 0.01 -0.004 88 3684 22 6 1.88 0.52 3624 76 99 0.64 3535 73 77 0.55 3486 182 87 Table 5.(continued) std. max. ~i/1o-' error error shape baseline vmax A&,: intensity a(2+3) mol cm-2 a(env)/a(res) ratio constant /cm-' /cm-/km mol-' /a(] +4)" 5.7680 0.85 3.75 13.27 0.00 -0.004 89 368 1 17 3 2.23 0.46 3625 84 55 0.58 3534 64 34 0.60 3484 121 37 6.0255 0.9 1 3.44 9.52 0.1 1 0.002 44 3683 17 2 2.96 0.42 3627 80 36 0.73 3538 71 32 0.66 3483 84 21 6.2521 0.88 3.07 10.73 0.00 0.000 67 3678 30 4 2.26 0.5 1 3622 73 47 0.62 3535 66 34 0.78 3502 119 32 6.4066 0.80 4.28 11.51 0.00 -0.001 06 3678 25 5 1.68 0.47 3617 81 63 0.59 3529 68 48 0.83 3474 201 61 6.7774 0.77 4.01 14.21 0.00 -0.006 75 3685 15 4 1.52 0.37 363 1 87 67 0.59 3534 77 47 0.59 3482 215 71 means and standard deviations 3681*4 22*6 4f2 3623*5 77*9 64 f27 3536*5 68f8 45 f20 3493 f13 135f55 57 f33 " a(2+ 3) stands for the sum of the areas of bands 2 and 3, a(l+4) for the sum of those of bands 1 and 4.23S. 0.Paul and T. A. Ford Table 6. Comparison of the band positions of the OH stretching vibrations of the ether-water complexes determined in the present work with those listed in previous publications 2 :1 complexes 1:1 complexes solvent v3 /cm-’ V1 /cm-’ G(non-bonded)/ cm-’ Y(bonded)/ cm-’ ref. di-n-propyl ether 3632 3 590 3583 3516 3682 3 500 this work 47 di-n-butyl ether 3647 3586 3588 3508 3687 3505 this work 47 tetrahydro fur an 3605 3573 3567 3508 3660 3687 3501 3483 this work 45 3572 3499 3683 3500 46,47 tetrahydropyran 3614 3580 3573 3512 3670 3 505 this work 47 1,4-dioxane 3622 3580 3653 3 509 this work 3 579 3516 3689 3513 45 3580 3509 3684 46 3584 3517 3688 3516 47 group of a 1 :1 complex, which possibly interacted weakly, through a van der Waals type interaction, with the alkyl groups of the solvent molecules.Bands 2,3 and 4 were assigned to the v3and v1stretching modes of the 2 :1 complexes and the stretching vibration of the bonded OH group in the 1 :1 complexes, respectively. These assignments have been discussed in detail. 1,2sy6 A comparison of the assignments and positions of the bands of the solvent-water complexes determined in this work with other published results is presented in table 6.Differences in the assignments of the ether-water bands are obvious. It is not clear how the overlapping bands whose positions have been p~blished~~-~~ were resolved; a difference in resolution methods may have led to the variations among some of the values listed. Bands 3 and 4 are the most intense bands of the ether-water complexes; in the discussions found in the literature, these two bands have been assigned to the vibrations of the 2 :1 comp1exes.4”47 The published V,,, values for the 1 :1 complexes, however, were determined in ternary solutions of water, base and solvent, and in some cases the positions of the bonded OH stretching band (1 :1) and of the v1 (2 :1) band virtually coincided. Thus it is difficult to see how these absorptions could be distinguished if the 2 :1 and 1 :1 complexes existed in equilibrium with each other in the same solution, as they do in our binary systems.Our assignments and those in the literat~re~~-~~ are therefore not comparable, since they depend on data derived in different ways. Bandwidths and Bandshapes The width of a typical infrared band is caused by various factors, including Doppler broadening, which is due to thermal motion of the molecules in or against the direction of incident radiation (this effect for a medium-sized molecule at ordinary temperatures is of the order of lop3cm-’ and can thus be ignored23924) and radiation damping, caused by the changes in energy of a vibrating dipole; this contribution is also insignificantly small, being of the order of 10-6~m-1.23924The main factor determining the widths of absorption bands, however, is collision broadening, which is the perturbation introduced into the frequency absorbed by a molecule due to interaction with its neighbours. The bands investigated in the present study exhibit a width which is only partly caused by resonance (collision) broadening and which may be regarded as a characteristic Resolution of Overlapping Absorption Bands feature of the stretching bands of molecules involved in hydrogen bonding?8 The half-widths of the OH stretching bands of the water molecules forming hydrogen bonds were found to be of the order of 100 cm-', while those of the bands which were due to only very weak interactions (the high-frequency band 1) were considerably smaller, typically ca.20 cm-'. Fermi resonance may be ruled out as a reason for the breadth of the bands because the overtone of the bending vibration of the bonded water molecules, 2v2, would be expected to occur at a wavenumber ca. 300cm-' lower than that of the symmetric stretching vibration vl . The low-frequency stretching mode, v,,~* of the OH. -.O group of the hydrogen-bonded species was not investigated. The coupling of v, with the v3 and vl modes would have an influence on the OH stretching vibrations and would result in a broadening of the bands. The observed breadth of the bands studied here was ascribed to the distribution of energies and geometries of the hydrogen bonds of the 1: 1 and 2: 1 complexes (a situation not unlike that found in solutions of HDO in H20 and in D20, where the half-widths of the v3 and v1 bands at 22 "C are 255 and 160cm-I, re~pectively~~).Evidence for this assumption was provided by the fact that the relative intensities of the bands changed when the temperatures of the solutions were varied,' indicating an equilibrium shift between the different hydrogen-bonded species present; this was the case even for the two-band systems, where only one hydrogen-bonded species appeared to be present at room temperature.The decrease in intensity and half-width of band 1indicated a weakening of the hydrogen bonds of the 2 :1complexes, while the relative increases in intensity and half-width of band 2 showed that a band which was closely overlapping with band 2 and which was caused by the vibration of the bonded OH group of the 1:1 complexes made its appearance.The isosbestic point' indicated that a band due to weakly interacting OH groups of the 1:1 complexed water molecules was present. The deductions about the distribution of two kinds of hydrogen-bonded complexes, even for the two-band systems, were substantiated by the factor-analysis and band- resolution results. The area ratios determined for the two-band systems at various concentrations were not constant; for some systems an increasing trend with increasing water concentration was observed (see table 4). Such a trend could be caused by the appearance of the bands of the 1:1 complexes at higher concentrations.Although the area ratios of the two-band systems varied, only two bands were discernible even at comparatively high concentrations. At ordinary temperatures the concentrations of the 1:1 complexes relative to those of the 2: 1 complexes could therefore be regarded as negligible; however, the presence of the former complexes was established qualitatively when the temperatures were varied.' This presence could be regarded as a contribution to the large half-widths of the observed bands. The parameters of the bands discussed below are those determined by assuming purely Gaussian band profiles. Analyses using the sum function showed that, although the bands were predominantly of Gaussian profile, a Lorentzian contribution was also present.The shape ratios were not constant. The half-width parameters, which are dependent on the bandshape, could nevertheless be correlated with other characteristic parameters of the hydrogen-bonded specie^.^'^'^ Spectroscopic Properties Derived from the Band-resolution Procedures The results of the band resolutions of all the systems investigated'.2 are summarised in tables 7 and 8. In the case of the spectra of the two-band systems, which are all ketone-water complexes, the similarity of the spectroscopic properties of all the com- plexes is illustrated by the remarkable consistency of the ti,,, values of the two bands; the means are 3615 cm-' (band 1) and 3518 cm-' (band 2). The separations of bands 1 and 2 are also remarkably constant, the mean separation being 97 cm-', very close to S.0.Paul and T. A. Ford Table 7. Results of the band resolutions in the OH stretching region of ketone-water complexes:a two-band systems total solvent intensity /kmmol-' band no. Vmax /cm-' A fil,21 /cm- intensity/ km mol-' acetone 216 1 3617 85 90 2 3523 117 122 ethyl methyl ketone 226 1 3616 89 104 2 3515 123 142 diethyl ketone 206 1 2 3619 3528 85 126 72 120 methyl n-propyl ketone 175 1 2 3627 3530 82 120 70 107 cyclopentanone 167 1 2 3605 3508 93 104 89 89 cyclohexanone 213 1 2 3604 3501 88 112 103 139 means and standard deviations 1 3615*12 87*6 88* 18 2 3518k17 117*13 120*31 a See ref. (1). that in water vap~ur,'~ 99 cm-I.The decrease in the separation, F3 -Fl ,of the coupled stretching wavenumbers of water molecules in symmetrical (C2")complexes with increas- ing hydrogen-bond strength has been referred to and is related to the decrease in the extent of intramolecular coupling as the hydrogen-bonding interaction becomes stronger.45 The near constancy of the separations of the six complexes in table 7 shows that the extents of coupling and the hydrogen-bond strengths are very similar. The half-widths, too, show very little variation among the six complexes, the mean values being 87 cm-' (band 1) and 117 cm-' (band 2). The lower-frequency, symmetric OH stretching band is invariably the broader of the two. It is in the values of the component band intensities that the greatest sensitivity to solvent is observed.With the exception of the values for cyclopentanone, band 2 is always more intense than band 1, mirroring the behaviour of the half-widths. Moreover, the two bands appear to increase in intensity in phase with one another, as shown in table 7. These intensity increases are accompanied by increases in the hydrogen-bond strength, which are manifested by increases in the values of the Kirkwood-Bauer-Magat function, the ionization energies and the protonation constants of the solvents.' The values of the parameters collected in table 8 are more sensitive, by and large, to the nature of the solvent than those in table 7. Table 8, of course, contains data for three types of complex (those of water with aliphatic ketones, aliphatic ethers and alicyclic ethers) and the parameters reflect the structural differences among these three types of solvent. The wavenumbers of bands 2 and 3, which correspond most closely with those of the two-band systems, cluster neatly into three distinct groups, having mean values of 3624,3636 and 3614 cm-' (band 2) and 3539,3584 and 3573 cm-' (band 3), in the order listed above.The wavenumbers of band 4, the bonded OH stretching mode of the 1 :1 complexes, separate the ketones (mean 3492 cm-') from both sets of ethers (mean 3504 cm-I), confirming the stronger interaction of water with the ketones than with the ethers, on average. Even the 'non-bonded' OH stretching band of the 1 :1 complexes (band 1) is sensitive to the structure of the solvent; the mean wavenumber for the complexes with non-cyclic solvents is 3684 cm-', while that for the aggregates with the cyclic ethers is significantly lower, at 3661 cm-I.Although band 1 is not due Table 8. Results of the band resolutions in the OH stretching region of ketone-watera and ether-waterb complexes: four-band systems total -,hall2, intensityintensity band *ma, solvent /kmmol-' no. /cm-' /cm-/kmmol-' di-n-propyl ketone 117 1 3681 24 5 2 3622 75 53 3 3536 66 31 4 3499 144 45 di-isopropyl ketone 45 1 3684 21 3 2 3627 70 30 3 3541 60 23 4 3486 62 8 di-n-butyl ketone 28 1 3680 22 2 2 3621 78 14 3 3540 73 12 4 3490 73 9 means and standard deviations 1 3682f2 22f2 3*2 2 3624*3 74*4 32*21 3 3539f3 66*7 22* 10 4 3492f7 93* 51 21 *24 di-n-propyl ether 28 1 3682 15 2 2 3632 50 4 3 3583 40 5 4 3500 99 15 di-isopropyl ether 35 1 3685 17 2 2 3632 74 7 3 3579 45 9 4 3502 82 16 di-n-butyl ether 14 1 3687 14 1 2 3647 63 2 3 3588 54 4 4 3505 75 8 di-n-amyl ether 11 1 3687 11 1 2 3633 58 1 3 3584 50 2 4 3503 72 5 means and standard deviations 1 3685f3 14f3 2*1 2 3636f11 61* 13 4*3 3 3584f5 47f7 5*4 4 3503*3 82* 17 11 f6 tetrahydro fur an 203 1 3660 32 6 2 3605 54 29 3 3567 48 33 4 3501 106 107 tetrahydrop yran 142 1 3670 27 4 2 3614 64 25 3 3573 45 25 4 3505 103 85 1,4-dioxane 168 1 3653 22 5 2 3622 35 18 3 3580 56 55 4 3509 91 89 means and standard deviations 1 3661f9 27*5 5fl 2 3614f9 51 f16 24f6 3 3573f7 50f6 38* 17 4 3505f4 100*9 94f 13 a See ref.(I). See ref. (2). S.0.Paul and T,A.Ford to a hydrogen-bonded interaction, the vander Waals forces acting between the OH groups and the alkyl group surfaces are clearly strongly influenced by the natures of the alkyl groups. The band half-width values likewise fall into the three distinct groups determined by the descriptions of the solvents. The half-width of band 1in each system is consistently the smallest, in line with its unique nature. The largest scatter in the half-width values is that for band 4, especially for the three ketone complexes. This is chiefly due to the greater difficulty in locating the position of band 4 accurately, as noted above.Comparison of the component intensities shows band 1 to be the weakest in all cases, as was the case for the half-width data. Bands 2 and 3 are generally the most intense for the ketones, and band 4 for both groups of ethers. The intensities of all bands of the cyclic ethers are substantially higher than those of their counterparts in the aliphatic ethers. The generalizations presented above lend confidence to the band-resolution pro- cedures empl~yed.~~-~~ They suggest that the conclusions reached in the early papers reporting this work*’2 are based on a sound quantitative analysis of the infrared spectra in terms of the component bands found in the OH stretching band envelope, and on reliable assignments of these component bands to the vibrational motions of the 1:1 and 2: 1 complexes which we believe are present in our solutions.T.A.F. acknowledges, with thanks, financial assistance provided by the South African Council for Scientific and Industrial Research and the University Senate Research Committee. The authors are grateful to Professors H. F. Shurvell, Queen’s University, Kingston, and L. M. Schwartz, University of Massachusetts, for providing copies of the computer programs CHISQ and GSAN, to Dr R. N. Jones, National Research Council of Canada, Ottawa, for making available his extensive set of band-resolution programs, and to Professor G. Brink, University of the Witwatersrand, for some valuable dis- cussions.References 1 S. 0. Paul and T. A. Ford, J. Chem. Soc., Faraday Trans. 2, 1981, 77, 33. 2 S. 0. Paul and T. A. Ford, Spectrochim. Acta, Part A, 1981, 37, 415. 3 S. 0. Paul and T. A. Ford, J. Crystallogr. Spectrosc. Res., 1986, 16, 811. 4 S. 0. Paul and T. A. Ford, J. Moi. Struct., 1987, 160, 67. 5 S. 0. Paul and T. A. Ford, Spectrochim. Acta, Part A, 1988, 44, 587. 6 S. 0.Paul and T. A. Ford, J. Mol. Struct., 1982, 80, 269. 7 S. 0. Paul and T. A. Ford, J. Mol. Struct., 1980, 61, 373. 8 S. 0. Paul and T. A. Ford, Spectrochim. Acta, Part A, 1986, 42, 681. 9 S. 0. Paul and T. A. Ford, S. Afr. J. Chem., in press. 10 S. 0. Paul and T. A. Ford, J. Mol. Struct.. in Dress. 11 J. T. Bulmer and H. F. Shurvell, J. Phys. Chek., 1973,77, 256. 12 J.T. Bulmer and H. F. Shurvell, J. Phys. Chem., 1973, 77, 2085. 13 J. T. Bulmer and H. F. Shurvell, Can. J. Chem., 1975, 53, 1251. 14 C. G. Broyden, Basic Matrices (Macmillan, London, 1975), pp. 124-126. 15 G. Weber, Nature (London), 1961, 190, 27. 16 G. Wernimont, Anal. Chem., 1967, 39, 554. 17 Z. Z. Hugus and A. A. El-Awady, J. Phys. Chem., 1971, 75, 2954. 18 J. J. Kankare, Anal. Chem., 1970, 42, 1322. 19 D. T. Finkbeiner 11, Introduction to Matrices and Linear Transformations (Freeman, San Francisco, 1960), pp. 178-181. 20 H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (van Nostrand, New York, 1943), pp. 304-307. 21 H. Margenau and W. W. Watson, Rev. Mod. Phys., 1936,8, 22. 22 J. H. van Vleck and V. F. Weisskopf, Rev.Mod. Phys., 1945, 17, 227. 23 K. S. Seshadri and R. N. Jones, Spectrochim. Acta, 1963, 19, 1013. 24 D. A. Ramsay, J. Am. Chem. Soc., 1952, 74, 72. 25 R. N. Jones, D. A. Ramsay, D. S. Keir and K. Dobriner, J. Am. Chem. SOC.,1952,74, 80. 26 J. Pitha and R. N. Jones, Can. J. Chem., 1967,45, 2347. Resolution of Overlapping Absorption Bands 27 S. Abramowitz and R. P. Bauman, J. Chem. Phys., 1963, 39, 2757. 28 J. T. Shimozawa and M. K. Wilson, Spectrochim. Acta, 1966, 22, 1591. 29 R. A. Russell and H. W. Thompson, Spectrochim. Acta, 1957, 9, 133. 30 J. G. David and H. E. Hallam, J. Mol. Struct., 1970, 5, 31. 31 M. R. Mander and H. W. Thompson, Trans. Faraday SOC., 1957, 53, 1402. 32 A. Cabana and C. Sandorfy, Spectrochim. Acta, 1960, 16, 335. 33 R.N. Jones, K. S. Seshadri, N. B. W. Jonathan and J. W. Hopkins, Can. J. Chem., 1963,41, 750. 34 P. J. Krueger and B. F. Hawkins, Can. J. Chem., 1973, 51, 3250. 35 G. E. Walrafen, J. Chem. Phys., 1968, 48, 244. 36 0. D. Bonner and Y. S. Choi, J. Phys. Chem., 1974, 78, 1723; 1727. 37 R. N. Jones, R. Venkataraghavan and J. W. Hopkins, Spectrochim. Acta, Part A, 1967, 23, 925. 38 J. Pitha and R. N. Jones, Program PC-118, NRCC Bulletin No. 12 (National Research Council of Canada, Ottawa, 2nd edn, 1976). 39 L. M. Schwartz, Anal. Chem., 1971,43, 1336. 40 L. M. Schwartz and K. V. Schwartz, Comp. Programs Biomed., 1972,2, 257. 41 J. Pitha and R. N. Jones, Program PC-116, NRCC Bulletin No. 12 (National Research Council of Canada, Ottawa, 2nd edn, 1976). 42 J. Pitha and R. N. Jones, Program PC-121, NRCC Bulletin No. 12 (National Research Council of Canada, Ottawa, 2nd end, 1976). 43 J. Pitha and R. N. Jones, Can. J. Chem., 1966,44, 3031. 44 J. Meiron, J. Opt. SOC. Am., 1965, 55, 1105. 45 L. J. Bellamy and R. J. Pace, Spectrochim. Acta, Part A, 1972, 28, 1869. 46 D. N. Clew and N. S. Rath, Can. J. Chem., 1971,49, 837. 47 J. R. Scherer, in Advances in Infrared and Raman Spectroscopy, ed. R. J. H. Clark and R. E. Hester IUevAen Tnnrlnn 1072) vnl 5 nn ld0-31h

ISSN:0300-9238    

DOI:10.1039/F29898500011

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1989, 85(1), 29-37 Ab Initio Study of the Vibrational Frequencies of H,BNH, (n = 1,2,3) and Related Compounds Paul Brint" and Benchang Sangchakr Department of Chemistry, University College, Cork, S. Ireland Patrick W. Fowler Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD The equilibrium geometries and vibrational frequencies of the H, BNH, (n = 1,2,3) molecules have been calculated at the SCF level using a 4-31G** basis set. Comparative calculations were carried out for the isoelectronic hydrocarbons. The borane-ammonia adduct was treated at the correlated second-order Moller- Plesset level, with analytic calculation of second deriva- tives. The B-N stretching vibration in H3BNH3is poorly described at the SCF level and shifts from 604to 679 cm-' on inclusion of electron correlation.Over the whole set of molecules, calculated SCF harmonic frequencies are uniformly higher than the experimental fundamentals by lo%, with a few exceptions that lead to proposed reassignments of some spectroscopic bands. A correlation between BH stretching frequency and nominal hybridisation is determined and its application to some related compounds discussed. It is well established that the infrared absorption frequencies of CH bonds are diagnostic of the hybridisation of the carbon atom, the frequency increasing with the carbon 2s component.' It is reasonable, therefore, to expect a similar variation for BH bonds. This effect appears never to have been quantified, however, and although some spectro- scopic work of high quality exists for simple BH-containing compounds, it is not comprehensive.We have therefore carried out a purely theoretical investigation of this effect using ab initio calculations and comparing results with experiment wherever possible. The object is not to show that the effect occurs (it obviously must), but to gauge its magnitude and determine whether observed vibrational frequencies are a sensitive test of boron hybridisation. The interest arises from a long-term study of the bonding of boranes and related clusters in which we have used theoretical and spectro- scopic methods.* We are currently investigating the information content of the infrared spectra of borane moiecules and their correspondence with theories of borane bonding.An application of the following to the spectra of closo-boranes will be reported in a later paper. The methodology of this study was first to establish an appropriate basis set and level of treatment of electron correlation, by calculating the equilibrium geometry of HCCH, a molecule which is sufficiently small to be computationally tractable and also contains a multiple bond, which is demanding in accuracy. The chosen level of calcula- tion was then applied to H3CCH3 and HzCCHz for equilibrium geometry and to all three hydrocarbons for the evaluation of fundamental vibrational frequencies, which were found to compare well with experiment. The same level of calculation was then applied to the boron-containing analogues H3BNH3 , H2BNH2 and HBNH to provide data to illustrate the frequency/ hybridisation relationship.Met hod of Calculation The GAUSSIAN 82 a6 initio program3 was used for most of the calculation,, taking the internal basis sets and default convergence criteria ( in energy). Vibrational 29 Vibrational Frequencies of H, BNH, Table 1. Equilibrium geometries of HCCH calculated with various basis sets at SCF and post-SCF levels CH cc STO-3G 1.065 1.168 4-31G 1.051 1.189 6-3 1G 1.053 1.194 4-31G** 1.056 1.183 6-31G** 1.057 1.186 MP2/4-31G** 1.061 1.215 CI D/ 4-31G** 1.059 1.199 expt 1.061 1.203 All geometries were linear. The values are given in 8, and the experimental results are taken from an re structure in ref.(5). frequencies were calculated using numerical fits to the potential-energy minima. In the cases of H3CCH3 and H3BNH3, the geometry was further optimised using the CADPAC program4 with a tolerance on gradients of a.u.; the vibrational frequencies of these molecules were then calculated using analytic second derivatives with the cRAYis ( ULCC) version of that program. The optimised structures all coincide in symmetry with those deduced from experi- ment. The symmetries were checked as follows: for each molecule the geometry was optimised within an assumed point group and the Hessian matrix (matrix of second derivatives of the energy) determined. Diagonalisation of the Hessian gave the correct number of zero frequencies (3N -6 or 3 N -5), thus characterising the stationary point as a true minimum.If the assumed symmetry had been too high, at least one imaginary frequency would have been found. If the assumed symmetry were too low, the optimised structure would exhibit a higher symmetry than the initial guess. Results The equilibrium geometry of HCCH calculated with various basis sets and at SCF and post-SCF levels is shown in table 1. As a compromise between accuracy and computa- tional time the 4-31G"" basis set was chosen and used at the SCF level in the rest of this work. It is a genuine compromise as it is clear from table 1 that electron correlation definitely improves the accuracy of the calculated CC bond length.5 The geometries and vibrational frequencies of H3CCH3, H2CCH2 and HCCH are given in tables 2-5 together with the experimental values.The agreement between calculated and experimental geometries is generally better in the saturated molecules, showing that multiple bonds are computationally more demanding. The calculated vibrational frequencies are higher than experimental frequencies, but consistently so, average percentage errors being 9.8 f2.1'/o for H3CCH3 and 10.0f2.1 '/O for H2CCH2. Such errors have been shown by Pople6 to be typically ca. 13% as a percentage of the experimental value, equivalent to our 10% of the calculated value. Allowing for this systematic error, the only values in significant disagreement with experiment are the degenerate modes of HCCH, both of which involve the triple bond and whose low value make any absolute error more significant, and for similar reasons the low-energy a,, mode of H3CCH3.The mTTgbending frequency of acetylene is notoriously dependent upon basis set; it is claimed' that f functions are required for its correct description at SCF and correlated levels. P. Brint, B. Sangchakr and P. W. Fowler Table 2. Equilibrium geometries calculated at the SCF level with the 4-31G** basis set species symmetry energy dipole moment geometric parameters H3BNH3 C3, -82.546510 5.5625 B-H 1.208 (1.210)" LHBN 104.4 (104.5) B-N 1.685 (1.672) LHNB 110.7 (109.9) N-H 1.002 (1.014) H2BNH2 c2v -81.419944 1.8322 B-H 1.192 LHBN 119.4 B-N 1.385 LHNB 123.1 N-H 0.993 HBNH C,, -80.2 17379 0.69 17 B-H 1.165 B-N 1.221 N-H 0.978 H3CCH3 D3, -79.16201 0 C-H 1.076 (1,091)' LHCH 111.2 (108.0) C-C 1.525 (1.536) HzCCH2 D2h -77.961 291 C-H 1.076 (1.086)' LHCC 121.8 (121.2) C-C 1.312 (1.339) HCCH ah -76.7443 79 C-H 1.056 (1.060)b C-C 1.183 (1.203) " Ref.(18). 'Ref. (4). Distances are quoted in A and angles in degrees. Experimental values are given in brackets (where known). The total energy is quoted in hartree, dipole moments in D. Table 3. Ground-state vibrational frequencies of H3BNH3 and H3CCH3 calculated in the 4-31G** basis set H3BNH3 H3CCH3 assignment calc. expt error (Yo) assignment calc. expt error (YO) 3820.3 3386 11.4 3256.5 2995.5 8-0 3692.1 3337 9.6 3230.8 2950.0 8.7 2589.3 2415 6.7 3183.2 2953.8 7.2 2544.0 2340 8.0 3178.2 2895.7 8.9 1802.6 1608 10.7 1635.8 1472.2 10.0 1446.0 1343 7.1 1630.2 1468.7 9.9 1302.7 1301 0.1 1567.7 1388.4 11.4 1289.9 ( 1052)" 18.0 1535.3 1379.1 10.1 1133.7 (1 186)" -4.7 1332.8 1 190.0 10.6 681.2 603 11.4 1059.2 944.8 10.7 604.2 (968) -60.0 889.7 821.5 7.4 257.1 (232)" 9.7 328.5 278.0 15.2 ' " Assignment disputed. See discussion in the text.Estimated [see ref. (lo)]. Assignments are ( vn, symmetry species) and frequencies are reported in cm-'. When making a comparison between theoretical and experimental frequencies, it is useful to bear in mind that the calculation gives purely harmonic frequencies for an isohted molecule.The fundamental bands measured in the i.r. spectrum are contami- nated by anharmonic contributions from the cubic and quartic terms in the force field, leading to values consistently lower than the true harmonic frequencies. Extrapolation from results for diatomics* would suggest that anharmonic effects account for ca. one third of the previously noted 10% discrepancy. Torsional vibrations may be poorly modelled by the single-well harmonic oscillator, and weak dative bonds (e.g. H3B+-NH3)are likely to show large anharmonicities. Spectra of transient species such as HBNH are recorded for molecules trapped in inert-gas matrices; matrix shifts of up to 60 cm-' have been observed for hydrogen halides in XeS9 Vibrational Frequencies of H,BNH, Table 4.Ground-state vibrational frequencies of H2BNH2 and H2CCH2 calculated in the 4-31G** basis set H2BNH2 H2CCH2 assignment calc. expt" error (YO) assignment calc. expt error (YO) 3941.5 3534 11.5 3396.1 3105.3 8.5 3837.4 345 1 11.2 3369.1 3102.5 7.9 2746.9 2564 7.1 3317.5 3026.4 5.7 268 1.2 2495 7.4 3293.4 2988.6 9.2 1789.2 1625 10.1 1860.6 1622.6 12.7 1450.9 1337 8.5 1600.7 1433.5 9.8 1232.0 1225 0.6 1493.2 1342.2 10.1 1226.9 1131 8.4 1350.0 1236 8.3 11 10.9 1005 10.4 1159.6 1027 11.5 879.9 763 15.3 1106.1 950 14.1 769.8 593 34.4 1096.6 949.2 13.4 641.9 670 -4.1 896.1 810.3 9.6 ~ ~~~~~~ a Ref. (20). Assignments are (v,, symmetry species). Table 5.Ground-state vibrational frequencies of HBNH and HCCH calculated in the 4-31G** basis set HBNH HCCH assignment calc. expt error ("/o) assignment calc. expt error (Yo) 1,u 4132.0 3700 10.4 1,ug 3697.5 3372.5 8.2 2,u 3002.9 3,uu 3584.5 3294.9 8.0 3,u 1983.1 1785 8.1 2,ug 2256.8 1973.5 12.5 4,r 837.5 5,ru 879.1 729.2 17.0 5,P 578.5 460 20.4 4,rg 801.6 611.7 23.7 " Ref. (24). Assignments are (v,, symmetry species). Tables 2-5 give equivalent data for the isoelectronic-isostrctural boron-nitrogen compounds. Again the geometries agree very well with experimental structures, where these are known, and the vibrational frequencies, with a few notable exceptions, are close to or within the +lo% error expected from the hydrocarbons.The overall agreement between calculation and experiment is extremely good and shows that SCF calculations in the 4-31G**basis provide a good representation of the vibrational ground state of these molecules. This conclusion is undoubtedly limited to the lower vibrational levels of the ground electronic state of these molecules as work on the dissociation of H3BNH3 has shown that a much larger basis and inclusion of electron correlation is required for accurate calculation away from the minimum.l0 The vibrational frequencies of H3BNH3 have been calculated previously" at the 6-31G"" level and the results are essentially identical to ours. The only large difference between the two sets of theoretical results is in the lowest-energy v6 mode, the i.r.-inactive hindered rotation about the BN bond.The value in table 3 shows the expected error of ca. +lo%, whilst that of ref. (11) is 11% below the estimated experimental value. We are reporting the harmonic frequency, whereas the authors of ref. (10) have used a hindered-rotor model to calculate a torsional fundamental of 198cm-I. The 'experimental' frequency of 232 cm-' is itself not directly observed, and the value depends upon use of the same model of the torsional barrier." The harmonic frequencies in 4-31G** and 6-3 lG* bases are very similar. P. Brint, B. Sangchakr and P. W. Fowler Of the notable deviations between calculated and experimental frequencies the following seem worth further consideration. (a) vs,a, Mode of H3BNH3 The -60% error reported in table 3 clearly suggests a major problem with the BN stretching mode.Independently of any disagreement with calculation, difficulties with the assignment of this mode have been noted before.12 Although H3BNH3 is highly polar (p= 5.216 Dt),13the BN stretch is predicted to be only weakly i.r.-active. In the matrix-isolation spe~trum'~ a weak band at 968 cm-' was assigned to "BN stretching, and various weak features in the range 931-987 cm-' were assigned to the BN stretch in different isotopomers. All previous on the free molecule, or on H3BNH3 in various solvents, gave v(BN) from 776 to 790 cm-'. A matrix shift of ca. 200 cm-' is larger than would be expected, even for this dissociative stretching mode. The authors of ref.(14) point out that their assignment gives a force constant 1.6 times greater than previous estimates and one that is larger than the estimated value for H3BN(CH3)3.'7 On chemical grounds one would expect the BN bond in the latter compound to have a much higher force constant since trimethylamine is a stronger base than ammonia. Our 4-31G** calculations give a force constant for the BN stretch of 177 N m-', which is in moderate agreement with early experimental estimates of 290 and 295 N m-', but not with the value of 456 N m-' derived in ref. (14). An independent estimate of the BN stretching force constant can be made from the microwave spectrum of H3BNH3. In a pseudo-diatomic model, taking the borane and ammonia subunits as rigid, the BN force constant is 167r2pB3 kBN = DJ where B is the rotational constant, Dj is the centrifugal distortion constant and p is the reduced mass of the oscillator.If B and Dj are in MHz and p in kg, then kBN is given in Nm-2. Results from seven isotopic forms [table 111, ref. (18)] give kBN= 220f60 N m-2, with five of the values lying within the range 220 * 10 N m-2. Although not expected to be very accurate estimates, these values are clearly more compatible with our lower BN stretching force constant, casting further doubt on the assignment made in ref. (14). However, even if it is accepted that the vs mode has an experimental frequency of 780* 10 cm-', there is still a discrepancy of some 180 cm-' (-29%) between the 4-31G** SCF value and experiment.Why should an SCF calculation underestimate this frequency in particular? It is conventional to describe the BN bond as a dative bond formed by donation of the ammonia lone pair to the empty pz orbital of BH3. A single-determinant SCF treatment does not give a correct account of the dissociation energy of this molecule. Several have shown that SCF wavefunctions recover only ca. two thirds of the estimated experimental D,; a correlated wavefunction is needed for the remaining third. Electron correlation would be expected to have an effect of similar magnitude on the BN force constant, causing both it and vsto increase. To check this hypothesis, the geometry of the E3BNH3molecule was optimised at the second-order Mprller-Plesset level using version 4.0 of the CADPAC programIg to calculate the MP2 force constants analytically.The results show minor changes in most of the geometric parameters when compared with the SCF calculations: r(B-H) = 1.200 A (-0.008 A), r(B-N) = 1.654A (-0.031 A), r(N-H) = 1.013A (-0.001 A),LHBN 104.5' (+0.1"), LHNB 107.8' (-2.9). The main effect is a shortening in the BN bondlength (by rather too much when compared with experiment). The MP2 frequencies are compared with the SCF and experimental values in table 6. Most of the modes fall in frequency. v2 and vg increase by small amounts (1.9 and 0.6%,respectively) but the t 1 D = 3.335 64 x lov3' C m. Vibrational Frequencies of H, BNH, Table 6. Effects of electron correlation on the vibrational frequencies of H3BNH3, calculated at the MP2 level in the 4-31G** basis assignment M P2 A expt error (MP2) (YO) 3683.6 -136.7 3386 8.1 3541.2 -150.9 3337 5.8 2639.6 50.3 2415 8.5 2559.7 15.7 2340 8.6 1715.1 -87.5 1608 6.2 1373.1 -72.9 1343 2.2 1270.7 -32.0 1301 -2.3 1254.6 -35.3 (1052)" (16.1) 1108.5 -25.2 (1 186)" (-7.0) 660.3 -20.9 603 8.7 679.0 74.8 (968)" (-42.6) 275.9 18.8 (232)b (15.9) " Assignment disputed.See discussion in the text. Estimated [see ref. (lo)]. The column headed A shows the change in frequency from the SCF calculations reported in table 3. significant changes are in the BN stretch v5 (+12.4%) and the torsional frequency v6 (+7.3%). Overall agreement with experiment is improved.The stretching force constant for the BN bond is 216 N m-' at the MP2 level, in better agreement with the estimate from centrifugal distortion constants. There is not yet sufficient experience with MP2 frequencies to give a precise estimate of their expected accuracy, but available calculations suggest that for DZP (double-zeta plus polarisation) basis sets MP2 frequencies are ca. twice as accurate as SCF results in the same basis, although with errors that may be of either sign, unlike the generally positive SCF It is not claimed here that the present 4-31G"" basis gives a quantitative account of the MP2 correlation effects, but it does seem likely that the broad conclusions (a BN stretching constant that is unusually sensitive to electron correlation and larger than the SCF value) will be stable against improvement in the basis.The BN stretching vibration in this complex is something of a special case, in that the SCF force constant is too small. The present authors agree with the conclusion of Binkley and Thorne" that such large errors are likely to be confined to those modes directly involving stretching of the dative bond. For other frequencies H3BNH3 shows only the 'normal' 10% SCF overestimation. Conclusions about the NH and BH stretches may usefully be drawn, even from an SCF calculation. (6) u4,a1 and ull, e Modes of H3BNH3 These are the symmetric and antisymmetric angular deformation modes of the BH3 group. The assignment in ref. (14) was v4 = 1052, vll = 1186 cm-', made on the ground that antisymmetric vibrations are usually higher in energy.The opposite assignment for the corresponding frequencies (1026 and 1175 cm-') was made by Taylor." The present calculation finds that the e mode has a higher frequency, both at SCF and MP2 levels. Reversing the experimental assignment would give SCF errors of 8.1% and 7.2%, respectively, which would be more consistent with the expected behaviour. (c) us,bl and u12,b2 Modes of H2BNH2 Table 4 shows poor agreement for both these modes and in this case the exper- imental assignments22 should be much more certain, being based both on characteristic P. Brint, B. Sangchakr and P. W. Fowler Table 7. Variation of the average X-H stretching frequency with nominal hybridisation X hybridisation B C N 2368 2964 3 169 2497 3077 3578 SP 2763 3350 3801 approx.range 400 390 730 The average calculated value is increased by 8% to allow for the systematic overestimation of experimental frequen- cies. Frequencies are quoted in cm-'. frequencies and also on symmetry assignment from rotational structure. It happens, however, that for these two modes there is no direct evidence. Their frequencies were inferred from combination bands v6-vs, v,+ v12 and even these are observed only through their interference with the rotational structure of the v4 fundamental. Whilst the analysis appears sound there is some scope for uncertainty in this rather complex assignment procedure, and it may be worth reconsideration as simply reversing the assignment of the two modes produces errors of the expected magnitude (1.6 and 7.6%, respectively). Conclusions The variation of experimentally observed vibrational frequency of BH stretches with nominal hybridisation is summarised in Table 7, and is clearly large enough to be used as a diagnostic of hybridisation.? The NH stretches show a considerably wider range and therefore a potentially more useful correlation.The values for CH stretches are in near perfect agreement with those quoted in standard texts. The values given in table 7 are, of course, only typical ones corresponding approximately to precise hybridisation and should really have a range on them, which from experimental data seems to be of the order of *50 cm-'.Alternatively the vibrational frequency can be considered as a continuous function of hybridisation and used to predict the s-p mixing in particular molecules. We note that the experimental BH stretching frequencies in borazole (2530, 2535 cm-1)23 and H3BN2H4(2210-2360 cm-')16 are within the predicted ranges for sp2 and sp3 hybridisation, respectively. Price et a1.23find an NH stretching mode at 3490 cm-' and note that this is higher than typical amine frequencies. It is in reasonable agreement with the sp2 value in table 7. The only question left in deciding the usefulness of the correlation for other molecules containing boron-hydrogen bonds is whether the B-N bonding is a sufficient perturba- tion to the nominal hybridisation to distort the result.As a check we consider the experimentally determined frequencies of B2H6. These are (for the BH stretches): ag 2524, 2104 cm-', bl, 2612 cm-', b2g 2591 cm-*, b2u 1915 cm-' and b3,, 2525 ~rn-l.~ The correspondence with hybridisation suggests that the four terminal BH bonds are intermediate between sp2 and sp hybridised, whilst the modes involving the bridging hydrogens are outside the range of table 7, having more p character than sp3, clearly t The nominal hybridisation is, of course, judged on the molecular geometry and atom connectivities (the nearness of the geometries to classic tetrahedron, trigonal and linear shapes). Other factors can effect the geometry-hydrisation relationship, but given the simplicity of these molecules and the small range of electronegativities involved the classic relationship is certainly applicable.36 Vibrational Frequencies of H,BNH, Table 8. Stretching force constants of H,BNH, molecules calculated at the SCF level with the 4-31G** basis set force constant/ lo2N m-’ H3BNH3 HZBNHZ HBNH B-H 3.62 4.02 4.70 B-N 1.77 7.55 16.3 N-H 7.78 8.39 9.33 MP2 correlation corrections raises the B-N force constant of H,BNH3 to 216 N rn-l (see text). very different from the simplest description of two sp2 hybridised BH3 groups weakly associated. This is supported by the geometric structure of the molecule which shows an Hb-B-Hb bond angle of 96.5°,25 consistent with large p character.BH3 should have hybridisation very close to sp2(exact in the absence of polarisation functions) and a calculation on this molecule finds one of the BH stretches in very good agreement with table 7 and the degenerate pair at slightly higher frequency than expected. This small inconsistency could arise because BH3 contains only one heavy atom whereas all other molecules considered contain two. Finally, table 8 summarises the stretching force constants calculated in the course of this work. We wish to acknowledge the S.E.R.C. for a grant of computer time, NBST (Ireland) for grant number 120.86under the terms of which the work was performedand University College Cork for a senior studentship to B.S. References 1 C. A. Coulson, Valence (Oxford University Press, Oxford, 2nd edn, 1961), p.210. 2 B. Sangchakr and P. Brint, J. Chem. SOC., Dalton Trans., 1988, 105. P. Brint, K. O’Cuill, and T. R. Spalding, Polyhedron, 1985, 5, 1791. 3 J. S. Binkley, M. J. Frisch, D. J. DeFrees, K. Raghavachari, R. A. Whiteside, H. B. Schlegel, G. Fluder and J. A. Pople, GAUSIAN 82, Carnegie-Mellon University, Pittsburgh, PA 15213. 4 R. D. Amos, cADPAc--The Cambridge Analytic Derivatives Package, S.E.R.C., Daresbury CCP1/84/4, 1984. 5 All geometric data and vibrational frequencies for the hydrocarbons were taken from: G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules (Van Nostrand, New York, 1966). 6 J. A. Pople, H. B. Schegel, R. Krishnan, D. J. DeFrees, J. S. Binkley, M.J. Frisch and R. A. Whiteside, Znt. J. Quantum Chem. Symp., 1981, 15, 269. 7 E. D. Simandiras, J. E. Rice, T. J. Lee, R. D. Amos and N. C. Handy, J. Chem. Phys., 1988,844, 3187. 8 W. J. Hehre, L. Radom, P.v.R. Schleyer and J. A. Pople, Ab initio Molecular Orbital Theory (Wiley, New York, 1986), p. 233. 9 A. J. Barnes, in Vibrational Spectroscopy of Trapped Species, ed. H. E. Hallam (Wiley, Chichester, 1973). 10 C. Zirc and R. Ahlrichs, J. Chem. Phys., 1981, 75, 4980. 11 J. S. Binkley and L. R. Thorne, J. Chem. Phys., 1983, 79, 2932. 12 W. Sawodny, in Gmelin Handbuch der Anorganischen Chemie, Band 52, Tie1 18 Borverbindungen (1978), p. 39. 13 R. D. Suendram and L. R. Thorne, Chem. Phys. Lett., 1981, 78, 157. 14 J. Smith, K. S. Seshadri and D.White, J. Mol. Spectrosc., 1973, 45, 327. 15 R. C. Taylor, Adv. Chem. Ser., 1964, 42, 59. 16 J. Goubeau and E. Ricker, 2. Anorg. Allg. Chem., 1961,310, 123. 17 W. Sawodny and J. Goubeau, 2. Phys. Chem. (Frankfurt), 1965,44, 227. 18 L. R. Thorne, R. D. Suendram and F. J. Lovas, J. Chem. Phys., 1983, 78, 167. 19. R. D. Amos and J. E. Rice, CADPAC: The Cambridge Analytic Derivative Package, issue 4.0, Cambridge, 1987. 20 E. D. Simandiras, R. D. Amos and N. C. Handy, Chem. Phys. Lett., 1987, 133, 324. 21 N. C. Handy, J. F. Gaw and E. D. Simandiras, J. Chern. SOC., Faraday Trans. 2, 1987, 83, 1577. 22 M.C. L. Gerry, W. Lewis-Bevan, A. J. Merer and N. P. C. Westwood, J. Mol. Spectrosc., 1985, 110, 153. P. Brint, B. Sangchakr and P. W. Fowler 23 W. C. Price, R. D. B. Fraser, T. S. Robinson and H. C. Longuet-Higgins, Discuss. Furuduy SOC.,1950, 9, 131. 24 E. R. Lory and R. F. Porter, J. Am. Chem. SOC.,1973, 95, 1766. 25 K. Kuchitsu, J. Chem. Phys., 1968, 49, 4456; W. J. Lafferty, A. G. Maki and T. D. Coyle, J. Mol. Spectrosc., 1970, 33, 345. Paper 8/02134A; Received 27th May, 1988

ISSN:0300-9238    

DOI:10.1039/F29898500029

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1989, 85(1), 39-51 Mechanism and Solvent Dependence of the Solvent-catalysed Pseudo-intramolecular Proton Transfer of 7-Hydroxyquinoline in the First Electronically Excited Singlet State and in the Ground State of its Tautomer Jan Konijnenberg, Gerben B. Ekelmans, A. Herbert Huizer and Cyril A. G. 0.Varma" Leyden University, Department of Chemistry, Gorlaeus Laboratories, P.0.Box 9502, 2300 RA Leyden, The Netherlands Picosecond time-resolved fluorescence of solutions of 7-hydroxyquinoline in neat alcohols has revealed two different excited-state tautomerization processes. There is a fast process which appears as the only one in the case of solutions in cyclohexane containing a small amount of alcohol. This fast process occurs within electronically excited 1:2 solute-alcohol complexes.The slower process is associated with tautomerization in excited solute- alcohol complexes which contain, at least initially, more than two solvent molecules. The size of the alcohol molecule determines the relative import- ance of the two processes in the phototautomerization. The reverse double proton transfer process of the tautomer in its ground state has been observed by transient absorption spectroscopy. The ground- state tautomer decays monoexponentially with a rate constant depending both on the nature of the alcohol and on its concentration in the solution. In the limit of low alcohol concentrations, the rate constant correlates with the proton donor strength of the alcohol. The rate constant is temperature- dependent, and has a deuterium isotope effect which is temperature-indepen- dent.A previously suggested explanation in terms of a two-step process also applies here. The first step involves thermally activated solvent reor- ganization to achieve a proper conformation of a solute-alcohol complex. The second step is considered to be a thermally unassisted proton-tunnelling process in the complex with the proper conformation. A large number of electronically excited organic molecules containing both an acidic and a basic functional group can tautomerize via an adiabatic excited-state proton- transfer process (ESIPT). In these cases a significant influence of the electronic charge redistribution in the excited state on the acid-base properties of the functional groups makes the tautomerization process energetically favourable.' ESIPT processes are gen- erally very fast if an intramolecular hydrogen bond is present, which provides the suitable geometry required for the rapid transfer of a proton within the lifetime of the excited If there are no intramolecular hydrogen bonds present, the phototautomerization may nevertheless be achieved via catalysis by a properly chosen so1vent.6-'2 Excited-state adiabatic proton-transfer processes are easily recognized by inspecting the fluorescence spectrum of the sample.In most cases the fluorescence spectrum consists then of a short-wavelength band (&), due to the primary excited species, and a long-wavelength band (FT)which can be attributed to emission from the adiabatically formed electronically excited tautomer.The reaction rate of the ESIPT process can be studied by time-resolved fluorescence spectroscopy. The rise-time of the fluorescence from the tautomer yields directly the lower limit of the proton-transfer rate. 39 Pseudo-intramolecular Proton Transfer I I exc f IN f IT Itr. abs. I II/ I T Fig. 1. Potential-energy surfaces for the first excited singlet state and the ground state for molecules showing excited-state intramolecular proton transfer (ESIPT). After its formation the phototautomer relaxes to the corresponding ground state by radiative (fluorescence) and non-radiative pathways. Since the tautomeric form of the molecule is metastable on the potential-energy surface of the electronic ground state, the electronically deactivated tautomer returns directly or via thermal activation to the original form of the molecule.The reverse (thermal) tautomerization may be studied by transient absorption spectroscopy (see fig. 1). Hydroxyquinolines belong to the class of molecules which can exist in enol and keto forms which can interconvert by keto-enol tautomerization. It has been shown that, in their electronic ground state, hydroxyquinolines with the hydroxyl group on the ben- zenoid ring are enolic, whereas 2-and 4-hydroxyquinoline are essentially ketonic. l3 The intramolecular acid-base equilibrium may be changed upon electronic e~citation.'~ In 7-hydroxyquinoline (7-HQ) the acidic hydroxyl group and the basic nitrogen atom in the ring are too far apart to form an intramolecular hydrogen bond (see fig.2). Phototautomerization of 7-HQ in alcohols takes place via a double proton transfer process in solute-solvent complexes.15i16 In this process the alcohol molecules in the solvent act as a proton-relay system. In the complex they deliver a proton to the N atom of the solute and receive in return a proton from the hydroxyl group of the solute, resulting in a tautomeric solute and unchanged alcohol molecules. Thistlethwaite and Corkill were the first to determine the reaction rate for the overall proton-transfer process of 7-HQ in methanol, using time-resolved fluorescence measure- ments with a streak came~a.'~ From the rise-time of the fluorescence they concluded that the process takes place in ca.170ps. J. Konijnenberg et a1. 41qJJA-0 1A L 0)hv I IH H Fig. 2. The photoinduced excited-state and thermal reverse tautomerization of 7-hydroxyquinoline. In 1983 Itoh et aL” reported the detection of the metastable ground-state tautomer in solution in methanol by transient absorption spectroscopy and by a two-step pulse- laser excitation (TSLE). The first pulse in the TSLE experiment creates the excited keto tautomer (T*), and therefore indirectly the keto tautomer (T) in its ground state. A delayed second excitation regenerates the strongly decayed fluorescence from T”. They found that whereas the excited-state tautomerization in solution in methanol occurs within ca.170 ps, the ground-state process requires at least 3.5 ps at room temperature. This paper discusses the mechanism of the excited-state tautomerization of 7- hydroxyquinoline and of the retautomerization of the tautomer in its ground state in several alcohols and in cyclohexane containing small amounts of alcohol. In the case of the retautomerization in solutions in methanol and deuterated methanol (CH,OD) the temperature dependence of the rate constant has been studied in detail. Experimental 7-Hydroxyquinoline was supplied by Eastman Kodak and was purified by crystallization from ethanol. The alcohols were of spectrograde quality and were used without further purification.Cyclohexane was carefully dried before use. Fluorescence spectra were recorded on a fluorescence spectrometer (Spex, Fluorolog 2) and were not corrected for instrumental distortion. Time-resolved optical absorptions were studied by primary excitation of the solutions with a laser pulse from a 308 nm excimer laser (Lambda Physik, EMG loo), having a pulse width of ca. 10ns. The induced transient absorption was monitored by a fast photomultiplier, supplying photocurrents up to 20 mA in the linear-response regime, using monochromatic light from a system consisting of a pulsed xenon lamp and a monochromator. The photomultiplier output signal was recorded on a transient digitizer (Tektronix R7912) and then transferred to a computer (PDP 11-10).Time-resolved fluorescence measurements were performed using the fourth harmonic (265 nm) of a laser pulse extracted from a passively mode-locked Nd-YAG laser for excitation and a streak camera (Hadland, Imacon 500) for detection of fluorescence. The overall time resolution was ca. 15 ps. The experimental details have been described elswhere.’ Results and Discussion The Excited-state Tautomerization Process The fluorescence spectrum of solutions of 7-hydroxyquinoline depends on the solvent. Solutions of 7-HQ in non-protic apolar solvents show a single fluorescence band, which is the mirror image of its first electronic absorption band and can therefore be attributed Pseudo-intramolecular Proton Transfer h .-x '! \c) \8 I '.\c) \ \.-'. '. '. \ *-. -.- I 300 500 700 A/nm Fig. 3. Absorption (-) and fluorescence (- * -) spectra of 7-hydroxyquinoline (7-HQ) in isopropyl alcohol. The transient absorption of the ketotautomer (T) in isopropyl alcohol is shown by the curve (---) drawn through the experimental points. to fluorescence from the first excited singlet state. Solutions of 7-HQ in alcohols exhibit dual fluorescence, as shown in fig. 3 for 7-HQ in isopropyl alcohol. In addition to the short-wavelength fluorescence band FNexhibited by solutions in apolar solvents, a new strongly Stokes-shifted fluorescence band FTappears around 525 nm. The large Stokes shift has been interpreted to be due to an adiabatic excited state intramolecular proton transfer process,14 which has been suggested to proceed via proton tunnelling." The time behaviour of the fluorescence FT in a solution in methanol, shown in fig.7(a) (later), reveals a rise-time TTR of this emission which is finite. In the case of solutions in methanol, we determined a value of ca. 200ps for TTR. FN(fig. 4) has a rise-time TNR,which is limited by the width of the excitation pulse. The decay of FN can only be represented accurately as a sum of two exponential functions, one with a short lifetime, TNS, and the other with a long lifetime, TNL. The lifetime TNS of the short-lived component in FN is equal to the rise-time of the fluorescence from the tautomer T", i.e. TNS= TTR. The decay of FNand the growth of FTof the solution of 7-HQ in methanol indicates that the ground-state solute exists in the solution in two distinct states of solvation.The ratio of the amplitudes of the two components in the decay of FNamounts to 1 and indicates that ca. 50% of the 7-HQ molecules in their ground state must be present in the form of a reactive solute-alcohol complex. This agrees reasonably well with the results of Thistlethwaite and Corkill." As in the case of the complexes of 7-azaindole and alcohols, the 7-HQ-alcohol complexes are held together by intermolecular hydrogen bonds. Recently Itoh et al. reported a study of the intensity of FTas a function of the methanol concentration in a solvent consisting of a mixture of hexane and methanol. They found a quadratic dependence of the intensity on the concentration of methanol and concluded that two alcohol molecules are involved in the excited-state double proton-transfer process of 7- HQ.l8 Only ground-state complexes containing two alcohol molecules are able to tautomerize after electronic excitation (see fig.5). J. Konijnenberg et al. 1 1 I 0 1 2 3 4 5 rlns Fig. 4. Time-resolved fluorescence of FNof 7-HQ in methanol. Fig. 5. Possible solute-solvent interactions between 7-HQ and alcohol molecules. The long-lived component in the fluorescence FNmust be due to solute molecules which do not meet the requirements for fast proton transfer. The fact that only 50% of the 7-HQ molecules in the solution in methanol are able to phototautomerize suggests that the process proceeds via a rather critical particular conformation of the excited solute-alcohol complex [presumably the structure shown in fig.5( a)]. The time behaviour of the intensity of the band FT of a solution of 7-HQ in cyclohexane with lop3mol dm-3 methanol is shown in fig. 6. An interesting feature of fig. 6 is that it reveals a rise-time of 50 ps, which is much shorter than the corresponding rise-time of 200 ps for the solution in methanol as the single solvent component. There are two conceivable explanations for this behaviour. The first attributes the difference to a difference in non-specific solute-solvent interactions, which may affect energy levels. The second is based on the assumption that a particular conformation of a complex with at least two alcohol molecules is required for the actual tautomerization to occur. In the latter scenario, the rise-time TTR of 200 ps has nothing to do with the tautomeriz- ation in excited 1:2 solute-solvent complexes, but concerns excited complexes containing more than two alcohol molecules and in which the additional alcohol molecules hinder Pseudo-intramolecular Proton Transfer N5! 0c" 0 0.2 0.4 0.6 0.8 Fig.6. Time-resolved fluorescence of FT of 7-HQ in a cyclohexane solution containing 50 mmol dm-3 methanol. the achievement of a suitable conformation for proton transfer as shown in fig. 5(6). Evidence in favour of the second explanation has been derived from the influence of the size of the alcohol molecules on the kinetics of the excited-state tautomerization.Variation of the size of the alcohol molecules in single-component alcohols, used as solvent for 7-HQ, reveals a growth of the tautomer fluorescence band, which cannot be represented by a single exponential function for alcohols other than methanol. This behaviour is shown in fig. 7. The growth may be represented by a sum of two exponential functions, one with a short rise-time, TTS, and the other with a long rise-time, TTL, and with amplitudes As and AL, respectively. Taking the fluorescence decay also into account, the overall fluorescence kinetics are described by a function FT(t),which is defined by: The values of parameters in this equation are obtained by fitting FT(t)to the observed time-profile of the fluorescence shown in fig.7. They are given in table 1. Within experimental error T~~ does not vary much with the size of the alcohol, and has a value equal to that found in the case of solutions in mixtures of cyclohexane and a small concentration alcohol. The relative amplitude A,/(AL+ A,) is ca. 13% in the case of methanol and increases with the size of the alcohol molecules. These two observations concerning the fast component in the growth of FTindicate that T~~ is associated with the value of the rate constant kzt for the excited-state double proton transfer in 1:2 solute-alcohol complexes. An increase in the size of the alcohol reduces the probability that the two alcohol molecules, hydrogen-bonded to the solute, become involved in hydrogen bonding with other alcohol molecules.The reduced probability for higher-order aggregates is responsible for the relative decrease in AL and therefore for the relative increase in A,. The magnitude of TTL is predominantly determined by the rate of the conformational changes required to achieve a particular suitable geometry for double proton transfer. J. Konijnenberg et al. Fig. 7. Time-resolved fluorescence of 7-HQ in several alcohols: (a) methanol, (b) ethanol, (c) isopropyl alcohol, (d)cyclohexanol, (e) t-butyl alcohol. (f)and (8)show the difference between the measured and fitted curves for isopropyl alcohol assuming double (f)and single (g)exponential rise, respectively. Table 1. Values yielding the best fit of eqn (1) to the time profiles in fig. 7 methanol 0.13 (kO.10) 50 (*15) 200 (*25) ethanol 0.18 (*O.OS) 42 (*15) 350 (*30) isopropyl alcohol 0.26 (ztO.05) 54 (*15) 550 (*80) cy clohexanol t-butyl alcohol 0.34 (*0.05) 0.57 (kO.05) 52 (*15) 110 (*65) 480 (*70) 500 (k70) The Ground-state Reverse Tautomerization Process Itoh et al.observed the electronically deactivated phototautomer T and found that it yields the original from of 7-HQ in a thermal reaction, whose rate constant, kpt,is much smaller than the rate constant, k:t, of the phototautomerization. They obtained a value of 0.29 x lo6s-* for k,, for solution in methanol at room temperature. Fig. 3 shows the u.v.-laser-induced transient optical absorption spectrum of a solution of 7-HQ in isopropyl alcohol.Its decay is not affected by the presence of oxygen and Pseudo-intramolecular Proton Transfer Table 2. Rate constants for the reverse proton-transfer process of 7-hydroxy- quinoline in pure solvents (kpt)and the values for the rate constants kp,(0) in alcohol-cyclohexane mixtures extrapolated for a zero concentration of alcohol solvent methanol 4.1 0.244 1.60 0.56 1 methanol-d ethanol [CH,02H] 23.0 10.6 0.044 0.094 0.85 1.068 ethanol-d CC2H502H1 38.8 0.026 propan- l-ol isopropyl alcohol 8.9 36.8 0.112 0.027 0.90 0.35 1.995 2.090 isopropyl alcohol-d butan- 1-01 [CH3CH(02H)CH3] 81.9 9.3 0.012 0.108 1.oo 2.607 s-butyl alcohol t-butyl alcohol hexan-l-ol 15.7 54.8 6.6 0.064 0.018 0.152 0.20 0.95 3.042 4.420 4.592 octan- l-ol 5.6 0.179 7.215 decan-1-01 4.8 0.208 0.95 11.8 cyclohexanol 22.0 0.046 trifluoroethanol >10 hexafluoropropanol >10 can therefore not be considered to be a triplet species.The transient absorption spectrum has a maximum at 430 nm. Relative to the first electronic absorption band of the solution, the Stokes shift of FNis 3500 cm-'. Based on this fact, we can assign the 430 nm transient absorption band to T by allowing a Stokes shift of 4200cm-' for the fluorescence (A,,, = 525 nm) from the T" relative to the first electronic absorption band of T. kgt for the adiabatic excited-state phototautomerization may be estimated from TTR or from the decay time 71\18.Since TTR and TNS depend on the proton-transfer process as well as on other decay processes, an accurate value for k:t is difficult to obtain. In contrast to this k,, for the thermal reverse tautomerization may be obtained easily from the inverse lifetime of the phototautomer, provided that the only thermal reaction of the phototautomer is its retautomerization. The latter condition holds in the case of the phototautomer T. As may be seen from table 2, k,, for solutions of 7-HQ in alcohols depends on the nature of the alcohol. The values of kpt,listed in table 2, reveal a considerable kinetic isotope effect (kH/k,) caused by deuteration of the OH group of the alcohol. The observed isotope effect is largest for methanol (kH/kD= 5.6), and decreases to 3.7 for ethanol and 2.2 for isopropyl alcohol.The kinetic isotope effect supports the assignment of the 430nm transient absorption band to the phototautomer in its ground state. k,, clearly depends on the nature of the particular alcohol; however, the explanation of this dependence is not obvious. The viscosity of the alcohol may be ruled out as an important parameter governing the process, because even in the series of linear alcohols an increase in viscosity is sometimes accompanied by a decrease and sometimes by an increase in kpt. Furthermore, k,, is relatively large in the case of solution in cyclohexanol, which, as a glassy solid, is a high-viscosity system at room temperature. Successive substitution of the H atoms in methanol by CH3 groups gradually reduces the acidity of the alcohol molecule owing to the electron-donating character of the CH, group.The substantial decrease in k,, in J. Konijnenberg et al. i 0 5 10 15 [alcohol]/ mol dme3 Fig. 8. Plot showing the dependence of the reverse ground-state tautomerization process on the concentration of alcohol molecules in cyclohexane: 0,methanol; El, ethanol; A,isopropyl alcohol; x ,butan-1-01; a, s-butyl alcohol; V, t-butyl alcohol; +, decan-1-01. going from methanol to ethanol, isopropyl alcohol and t-butyl alcohol might suggest at first sight that the value is predominantly determined by the number of methyl groups substituted at the a-carbon atom, because successive substitution of the H atoms in methanol by CH, groups will affect steric factors and will also gradually reduce the acidity of the alcohol molecule owing to the electron-donor character of the CH3 group.However, at this stage of our discussion the suggestion seems premature, because in the case of longer linear alcohols k,, increases, whereas the acidity and the amount of steric hindrance are not expected to change much. The origin of the large k,, for the solutions in the long linear alcohols compared to the case of ethanol has been revealed by studying solutions in mixtures of these alcohols and an alkane. In a study of the solvent-assisted pseudo-intramolecular proton transfer of 7-azaindole we noticed that these alcohols behave like dilute solutions of ethanol in an alkane.' Fig.8 shows that k,, depends on the concentration of alcohol present in the solvent mixture. k,, for a given alcohol can increase by an order of magnitude by replacing the alcohol by a mixture of the alcohol and cyclohexane as solvent. For instance, the replacement of methanol by a mixture of lo-, mol dm-3 methanol in cyclohexane leads to an increase of k,, by a factor of 6.5. Fig. 8 shows that the values k,,(O) of the rate constant k,, in the limit of zero alcohol concentration are grouped around a number of distinct values. The values of k,,(O) are also listed in table 2. They are obtained by extrapolating the curves shown in fig. 8 to zero concentration and they are much less accurate than the values for the cases where the alcohols are the only solvent component. It should be emphasized that the ground- state phototautomer T is born as a complex with alcohol, after photoexcitation of a complex of 7-HQ with the alcohol.Therefore there are immediately alcohol molecules as nearest neighbours around the solute molecule T. Both the equilibrium between alcohol complexes of 7-HQ and bare 7-HQ molecules and the minimum detectable Pseudo-intramolecular Proton Transfer transient absorption pose a lower limit to the concentration alcohol, which can be used in practice. Photo excitation of 1:1 7-HQ-alcohol complexes and bare 7-HQ molecules does not lead to phototautomerization. The values of k,,(O) show clearly that viscosity and steric factors are not rate- determining.k,,(O) is seen to depend on the number of hydrogen atoms on the a carbon atom of the alcohol. This implies a good correlation between k,, and the proton-donating strength of the alcohol. The proton-donating strength of the alcohol may be influenced drastically by substitution with strong electron-withdrawing atoms like fluorine. As can be seen from fig. 9, a solution of 7-HQ in cyclohexane saturated with 2,2,2-trifluoroethanol (TFE) or with (ca. 0.3% vol) 1,1,1,3,3,3-hexafluoropropanol(HFP) exhibits a fluorescence spectrum dominated by the band at 525 nm due to tautomerized species. The rise-time of the tautomer fluorescence in these solutions is ca. 10ps, which is at the limit of our instrumental time resolution. These results clearly show that fluorinated alcohols are very efficient as catalysts for excited-state proton transfer in 7-HQ".Nevertheless, the ground-state tautomer T cannot be observed in these alcohols by transient absorption spectroscopy on the nanosecond timescale. Apparently they also cause k,, to increase above a value of say lo8s-', which makes T invisible on the nanosecond timescale. The only transient absorption observed then is due to triplet-state species. The enhancement of k,, supports the suggestion of a strong dependence of k,, on the proton-donating strength of the alcohol in the complex with T. Two explanations may be offered for this dependence. Since the distance between the proton donor and acceptor sites, in 7-HQ is large and the phototautomeriz- ation is very fast in its complexes with alcohols, the complexes, existing in the ground state, must contain two alcohol molecules,'* one hydrogen-bonded to the keto group and the other hydrogen-bonded to the N atom.The first explanation considers the retautomerization to consist of two consecutive intramolecular processes in the complex J. Konijnenberg et al. 3 3.5 4 4.5 5 lo3 KIT Fig. 10. Arrhenius plots for the rate constant k,,(T) for the reverse ground-state proton-transfer process of T in alcohols. Methanol-d =CH,02H; ethanol-d =C2H,02H: 0, methanol; 0, methanol-d; 0,ethanol; a, ethanol-d; x, n-hexane with 1mmol dm-3 methanol. of the alcohol with T. The first step is rate-determining and involves thermally activated intramolecular protonation of the keto group by the alcohol molecule hydrogen-bonded to it.Since this produces ionic species, it is not very likely to happen in solutions in practically non-polar mixtures of cyclohexane and small concentrations of alcohol. The second step involves intramolecular deprotonation of the N atom in the tautomer by the other alcohol molecule in the complex. This model implies a necessarily temperature- dependent kinetic isotope effect, when the OH group in the alcohol is replaced by an 02H group. The second explanation is based on the assumption that the two alcohol molecules in the complex must be interconnected by a hydrogen bond, and it considers the retautomerization as a concerted double proton transfer process. This concerted process may proceed through thermally activated barrier-crossing or through proton tunnelling.The strengths of the hydrogen bonds with the keto group and with the N atom, and therefore the proton transfer distances and barriers, should depend on the proton-donating strength of the alcohol. Which of the two explanations is the appropriate one will be decided in the next section. Note that we prefer now to refer to the proton-donating strength, measured as the strength of a hydrogen bond with a reference proton acceptor, rather than to the acidity of the alcohol as previously,' basically because solvation of the ions in the ionic equilibrium involved in the determination of the acidity has an influence on the ordering of the alcohols on the acidity scale.The ordering on the two scales is not expected to be very different if the choice of solvent in the measurements of the acidities is kept fixed. Temperature Dependence of the Retautomerization of the Phototautomer in its Ground State The lifetime of tautomer T is found to be temperature dependent. Fig. 10shows Arrhenius plots of k,, obtained for solutions in methanol and ethanol. The experimental values Pseudo-intramolecular Proton Transfer Table 3. Arrhenius parameters derived from fig. 10 methanol methanol-d 21.3 (k0.4) 1.6 (k0.3) x lo9 ethanol ethanol-d [CH302H] 24.7 (k0.4) 22.2 ( *0.4) 2.3 (k0.3) x lo92.7 (k0.3) x lo8 5.9 5.6 n-hexane-[C2H5O2HI 25.1 (k0.8) 6(*1.0) X 10' 3.8 3.7 1 mmol dm-3 methanol 21.2 (k0.4) 1.4 (k0.2) X 10" of k,,(T) satisfy an equation of the form: kpt(T) = A0 exp (-Eact/kB TI-(2) The values of A, and E,,,, as well as those of the deuterium isotope effect Ao(H)/A,(D) on A, and of the deuterium kinetic isotope effect (kH/kD) of k,, at 293 K are listed in table 3.In both cases E,,, is less than 25.lkJ.mol-'. The lower value of k,, up to T =293 K for the solution in ethanol is seen to be due mainly to the activation energy, which is higher than for the solution in methanol. Although there is a relatively large kinetic isotope effect, this does not arise as usually from an effect on the activation energy, but rather from an effect on the factor A,. This follows from the fact that for each of the two alcohols the lines in the Arrhenius plots for the O'H and the 02H case are exactly parallel to each other. In other words, the kinetic isotope effect is temperature independent. This is revealed clearly by the equality of kH/kD and A,(H)/A,(D) in table 3. Another interesting feature of the Arrhenius plots in fig.10 is the observation that the increase in k,, upon decreasing the alcohol concentration is not caused by a reduction in the energy barrier, but is merely the result of a higher pre-exponential factor. The temperature independence of the kinetic isotope effect does not fit within the framework of standard transition-state theory, which would predict a temperature dependence arising from an isotope-dependent activation energy, resulting from the iso-tope-dependent zero-point energy of the vibration along the reaction coordinate.Since the ground-state proton transfer of T involves disruption of both an N-H bond of the tautomeric solute and an 0-H bond of the alcohol the reaction coordinate must be described by a vibrational coordinate involving stretching of both an N-H and an 0-H bond. The kinetic isotope effect of 5.6 for the solution in methanol at 293 K would then imply a difference in zero-point energy of 3.8 kJ mol-'. Table 3 shows that this is much larger than the actual isotope-induced difference in activation energy. Apparently the activation energy cannot be associated with accumulation of energy in the reaction coordinate. The proper explanation for the temperature-independent kinetic isotope effect must be similar to the one offered previously in the case of the solvent-assisted excited-state proton-transfer processes in a trimethylated pyrichrominium cation as well as in the solvent-assisted proton transfer of 7-azaindole.It is an extension of the second explana- tion given above for the dependence of k,, on the proton-donating strength of the alcohol and it may be phrased as follows. In conformity with the fact that k,, is not correlated with the viscosity of the solvent, the retautomerization must take place within an already existing complex. Two steps are required to achieve the tautomerization. The first is to reach, through thermally induced fluctuations, a single structurally well defined conformation of the complex suitable for double proton transfer, i.e.with resonant zero J. Konijnenberg et al. 51 levels in each of the double-minimum potential wells. The second step involves proton tunnelling from the occupied zero levels in the double-minimum wells. The first step is isotope independent and temperature dependent and its activation energy must be related to structural reorganization of the alcohol molecules in the complex to achieve a hydrogen-bonded cyclic structure. The second step is temperature independent, but isotope dependent. This picture also offers an explanation for the effect of the alcohol concentration on the reaction rate in alkane-alcohol mixtures. After the excited-state tautomerization a hydrogen bond in the cyclic 1:2 solute-solvent complex may be broken or excess alcohol molecules may interfere to yield non-cyclic open structures which are not able to tautomerize rapidly.In order to obtain the particular complex with a closed structure, required for the retautomerization, considerable rearrangements of solvent molecules near the solute are necessary. The fact that k,, does not increase with the number of alcohol molecules available for catalysis seems to fit only within the picture restricting tautomerization to a particular complex of T with the alcohol. This work was supported by the Foundation for Chemical Research in The Netherlands (S.O.N.) with financial aid from the Netherlands Organization For Scientific Research (NWO). References 1 M. Kasha, J. Chem. SOC., Faraday Trans.2, 1986, 82, 2379. 2 G. J. Woolfe and P. J. Thistlethwaite, J. Am. Chem. SOC., 1981, 103, 6916. 3 G. J. Woolfe, M. Melzig, S. Schneider and F. Dorr, Chem. Phys., 1983, 77, 213. 4 M. Cohen and S. Flavian, J. Chem. SOC. B, 1967, 321. 5 A. J. G. Strandjord and P. F. Barbara, Chem. Phys. Lett., 1983, 98, 21. 6 P. Avouris, L. L. Yang and M. A. El-Bayoumi, Photochem. Photobiol., 1979, 24, 211. 7 J. Konijnenberg, A. H. Huizer and C. A. G. 0.Varma, J. Chem. SOC., Faraday Trans. 2, 1988,84, 1163. 8 J. Koput, B. Marciniak and S. Paszyc, Z. Naturfosch., Ted A, 1986, 41, 661. 9 J. Konijnenberg, A. H. Huizer, F. Th. Chaudron, C. A. G. 0.Varma, B. Marciniak and S. Paszyc, J. Chem. Sac., Faraday Trans. 2, 1987, 83, 1475. 10 D. McMorrow and Th. Aartsma, Chem. Phys. Lett., 1986, 125, 581. 11 K. Inuzuka and A. Fujimoto, Spectrochim. Acta, Part A, 1986, 42a, 929. 12 J. Konijnenberg, A. H. Huizer and C. A. G. 0.Varma, to be published. 13 G. W. Ewing and E. A. Steck, J. Am. Chem. SOC.,1946, 68, 2181. 14 S. F. Mason, J. Philip and B. E. Smith, J. Chem. SOC. A, 1968, 3051. 15 P. J. Thistlethwaite and P. J. Corkill, Chem. Phys. Lett., 1982, 85, 317. 16 P. J. Thistlethwaite, Chem. Phys. Lett., 1983, 96, 509. 17 M. Itoh, T. Adachi and K. Tokumura, J. Am. Chem. SOC.,1983, 105,4828; K. Tokumura and M. Itoh, J. Phys. Chem., 1984,88, 3921. 18 M. Itoh, T. Adachi and K. Tokumura, J. Am. Chem. SOC., 1984, 106, 850. Paper 8/02266F; Received 6th June, 1988

ISSN:0300-9238    

DOI:10.1039/F29898500039

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC.,Furaduy Trans. 2, 1989, 85( l), 53-64 Hydrogen Disorder in Potassium Hydrogen Carbonate Jacqueline B. Larcombe-McDouallt and John A. S. Smith* Chemistry Department, King's College, University of London, Strand, London WC2R 2LS 170 Quadrupole double resonance frequencies from the hydrogen-bonded C170Hand C= 170. -.Hgroups in the (HC0,);-dimer in crystalline KHC03 have been recorded in natural abundance between 77 and 360 K. The two sets of transitions corresponding to the 1/2 ---* 3/2 and 3/2 ---* 5/2 transitions for each group collapse to a single set at 341 K. It has been shown that this behaviour can only be explained by fast concerted two-proton flips between two positions available for the hydrogen atoms within the (HC0,);-dimer and not by 180" flips of the ion as a whole about its C--Caxis.The two positions differ in energy, this energy difference being itself a function of temperature and hence of the degree of order (s), varying from cu. 6 kJ mol-' at 77 K(s= 1) to 0.2 kJ mol-' at 360 K (s =O). There appears to be a hydrogen-deuterium isotope effect, the energy difference increasing with the degree of deuteration. It has been known for some years that the (HC03):- hydrogen-bonded dimers in KHC03 are disordered. The first definite evidence to be reported came from neutron diffraction data,' which were interpreted in terms of a two-site model with 'occupation numbers' or population ratios at 298 K of 0.24 in KHCO, and 0.14 in KDCO,. Estimates based on potential-energy functions for the hydrogen and deuterium stretching modes derived from band profiles in the low-temperature Raman spectra2 gave values of 0.34 at 298 K in both KHC03 and KDC03.Preliminary calculations3 based on the 170 quadrupole double-resonance spectra for KHC03 recorded at 774,5and 291 K5 yielded a ratio of 0.15, and a recent analysis6 of 2H spin-lattice relaxation in single crystals of KDC03 gives 0.18 at 300 K. Despite the unanimity of opinion that the room-temperature structure is disordered, there is some disagreement on the values of the population ratio, and the mechanism by which this disordering occurs is in dispute. Two models have been suggested, that of concerted two-proton jumps within the nearly planar hydrogen-bonded dimer (I), as have been postulated to occur in the closely related dimers found in some carboxylic acids in the solid and a 180"rotation of the dimer'7,'8 (or the (1) (a t Present address: MR Center, Harper Hospital, 3990 John R, Detroit, MI 48201, U.S.A.53 Hydrogen Disorder in KHC03 cold nitrogen/ hot air Fig. 1. Block diagram of the double-resonance spectrometer. molecule as a whole19) about the OC.-CO axis passing through the dimer's centre of symmetry (11). Both have been stated to occur in acetylenedicarboxylic acid.20 However, much of the evidence is inconclusive as to the mechanism; we show in this paper that the I7O quadrupole double resonance data for KHC03 firmly support the two-proton jump model, in which the nuclei move together or in quick succession. The Double-resonance Spectrometer 0 Quadrupole resonance signals in natural abundance were recorded on a variable- temperature field-cycling spectrometer in which the sample was transported mechani- cally2' from high to zero field by the same gas stream as was used to vary the sample temperature. A block diagram of the spectrometer is shown in fig.1. The 'H magnetic resonance spectrometer was a Bruker 'Minispec' operating at a frequency of 39.5 MHz (Bo=0.928 T) in the field of a permanent magnet of pole gap 30 mm and pole diameter 135 mm. The high-field probe containing the 'H r.f. coil, of 8 turns of 19 S.W.G. silver wire of diameter 14mm, is shown in fig. 2; the gas stream, either from boiling liquid nitrogen or heated air, entered at ports A or B.At A, the PTFE sample container of outer diameter 9 mm, wall thickness 1 mm, containing CQ. 0.9 cm3 of sample, was blown to the right along the sample-transfer glass tube to the "0irradiation coil in zero field, J. B. Larcombe-McDouall and J. A. S. Smith Fig. 2. Design of the variable-temperature r.f. probe. as shown in fig. 2, the gas stream escaping via the 2 mm gap between the outside of the transfer tube and the inside of the long glass unsilvered Dewar of outside diameter 28 mm. Switching the gas stream to B (at low temperatures, by means of a pair of Peter-Paul 26KK9ZCV solenoid values) reversed this process and brought the sample back, both arrival times in high or zero field being monitored by a photodiode, the interruption of whose output caused the microprocessor timing-control unit to count down the programmed residence time, rpor rQ,according to whether the sample was in the high field 'H(P) coil or the zero-field 170 (Q) coil.The same voltage triggered the spectrometer with a pre-set delay time variable between 0.4 to 0.6 s. The transit time from one coil to the other usually lay between 0.1 and 0.6s. For temperatures aboie ambient, $he Dewar was replaced by a Pyrex glass tube closed at one end and non-inductively *wound with heating tape, the hot-air stream being switched by means of Burkert 355-C-MCG/ 1 high-temperature valves with PTFE seals. The Q coil for "0 experiments between 1 and 2.3 MHz consisted of 70-100 turns of S.W.G.35 enamelled copper wire, with a tapping position at typically 2 to 3 turns to match the coil to the output of an EN1 550L r.f. power amplifier supplied by a PTS 160 frequency source; the Q coil itself was tuned for optimum matching by means of a Jackson 600 pF, 6 kV tuning capacitor and generated B1fields of between 0.1 and 0.2 mT in amplitude. The r.f. signal was gated off during the capture of the 'H free-induction decay in high field. A thermocouple at port A monitored the temperature of the gas stream but this usually differed by up to 15 K from that of the sample. The calibration was provided by recording 35Cl quadrupole double resonance in p-chlorobenzoic acid, the temperature dependence of whose frequencies had been previously recorded on a DECCA super- regenerative oscillator spectrometer between 140and 390 K.This compound gives good 56 Hydrogen Disorder in KHCO, thermal-mixing spectra up to 360 K with residence times of 7p= 10 s and 7Q= 1 s."~'~ The system took ca. 40min to achieve a pre-set temperature, which was subsequently maintained with a stability of *l K by means of an Oxford Instruments DTC2 tem-perature controller. The working temperature range of the spectrometer was 215-365 K. Results and Discussion Well resolved I7O signals were seen in KHC03 in natural abundance from both the C-I7OH and C='70.--Hgroups, but not from the non-hydrogen-bonded C=I7O, whose frequencies have been recorded by other double resonance technique^.^ Each I7O nucleus, of spin 5/2, gives rise to two signals conveniently labelled as *1/2+ *3/2 and *3/2 + f5/2.The transition f1/2 + *5/2 is also partially allowed in non-axial electric field gradients and has been detected in previous experiments on KHC03 at both 77 and 291 K. The present experiments rely on the presence of a strong dipolar coupling between 'H and the attached or hydrogen-bonded 170; irradiation within the dipolar-split 170 resonance line transfers energy to the 'H dipolar bath, the cycle being completed by fast I7O spin-lattice rela~ation.~ Under these conditions, the I7O lines are usually observed as doublets with an intensity proportional to WA', where A = w -oois the frequency off-set from the line centre and W is the quadrupole transition probability proportional to B:g(A), g(A) being the dipolar-split 170 lineshape.Because of the factor A', the wings of the lineshape function become preferentially weighted with respect to the centre, generally producing a simple doublet despite the complex structure of g(A). Some 1/2 -+3/2 transitions of C-170H and C='70---Hare shown in fig. 3, the doublet structure being clear1 visible in the C-"OH line near 1080 kHz at 322 K, but less well resolved in the C=I'O---lH line near 1250 kHz, presumably as a consequence of the weaker 170---1Hdipolar coupling. As the temperature is raised the two lines come together (at 327 K), coalesce at 341 K, and the doublet structure of a single combined C=170-*1Hand C-"OH line reappears near 350 K. An almost identical collapse is observed in the 3/2+ 5/2 transitions, but with a poorer signal-to-noise ratio.The doublet splittings also decrease between 230 and 320 K, from 97 to 69 kHz for Ci70H and 78 to 55 kHz for C=170-.H, i.e. moving towards equality. The line-centre frequen- cies are plotted against temperature in fig. 4, showing that both sets collapse to a single doublet by 341 f2 K. It is immediately obvious that the temperature dependence of the 170 frequencies, and their number, is not consistent with the static disorder model inferred from the neutron diffraction structure analysis.' The number of I7Olines observed is in agreement with the ideal crystallographic point symmetry (1)of (HC03)f-in the crystal (P2J a, 2 = 4) and their relative intensities show no consistent change with temperature.Nor can the results in figure 4 to be explained exclusively in terms of 180"flips of the (HC03)f-dimer about the OC-.CO axis; such motion would separately average each tensor, C-l'OH and C=l7O-.-H,by a rotation of 180"about a line passing through the centre of symmetry of the dimer and lying in the mean molecular plane, but the averaged tensors for the two groups would remain distinct and no collapse of the two sets of lines to just one above 341 K would be observed. Such behaviour however is consistent with the concerted two-proton jump model, since this does transform C-170H into C='70-..H, and the collapse of the four-line pattern to two is then a direct consequence. This interpretation is confirmed by calculations of the temperature dependence of the 170 quadrupole tensors.One advantage of resolving 170--'H dipolar structure on I7O double resonance spectra is that the direction and sign of the 170 quadrupole coupling tensor with respect to the 170-1H axis can often be inferred from a detailed analysis of the two frequency line shape^.^^ Such an analysis has been performed5 for KHC03 at 77 K and the most likely orientation of the C-170H quadrupole tensor at that temperature is shown in fig. J. B. Larcombe-McDouaN and J. A. S. Smith 1 1 1 I 1 I I 1300 1200 1100 1000 1300 1200 1100 I I 1 900 1000 1100 1200 1100 1200 1300 frequency/kHz Fig. 3. 1/2-3/2 I7O transitions of C-I7OH and C=170.-H in KHC03 at four different =temperatures (T~20 s, T~ = 2s, 1 kHz steps): (a) 322 K, (b) 327 K, (c) 332 K, (d) 350 K.5. The same diagram shows the signs and axial system of the C=i70.-H tensor at 77 K for which the assignments are less certain because of the closeness of the y and z components; the orientation (and sign) which are shown differ from those previously published' mainly by an interchange of these two components, and hence a change of sign. The main justification for this change is a much better fit to the experimentally observed temperature dependence. We assume that the two I7O tensors at 77 K given in fig. 5, D, and D2,refer to the fully ordered state of a bicarbonate ion dimer, which is consistent with the analysis of the 2H relaxation data;6 as the temperature is raised, fast proton motion is assumed to occur between this state and a new state of higher energy AEoin which the two protons have jumped across the O...H-O hydrogen bonds (I).The observed quadrupole tensor D is therefore assumed to be a population-weighted average of the two states D = a@+ (1 -a)& (1) Hydrogen Disorder in KHC03 I 1 1 77 250 300 350 T/ K Fig. 4. Temperature dependence of the 170 quadrupole resonance frequencies in KHC03. Open symbols, 3/2 -+5/2; filled symbols, 1/2 -+3/2. A,A, Ci70-H; 0,a, Ci70H. where a and (1 -a)are the relative populations, the ratio of which varies with tem- perature according to the equation a -exp( -AE"/RT). (2)1-CU There are two observed values for a according to whether D, is taken as the C-l'OH or C='70...H tensor; as the temperature rises, both should approach a common value of 0.5 following eqn (2), after which the two tensors become identical.These conclusions were first tested against the data obtained at 300 K, which predict e'qQ/ h =-7.322 MHz, 7=0.164 for C-170H and e2qQ/h=-6.783 MHz, 7=0.639 for C"=O-H. A planar system was assumed, and the two angles in fig. 5, together with a, were varied until the best fit between theory and experiment was reached with 8 =22", 4 =40°, and a=0.165 J. B. Larcombe-McDouall and J. A. S. Smith qxx-0.223MHz qzz qzz 6.765 MHz -7.709 MHz Fig. 5. Most probable orientations and signs of the C-I7OH and Ci70-.H quadrupole tensors in KHC03 at 77 K.for Ci70H and 0.11 for C='70.--H, giving values of e2qQ/h= -7.338 MHz, 7=0.237 for the former and e2qQ/h= -6.624 MHz, 7=0.684 for the latter. For C="O. ..H, qzz was the component subtending an angle of 22" with the O.-.H-O direction, and was given a positive sign in the ordered configuration of the dimer at 77 K. However, the assumption that the (HC0,):- dimer is planar is incorrect;' there is a difference of 0.21 8, between the two parallel and nearly planar C03 groups, with which the plane of the hydrogen-bonded ring makes an angle of 4.7". The calculation was therefore repeated in this new frame of reference, the best fit now being achieved with 8 =27", 4 = 50°, and a =0.21 for CI7OH and 0.26 for C"O...H, giving values of e2qQ/h= -7.321 MHz, 7 =0.167 for the former and e2qQ/h= -6.685 MHz, 7=0.638 for the latter.Note that in both calculations, one effect of disorder at room temperature is to interchange the directions of qYyand qzzfor the C='70-H group in fig. 5 and hence the sign of the quadrupole coupling constant. The next stage was to calculate from eqn (1) the CI7OH and C='70-m-H quadrupole coupling constants and asymmetry parameters as a function of a. The experimental frequency vs. temperature plots were fitted by a set of optimized curves shown as continuous lines in fig. 4, from which 'experimental' values of the 170 quadrupole coupling constant (e2qQ/h)and asymmetry parameter 7 were derived by means of published analytic solutions of the quadrupolar Hamilt~nian.~~?~~ The values of 7 were then matched to the values calculated from eqn (l), giving the corresponding relative populations a as a function of temperature; two values of a are obtained (table 1) from either the C-"OH or C='70---H group.They do not follow eqn (2); if differences between population ratios at 10"intervals are calculated, the AEO values derived (table 2) decrease with temperature, from an average of 4.2 kJ mol-' at 230 K to 0.2 kJ mol-' at 360 K. At the former temperature, they are (to within experimental error) identical with the value of 4.3 kJ mol-' deduced from an analysis of the *H spin-lattice relaxation times.6 The analysis of the results may be displayed in a different fashion by plotting the observed 170 quadrupole coupling constants at a given temperature against the asymmetry parameter.This has been done in fig. 6, in which the open triangles represent Ci70H and the open squares C= 170-.-H. The continuous line represents the predictions of the concerted two-proton jump model (I) as given in table 1, and the dashed line the curves expected for the 180O-flip model (11). There is no correspondence with experiment in the latter case, and the quadrupole parameters of the two types of I7O do not even coincide when a = 0.5, as we have already predicted. Even above the coalescence point at 341 K, the observed frequencies show little further variation with temperature, suggesting that model (I) is almost sufficient to account for the observed temperature variation, at least up to 360 K.Furthermore, the two-proton jump model gives an excellent fit with experiment, faithfully reproducing the two axial interchanges Hydrogen Disorder in KHC03 Table 1. Comparison of experimental and calculated results for KHC03 T/K V1 /MHz V2 /MHz ' 77 (exptl) QCC(exptl)/MHz a rl (calc.) QCC(calc.)/MHz ci70~ 230 1.275 2.230 0.340 -7.597 0.07 0.341 -7.570 240 1.255 2.225 0.321 -7.563 0.085 0.323 -7.542 250 1.237 2.225 0.299 -7.545 0.105 0.298 -7.504 260 1.217 2.220 0.277 -7.510 0.12 0.280 -7.477 270 1.195 2.217 0.248 -7.480 0.145 0.249 -7.432 280 1.175 2.2 10 0.223 -7.439 0.165 0.224 -7.397 290 1.155 2.198 0.200 -7.385 0.185 0.198 -7.363 300 1.130 2.185 0.164 -7.322 0.21 0.167 -7.321 310 1.110 2.162 0.144 -7.237 0.225 0.147 -7.296 320 1.090 2.135 0.128 -7.140 0.24 0.128 -7.272 330 1.075 2.1 10 0.121 -7.054 0.245 0.122 -7.264 340 1.070 2.075 0.156 -6.95 1 0.43 0.155 -7.000 350 1.080 2.065 0.190 -6.933 0.455 0.191 -6.969 360 1.100 2.065 0.277 -6.953 0.48 0.288 -6.939 ~170...H 230 1.605 1.812 0.855 -6.690 0.13 0.852 -6.599 240 1.580 1.820 0.832 -6.693 0.14 0.836 -6.605 250 1.555 1.823 0.8 10 -6.684 0.155 0.81 1 -6.614 260 1.522 1.832 0.78 1 -6.681 0.17 0.786 -6.623 270 1.540 1.845 0.749 -6.789 0.19 0.753 -6.635 280 1.460 1.857 0.719 -6.701 0.21 0.720 -6.685 290 1.430 1.875 0.685 -6.727 0.23 0.687 -6.663 300 1.395 1.905 0.639 -6.783 0.26 0.638 -6.685 3 10 1.340 1.930 0.579 -6.804 0.295 0.581 -6.713 320 1.265 1.957 0.496 -6.81 1 0.345 0.500 -6.756 330 1.157 2.000 0.356 -6.828 0.435 0.358 -6.884 340 1.070 2.050 0.185 -6.880 0.55 0.184 -6.975 350 1.080 2.065 0.190 -6.933 0.545 0.191 -6.969 360 1.100 2.065 0.227 -6.953 0.52 0.228 -6.939 Table 2.Values of the energy difference AEo between ordered and disordered forms calculated at temperature intervals of 10 K T/ K AEo(C'70H)/kJmol-' AE0(C170..-H)/kJmol-' 230 4.9 3.6 240 4.7 3.6 250 4.5 3.5 260 4.3 3.4 270 4.0 3.3 280 3.8 3.1 290 3.6 2.9 300 3.3 2.6 310 3.2 2.2 320 3.1 1.7 330 3.1 0.7 340 0.8 0.5 350 0.5 0.5 360 0.2 0.2 J.B. Larcombe-McDouall and J. A. S. Smith 1.a 0.8 0.6 77 0.4 0.2 I I I I I OA 3 4 5 6 7 8 le2qQ/hI/ MHz Fig. 6. Plot of observed I7Oquadrupole coupling constant (I e'qQ/ h I) against asymmetry parameter (7)) for Ci70H (A) and C170...H(0)in KHC03 prediction of the concerted two-proton jump model, (---) prediction for 180" flips. observed at le'qQ/ hi= 6.6 and 7.2 MHz, the fomer corresponding to the y-z interchange already referred to, and the latter to an x-z interchange. The fit is not improved if a triple rather than a double potential well is considered, with the additional minimum at the centre of the O-H---O hydrogen bond, at which position the 170 quadrupole coupling tensor is assumed to be similar to that observed in the centrosymmetric hydrogen bond in potassium hydrogen maleate.27,28 Nor would a model involving uncorrelated proton jumps fit the "0results, in agreement with a recent analysis12 of the zero-field 'H magnetic resonance spectrum of the carboxylic protons in p-toluic acid. It should, however, be emphasized that the present analysis tells us little of the path that the hydrogen atoms follow; a fast proton jump from COH to CO within the same HCO, ion would be equally consistent with the calculations. The model also assumes that the whole of the temperature dependence between 77 and 340 K is due to the order-disorder process and so neglects the natural temperature dependence of all nuclear quadrupole resonance freq~encies,~~ which in KHC03 could be largely associated, for example, with bending and stretching modes of the hydrogen bond.30y31 The conclusion from this analysis is that in KHC03 the proton disorder observed in the 170 quadrupole resonance spectrum between 230 and 360 K arises from concerted two-proton jumps in an asymmetric double well, the asymmetry of which diminishes as the temperature rises.Several other examples of similar proton order-disorder phenomena unaccompanied by a phase transition have already been studied; naph- thazarin B32 and benzoic acid' by 13C magnetic resonance, terephthalic and p-toluic acid-d:I3l2 by 'H dipolar spectroscopy and benzoic-d5 de~anoic,'~terephthalic,' acetyl-enedicarboxylic*' and p-nitrobenzoic2' acids by 'H and/ or 2H spin-lattice relaxation measurements.Invariably any analysis of the dynamic or equilibrium behaviour of such systems has assumed activation energies or equilibrium potential-energy differences which are independent of temperature, despite the generally recognized fact that the Hydrogen Disorder in KHCO, asymmetry in the potential-energy curves is largely intermolecular in origin. It is clear that this assumption breaks down in the case of KHC03 (and may well be an unjustified approximation in previous work). In this crystal, the near-planar (HC03);-ions form stacks, the perpendicular to which is nearly parallel to the c axis and is almost coincident with the direction of maximum thermal expansion.' The major intermolecular interac- tions may therefore be with nearest neighbours in this array above and below the plane of a given dimer, from which it is reasonable to infer that diminishing order may also reduce the energy inequivalence of the two forms to an almost vanishing value by 360 K.The process therefore bears a close resemblance' to order-disorder phase transitions in solids.33 If we define an order parameter s, given by s=1-2a (31 the variation of AE" in table 2 can be fitted to an expression of the kind AE"=AELs (4) in which AE; is the energy required to transfer N protons per mole of KHCO, in the completely ordered state; the values of AEo obtained are 6.7k 1.0 kJ for C-I'OH and 5.3*0.4 kJ for C=I7O-..'H, the latter being the more reliable.Integration of eqn (4) leads to an energy difference between complete order and complete disorder of AE;/2 = 2.7 kJ mol-I, which is very small compared to the lattice energy of ca. 740 kJ mol-I, but should make a noticeable contribution to the heat capacity. The corresponding entropy difference is R In 2 = 5.76 J K-' mol-', which is a rather larger proportion of the entropy of 115.5 J K-' mol-' at 298.15 K. Finally, up to 330 K, the order parameter follows an equation of the form sK(T,-T)? (5) Taking T, = 341 K and averaged values of s from table 1 gives a value for p of ca. 0.4; compare this with p = 0.45 *0.08 deduced from the "0 quadrupole parameters in PbHP0i3 prior to the second-order phase transition at 37°C. The question remains of whether or not the equilibrium or dynamic behaviour of the order-disorder process in solid KHCO, shows any significant isotope effect.In solution, both equilibrium constants34 and rate constants35 for the HCO, ion show significant changes on deuteration, but the mechanism of proton exchange is very different from that in the solid state. In the latter phase the energy difference between the two potential minima, derived from the analysis of the 170 quadrupole resonance frequencies, AG = 5.3*0.4 kJ mol-*, does differ from the value of AEo= 3.9 kJ mol-' derived from 'H spin-lattice relaxation in KDC03, but unfortunately these terms refer to different quantities since the *H relaxation analysis fails to allow for the dependence of AEO on the degree of order.Single-crystal 'H or 2H magnetic resonance studies of KHCO, or KDCO,, undertaken to obtain the 'H chemical shift36 or 2H quadrupole coupling were performed at a fixed temperature, and because of fast exchange under these conditions, shed no light on the question. No 'H dipolar spectroscopy or zero-field magnetic resonance results have yet been published for partially deuterated KHC03. The dipolar splitting in the high-field 'H spectrum is consistent with an intra-dimer proton-proton distance of 2.27 A, which is larger than the value of 2.21 A predicted by the neutron diffraction structure analysis.' A similar discrepancy in the derived interproton distance (2.28 A) is observed in an analysis39 of the dipolar structure carried by the 39Kquadrupole double resonance spectrum in KHC03,4o whereas a study of the deuteron-deuteron splitting in a single crystal of KDC03,' gives a rather smaller distance of 2.22 A.It would be expected that at least part of these differences between theory and experiment is due to the order-disorder process we have been discussing: for fast two-proton jumps, the effect on the intra-dimer proton dipolar coupling is similar to that already observed for the NH2 inter-proton coupling in urea and thiourea as a J. B. Larcombe-McDouall and J. A. S. Smith 63 result of fast 180" flips about an axis passing through the C=O or C=S bonds:' In the disordered state (s =0), the second moment of the 'H magnetic resonance line is reduced by a factor 1/4 (1 +3 cos'p), where p is the angle between the two interhydrogen vectors in a disordered (HC03)f- ion.The neutron diffraction structure analysis' gives p = 33" for an inter-hydrogen distance of 2.205A, and hence a reduction factor of 0.781, which would have led to an interhydrogen distance of 2.20(0.781)-''6 =2.29 A being deduced. The observed distance of 2.27 A at room temperature39p40 corresponds to s =0.2, compared to a value of 0.5'4 deduced from eqn (4). By the same argument, the lower value for the 'H--e2H distance of 2.22 A observed in KDC03 at the same tem- perature3* corresponds to a larger value of s of ca. 0.7, suggesting a larger distance between the two potential-energy minima in the deuterated form. Unfortunately, this analysis is not conclusive, since other have reported no significant change in the 'H spectrum down to -180°C.The most obvious way of looking for deuteration effects would be to repeat the 170experiments on fully deuterated KHC03 ;unfortunately this removes the strong 'H signals on which the success of these double resonance experiments depends. Even partial deuteration weakens them, but 170 signals for both C170H and C='70.-.H have been detected at 291 K up to 25% deuterium content,' and the small shifts in quadrupole coupling constant and asymmetry parameter suggest that the order parameter is increasing with increasing deuteration, so that at least in the HD dimer the two potential-energy minima appear to move further apart, consistent with the lengthening of the O-H--.O hydrogen bond on deuteration.It is of interest that the *H quadrupole double resonance spectra at 291 K show two sets of lines which have been assigned to the HD and DD dimers, whose intensities change in a predictable way with the degree of de~teration.~~ The HD form has mean values of e'qQ/ h = 152.4 kHz and r) =0.195 compared to values of e'qQ/ h = 154.9 kHz, r) =0.187 for DD, both at 291 K; comparing these with the data of Benz et aL6 between 77 and 250 K, which predict e*qQ/h= 157.0 kHz, r) = 0.178 for the ordered state and e2qQ/h= 155.7 kHz, r) =0.183 for the state of complete disorder, we see that the experimental difference between HD and DD could in part be explained by a higher degree of order in the former relative to the latter.These arguments however neglect the natural temperature dependence of the 2H quadrupole coupling parameters and the extent to which these quantities are influenced by changes in the structure of hydrogen bond and in the stretching and bending modes on deuteration. At best, there does seem to be some isotope effect on the order-disorder equilibrium with the energy difference between the two potential minima increasing on going from the HH to the HD form. In carboxylic acid dimers, such as those of benzoic, glutaric and p-formylbenzoic acids, recent Tl meas~rements~~ show that the energy barriers to classical 'H jumps and tunnelling increase with deuter- ation and it is reasonable to suppose that a similar effect would be observable in KHC03.Conclusions The collapse of the two sets of 170 quadrupole resonance frequencies arising from the C-170H and C='70-H groups in KHC03 to a single set at 341 K shows conclusively that the mechanism of the proton disordering in this crystal proceeds by fast concerted two-proton jumps within the (HC0,)f- dimer and not by 180" flips about the C..C axis. There is no evidence for any phase transition, but the behaviour of the 170 frequencies shows many similarities to that observed in 170 studies of other order- disorder processes which do lead to a phase transition, such as in KH2P0, and PbH PO,. Thus it is possible to define an order parameter s which governs the equilibrium distribution of the two forms of the (HC03):- dimer in an asymmetric double potential well.The temperature behaviour of this quantity suggests that the asymmetry of the potential-energy function changes with temperature, as would be expected for a feature which is wholly intermolecular in origin. The difference between the potential-energy 64 Hydrogen Disorder in KHC03 minima varies from 6.0* 0.7 kJ mol-' at 77 K to 0.2 kJ mol-' at 341 K. There is some evidence for an isotope effect; a consideration of other 'H and 2H magnetic resonance studies suggests that the difference between the two potential-energy minima increases on deuteration, as would be expected from the observed increase in the O...O hydrogen-bonding distance. We thank the S.E.R.C. for grants, Professor H. Chihara for allowing us to see his paper prior to publication and Mrs K.Gray for the probe design. References 1 J. 0.Thomas, R. Tellgren and I. Olovsson, Acta Crystallogr., Sect. B, 1974, 30, 1155; 2540. 2 F. Fillaux, Chem. Phys., 1983, 74, 405. 3 A. Gough, M. M. I. Haq and J. A. S. Smith, Chem. Phys. Lett., 1985, 117, 389. 4 C. P. Cheng and T. L. Brown, J. Am. Chem. SOC., 1979, 101, 2327. 5 I. J. F. Poplett and J. A. S. Smith, J. Chem. SOC.,Faraday Trans. 2, 1981, 77, 761. 6 S. Benz, U. Haeberlen and J. Tegenfeldt, J. Magn. Reson., 1986, 66, 125. 7 S. Hayashi and N. Kimura, Bull. Inst. Chem. Res. Kyoto Univ., 1966, 44, 335. 8 R. Feld, M. S. Lehmann, K. W. Muir and J. L. Speakman, 2. Kristallogr., 1981, 157, 251. 9 S. Nagaoka, T. Terao, F. Imashiro, A.Saika, N. Hirota and S. Hayashi, Chem. Phys. Lett., 1981, 80, 580; J. Chem. Phys., 1983, 79, 4694. 10 F. Graf, R. Meyer, T-K. Ha and R. R. Ernst, J. Chem. Phys., 1981, 75, 2914. 11 B. H. Meir, F. Graf and R. R. Ernst, J. Chem. Phys., 1982, 76, 767. 12 T. P. Jarvie, A. M. Thayer, J. M. Millar and A. Pines, J. Phys. Chem., 1987, 91, 2240. 13 S. Nagaoka, T. Terao, F. Imashiro, N. Hirota and S. Hayashi, Chem. Phys. Lett., 1984, 108, 524. 14 B. H. Meier, R. Meyer, R. R. Ernst, A. Stockli, A. Furrer, W. Halg and I. Anderson, Chem. Phys. Lett., 1984, 108, 522. 15 B. H. Meier and R. R. Ernst, J. Solid State Chem., 1986, 61, 126. 16 P. Fisher, P. Zolliker, B. H. Meier, R. R. Ernst, A. W. Hewat, J. D. Jorgensen and F. J. Rotella, J. Solid State Chem., 1986, 61, 109.17 K. Furik, Chem. Phys. Left., 1984, 108, 518. 18 K. FuriC, Chem. Phys. Lett., 1985, 117, 394. 19 N. Kirov and P. Simova, Spectrochim. Acra, Part A, 1973, 29, 55. 20 N. Imaoka, S. Takeda and H. Chihara, personal communication. 21 H. Budak, M. L. S. Garcia, I. C. Ewart, I. J. F. Poplett and J. A. S. Smith, J. Magn. Reson., 1979, 35, 309. 22 M. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids (Clarendon Press, Oxford, 1970). chap. 7. 23 D. Stephenson and J. A. S. Smith, J. Mol. Struct., 1983, 111, 43. 24 I. J. F. Poplett, Adv. Nucl. Quad. Res., 1980, 4, 155. 25 A. F. Volkov, Radiospektroscopiya, 1979, 12, 73. 26 R. B. Creel, H. R. Brooker and R. G. Barnes, J. Magn. Reson., 1980, 41, 146. 27 I. J. F. Poplett, M.Sabir and J. A. S. Smith, J. Chem. SOC.,Faraday Trans. 2, 1981, 77, 1651. 28 M. Suhara and J. A. S. Smith, J. Magn. Reson., 1982, 50, 237. 29 H. Chihara and N. Nakamura, Adu. Nucl. Quad. Res., 1980, 4, 1. 30 A. Novak, J. Chim. Phys. Phys.-Chim. Biol., 1975, 72, 981. 31 K. P. Brierley, J. Howard, C. J. Ludman, K. Robson and T. C. Waddington, Chem. Phys. Lett., 1978, 59, 467. 32 C. A. Fyfe, Solid Stare NMR for Chemists (CFC Press, Guelph, 1983). p. 417. 33 J. Seliger, V. Zagar and R. Blinc, J. Magn. Reson., 1984, 58, 359; Phys. Lett. A, 1983, 93, 149. 34 P. Salomaa, R. Hakala, A. Vesala, S. Vesala and T. Asalto, Acta Chem. Scand., 1969, 23, 2107. 35 Y. Pocker and D. W. Bjorkquist, J. Am. Chem. SOC.,1977, 99, 6537. 36 H. Feucht, U. Haeberlen, M. Pollak-Stachura and H. W. Spiess, Z. Naturforsch., Teil A, 1976,31, 1173. 37 T. Chiba, J. Chem. Phys., 1964, 41, 1352. 38 A. Achlama, J. Chem. Phys., 1981, 74, 3623. 39 B. Pedersen, Acta Crystallogr., 1968, 24, 478. 40 I. J. F. Poplett and J. A. S. Smith, J. Chem. Soc., Faraday Trans. 2, 1981, 77, 1155. 41 J. W. Emsley and J. A. S. Smith, Trahs. Faraday. SOC.,1961, 57, 1233. 42 K. Kume and Y. Kakiuchi, J. Phys. SOC. Jpn, 1960, 15, 1277. 43 I. J. F. Poplett and J. A. S. Smith, J. Chem. Soc., Faraday Trans. 2, 1979, 75, 1054. 44 T. Agaki, F. Imashiro, T. Terao, N. Hirota and S. Hayashi, Chem. Phys. Lett., 1987, 139, 331. Paper 8/02556H; Received 24th June, 1988

ISSN:0300-9238    

DOI:10.1039/F29898500053

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1989,85(l), 65-74 Rotamerism in 2,2'-Binaphthyl A Study based on Fluorescence Analysis and CS-INDO/CI Calculations Ivan Baraldi," Maria Cristina Bruni, Monica Caselli and Glauco Ponterini Dipartimento di Chimica, Universitd di Modena, Via Campi 183, 41 100 Modena, Italy The torsional isomerism of 2,2'-binaphthyl in the ground state and lowest excited singlet states has been investigated theoretically and experimentally. The combined results of a fluorescence steady-state and time-resolved analy- sis and of CS-INDO/CI calculations showed that this molecule exists in the ground state in two rotameric forms in which the naphthyls are rotated around the interconnecting quasi-single bond by different angles (4=35 and 145"). The absorption spectrum of 2,2'-binaphthyl was assigned and resolved into the individual spectra of the two rotamers.The fluorescence spectra, lifetimes and quantum yields of the two isomers at room temperature were also dkrived. The effects of solvent viscosity increase and of temperature decrease on the measured fluorescence lifetimes were found to be small. Lastly, a discussion of the rotational behaviour of this molecule as opposed to that of other biaryls is offered on the basis of the calculated torsional energy curves. Analysis of rotational isomerism in the ground and excited electronic states is a well established field of both experimental and theoretical investigation. In particular, fluorescence emission spectroscopy has been widely used to obtain information on the ground-state conformational equilibrium of diarylethylenes, 1,2 while the frequencies of the torsional progressions both in the ground and in some excited states, and hence the corresponding torsional potentials, have been provided by laser-spectroscopic studies of jet-cooled flexible m01ecules.~~~ As to the theoretical tools, CS-INDO' has proved a very efficient semiempirical method in the analysis of the ground-state conformations of p-, rn-and o-terphenyl," of the torsional potentials in the ground and lowest excited states of 1 ,l'-binaphthyl' and of some derivatives of 3,5-diphenylaminobenzene' and of the photoisomerization pathways of several styri1phenanthrenes2 and polymethine cyanines.' In molecules composed of v subsystems connected by essentially single bonds, the ground-state conformations arise from the competition between 7r-conjugation effects, which favour the planar forms, and steric hindrance which opposes planarization.Analysis of the ground-state torsional curves of the much-studied diarylethylenes shows that, in a series of compounds such as 1-naphthylethylene," 1-styrilnaphthalene,*' 1 -and 9-~tyrilphenanthrenes~ and 1,2'-dinaphthylethylene,'" which are characterized by the same type of short-range steric interactions in their planar forms, the features of the ground-state curves are roughly the same. This suggests that a change in the extension of the 7r-subsystems connected by the single bond produces minor effects on the curve shape. The same holds good through the series of the corresponding 2-naphthyl'" and 2-and 3-phenanthryl derivatives.2 If we assume that biaryls behave in the same way, i.e.that it is the type of short-range steric interactions which governs the shape of the ground-state torsional potential rather than the extension of the 7r-subsystems, then we may expect 2,2'-binaphthyl (2,2'-BN) to exhibit a torsional curve much more similar to that of biphenyl than to that of 1,l'-binaphthyl. The planar forms of the latter compound are very crowded, so that its ground-state torsional curve is characterized by a flat and 65 Rotamerism in 2,2'-Binaphthyl Scheme 1 wide potential well located around the perpendicular conformation and delimited by steep walls which prevent coplanarity.' On the other hand, biphenyl as well as 2,2'-BN are characterized in their planar forms by much less severe ortho- hydrogen interactions. As a result, the ground-state torsional curve of biphenyl is characterized by the presence of two equivalent partially rotated minima, corresponding to indistinguishable rotamers and by relatively small energy barriers at the planar forms (a CS-INDO calculation = 1.2 kcal m~l-',~ found 6,=35" and AE(O-350) while the experiment gave 6, =44.4" and AE(O-440)= 1.4 kcal mol-' ").As long as the analogy with biphenyl holds, we may expect the ground-state torsional curves of 2,2'-BN to exhibit two almost isoenergetic partially rotated minima corresponding to the two distinguishable rotamers of scheme 1. Analysis of this example of rotamerism is the subject of this paper.The investigation was carried out both experimentally and theoretically. Fluorescence steady-state and time-resolved experiments confirmed the predicted existence of two rotamers of 2,2'-BN in both fluid and rigid solvents, at room temperature and at 90K. The individual absorption and emission properties of the two rotamers were obtained, together with the ground-state relative abundances, from the classical analysis of ref. (12). Iden- tification of the experimentally observed rotamers with the predicted ones (scheme 1) is provided by CS-INDO/CI calculations, together with an assignment of the electronic spectrum of 2,2'-BN and a detailed description of the torsional potential curves of its ground and lowest excited singlet states.Experimental 2,2'-Binaphthyl (K&K Labs) was recrystallised twice from ethanol and benzene. Methanol (Merck, p.a.) was fractionally distilled. Both were checked for impurity emissions. The absorption spectrum was measured with a Beckman DU-8 spectro- photometer. The fluorescence spectra were measured with a Jobin Yvon JY3CS spectro-fluorimeter and corrected for the A dependence of the instrumental response. For the determination of the quantum yields, a-NPD in cyclohexane (q=0.7013) was used as a standard and the usual correction (l/n2) due to the refractive index variation was applied14 (sodium D-line refractive indices were used). Fluorescence-decay curves were obtained with an SP70 Applied Photophysics single-photon counting instrument inter- faced to an HP85 PC, and were analysed using a Fortran program running on VAX 750 and based on the least-squares iterative reconvolution technique" for a double-exponen- tial decay law.Good fitting parameters (x2)and residual distributions were obtained. Analysis of the results was performed following the procedure of ref. (12). The resolved fluorescence and absorption spectra of the two conformers were found not to depend on the excitation wavelengths used for the analysis. Low-temperature experiments were performed in a Thor C610 cryostat. All the samples were deaerated either by repeated freeze-pump-thaw cycles or by prolonged nitrogen bubbling.Computational Details The two naphthalenic moieties of 2,2'-BN were given the experimental geometry of naphtha1ene.l6 The interannular bond distance was assumed to be 1.50 A and the C-H I. Baraldi et al. bond lengths were 1.10 A. The CS-INDO/CI calculation procedure adopted for 2,2'-BN reproduces that which has yielded good results on the torsional potential of 1,l'-bina~hthyl.~The electron-repulsion integrals YAB were evaluated using the Mataga- Nishimoto f~rmula.'~ The configuration interaction was limited to the singly excited configurations built up by using the nine HOMOS and seven LUMOs. A rigid rotation around the naphthyl-naphthyl bond was carried out. Energies were calculated for the ground and the four lowest excited states at intervals of 30" between 4 = 0 and 180" and at 4 = 35 and 145".The calculated torsional potential-energy curves for the ground and three lowest singlet excited states were interpolated by the function V(+)=1/2 C",=, V, (1-cos n4).The corresponding Schrodinger equation was solved using the matrix method in the free-rotor representation." 80 cosine and 80 sine functions were chosen as the basis set. Results Fluorescence Analysis The fluorescence spectrum, quantum yield and decay of 2,2'-BN in methanol were measured at room temperature (20°C) and were found to depend on the excitation wavelength (Aexc). The A,,, dependence of the emission spectrum is illustrated in fig. l(a). Analysis of the changes of the shape of the fluorescence spectrum as A,,, is changed from 340 to 295nm shows that the total spectrum can be considered as the sum of two spectra characterized by maxima at 350 and 368 nm (emission A), and 355 and 373 nm (emission B).The relative contribution of emission A to the total spectrum is maximum at A,,, = 330-335 nm. The working hypothesis suggested by these observa- tions is that the two emissions belong to ground-state conformers of 2,2'-BN characterized by different absorption and fluorescence spectra. Since all the fluorescence spectra measured with A,,, in the range 295-340 nm show several isoemissive (*8%) wavelengths (353,359,372,381,390,404 nm), the analysis given in ref. (12) can be applied to 2,2'-BN to determine the individual absorption spectra and fluorescence properties of the two conformers.The fluorescence decays were observed at 353 nm, with A,,, between 265 and 343 nm. Deconvolution of the biexponential decays yielded the lifetimes reported in table 1 together with the fractions fA,B of the excited conformers as obtained from the decay parameters.12 The fraction of the shorter-lived excited conformer shows a Aexc depen-dence similar to that of emission A. We thus assign the shorter lifetime ( T = 22.2 ns) to the hypsochromically shifted A emission, and the longer lifetime ( T = 56.3 ns) to the bathochromically shifted B emission. This assignment is confirmed by the differential quenching of the B emission relative to the A emission observed in aerated solutions. Use of thefA andf, values at A,,, = 335 and 295 nm enabled the separate fluorescence spectra of the two conformers to be obtained [fig.l(b)]. Both spectra show a vibronic structure with peak separation of ca. 1400 cm-', probably due to a CC stretching vibration of the naphthalene skeleton." Emission A is hypsochromically shifted by ca. 400 cm-' with respect to emission B. Similarly to the procedure with the fluorescence spectrum, the absorption spectrum of 2,2'-BN in methanol in the region 265-340 nm was resolved into the spectra of the two conformers (fig. 2). The absorption of the shorter-lived A conformer prevails (fA >fB) at A S 275 nm and at A b325 nm. ?'he A conformer absorp- tion band is slightly bathochromically shifted (6-8 nm) relative to the B conformer band, so that its onset is located at a longer wavelength.Comparison of these features with the spectra calculated with the CS-INDO/CI procedure enables the nature of the A and B conformers to be identified (see the Discussion). Measurement of the total fluorescence quantum yield as a function of he,, (table 1) and application of the usual analysis'* gave the individual fluorescence quantum yields Rotamerism in 2,2’-Binaphthyl wavelength/nm a),Fig. 1. (a)Fluorescence spectra of 2,2’-BN in methanol. A,,, = 295 nm (-320 nm (-), 335 nm (---). The spectra are normalized to the same number of absorbed quanta. (b) Resolved fluorescence spectra of the conformers A (-) and B (---), as obtained from the analysis in ref. (12) and the fA and fB values at A,,, = 295 and 335 nm (see text).Table 1. Fluorescence lifetimes (T) and fractions (f)of the excited conformers, and total fluorescence quantum yield (ij) of 2,2’-BN in methanol as functions of the excitation wavelength TA/ns rB/ns fA fB 4 265 23.5 57.2 0.52 0.48 280 22.0 54.9 0.44 0.56 295 21.7 57.1 0.31 0.69 0.53 310 24.6 60.1 0.38 0.62 0.52 320 22.5 57.5 0.42 0.58 0.53 327 21.9 53.6 0.55 0.45 0.58 335 22.4 53.3 0.66 0.34 0.55 340 0.52 343 18.9 56.5 0.57 0.43 I. Baraldi et al. 30 20 10 0 260 300 340 wavelength/nm Fig. 2. Absorption spectrum of 2,2’-BN in methanol (-) and relative absorption spectra of the two conformers: eAcA/ctot (0);€BcB/ctot(a).The E values refer to the total spectrum and are taken from ref.(22). E~c~/c~~~was obtained by interpolation of the data points E (total spectrum)&; E~c*/ctot by subtraction of EBcB/ c,,, from the total spectrum. Table 2. Fluorescence lifetimes ( T)and quantum yields (q), radiative rate constants ( kF)and relative ground-state abund- ances of the two rotamers T/ns q kF/107s-’ c/ ctot A (‘cis’) 22.2 0.57 2.6 0.4 B (‘trans’) 56.3 0.50 0.9 0.6 qA=O.57 and qB=0.50. From these and the lifetimes, we obtained the radiative rate constants k,, = 2.6 x lo7 s-’ and kF,B= 0.9 x lo7s-’. A combination of these radiative rate constants with the relative absorption spectra’* yields an estimate of the fractions of the A and B conformers in the ground-state equilibrium mixture: A ctot=0.4,CB/Ctot = 0.6, corresponding to an enthalpy difference of ca.0.2 kcal mol- 9. Some of the individual properties of the two rotamers are listed in table 2. Finally, it must be stressed that the behaviour described, suggesting the existence of two distinct rotamers, is by no means limited to the room-temperature alcoholic solution. In fact, the emission spectrum of 2,2’-BN shows a dependence on Aexc similar to that of fig. 1(a) in room-temperature methylcyclohexane, 1:3 ethanol-glycerol and in 1: 1 ethanol-methanol at 90 K. Under the latter conditions, the fluorescence decays were still biexponential, but the lifetimes obtained from their deconvolutions showed a Rotametism in 2,2'-Binaphthyl 110 \ 105 I I ? I I I I I I \ \ \ t \ \ \ \ \ I1 \ 2'8 \ \ \ c I -i- 100 /0 / \ t t 0 \ 1 \ kl 95 1 0 -1 SO 180 Fig.3. Calculated potential-energy curves of the ground state and four lowest excited singlet states of 2,2'-BN as functions of the torsion angle around the internaphthyl bond (4). dependence on Aexc: rAranged from 17.7 to 28.9 ns and 78 from 64.0 to 92.9 ns as A,,, was changed from 340 to 320 nm. CS-INDO/CI Calculations So Torsional Curve The potential energies of the ground state and the four lowest excited singlet states of 2,2'-BN have been calculated as functions of the angle of torsion around the inter- annular bond and are shown in fig. 3. The ground 1 'A state features an almost symmetric double-minimum curve, with nearly isoenergetic minima at 4=35 and 145" and maxima at the perpendicular and planar conformations.The energy barriers preventing planariz- = 1.2 kcal mol-', AE(145-1800)ation [AE(3S-Oo) = 1.3 kcal mol-'1 are mainly due to the ortho-hydrogen steric hindrance, which is slightly larger in the s-cis (180O) than in the I. Baraldi et al. Table 3. Electronic spectrum of 2,2'-BN calculated at the So minimum-energy conformations calcd (4 =35") calcd (4 = 145") obsd AE/eV f AEIeV f AE/eV log &peak 2 'A 'Lb(+) 1 'B 'Lb(-) 2 'B 'La(-) 3 'A 'La(+) 4 'A 4.111 4.117 4.491 4.754 5.105 0.000 0.044 0.707 0.038 0.000 4.112 4.124 4.434 4.793 5.263 0.000 0.042 0.417 0.295 0.002 3.72 4.07 3.18 (sh) 4.28 3 'B 5.132 2.348 5.119 1.917 4.88 4.99 The experimental data are taken from ref.(22). s-trans (0') form, owing to the adoption of the actual naphthalenic geometry, similarly to the situation with 2-styrylnaphthalene. '' The potential-energy barrier separating the two minima (AE,,oo,= 1.7 kcal mol-' = 595 cm-') is sufficiently high to prevent free rotation at room temperature. These results show that the assumption made in the Introduction, i.e. that the torsional potential in ground-state 2,2'-BN does not differ very much from that of biphenyl, is sound. Our calculated ground-state equilibrium conforma- tions are in good agreement with a MIM calculation:' whereas a PPP study found +*in < A fitting of the calculated points of the ground-state torsional curve was performed with a six-term cosine potential function, and the corresponding Schrodinger equation was solved to obtain the torsional levels.The average separation between the lowest torsional levels was found to be ca. 40 cm-'. Electronic Spectrum The measured electronic absorption spectrum of 2,2'-BN2* differs sharply from that of naphthalene, a fact which clearly suggests that a large interaction between the 7r systems of the two naphthyl moieties occurs, contrary to what is observed in the case of 1, l'-BN,7y22 which is forced to assume a perpendicular minimum-interaction conforma- tion by very strong steric constraints. The six lowest S, +So transition energies and oscillator strengths have been calcu- lated at the two ground-state equilibrium conformations, and the results are reported in table 3 together with the corresponding experimental data.All the calculated transition energies are slightly overestimated (0.3-0.4 eV) relative to the experimental results. This hypsochromic shift may be imputed, at least in part, to the truncation of the CI expansion. It reduces further if we take into account that molecules are probably less twisted in solution than in the vapour phase. The first two excited states 2 'A and 1 'B are almost degenerate at both equilibrium- conformation angles. Analysis of their wavefunctions, carried out at + =90°, showed that they originate from the small splitting of the 'Lb states localized on the naphthalenic moieties.They derive from the out-of-phase (-) (1 'B) and in-phase (+) (2 'A) superposi- tions of the locally excited states.? Both states carry an additional CT contribution. The 2 'A +1 'A transition is forbidden, while the 1 'B +1 'A transition is responsible for the absorptiop shoulder observed around 3.72 eV (335 nm). The 2 'B and 3 'A states are of 'La(-) and 'La(+) type, respectively, since they derive from the out-of-phase and in-phase splittings of the localized 'La naphthalenic states. They also include CT t Details of the application of the exciton model to the electronic spectrum of a biaryl (1,l'-BN) are given in ref. (7). Rotamerism in 2,2'-Binaphthyl contributions. The 2 'B +,1 'A transition is responsible for the absorption band with a maximum at 4.07 eV (305 nm).It is stronger and shifted to higher energy for the trans-like conformer relative to the cis-like one. This fact has important experimental conse-quences, since it allows a partial photoselection of the cis-like conformer and will eventually lead to identification of the experimentally observed A and B conformers (see the Discussion). Finally, the strong absorption band with a maximum at 4.88 eV (254 nm),22 is assigned to the 3 'B +1 'A transition. Excited-state Torsional Curves The torsional potential-energy curves of the Lb type (2 'A and 1 'B) states (fig. 3) stay very close to each other at all 4 values and feature two nearly isoenergetic flat minima at 4 ==20-30"and 4 == 150-160", separated by barriers of ca.4.5 kcal molF'. The several curve crossings, allowed in C2symmetry, are removed by non-totally symmetric vibrations. The 2 'B [La(-)] state curve shows two well pronounced minima at the planar conformations, with the s-cis conformation being more stable than the s-trans =one by ca. 2 kcal mol-'. A high energy barrier ( AE(o-900, 11 kcal mol-') separates the two minima. The 3 'A ['La(+)] state curve has minima at 4 == 30" and 4 = 145" and crosses the 2 'B ['La( -)] curve at 4 = 90", where the exciton splitting is almost negligible. As a consequence of the described curve characteristics, the population of the three lowest singlet excited states will cause a substantial planarization of the molecule, which will be complete in the 2 'B ['La(-)] state.However, since the energy of this state remains well above the energies of the 2 'A and 1 'B ('Lb) states at all 4 angles, its photophysical role is expected not to be a prominent one, contrary to the situation with l,l'-BN7. Calculation of the torsional energy levels of the 2 'A, 1 'B and 2 'B excited states yielded a typical energy separation of 30-40 cm-', in agreement with the torsional frequencies observed in jet-cooled 9-(2-naphthyl)anthracene.' Discussion The fluorescence analysis of 2,2'-BN in solution and the CS-INDO/CI calculations on the isolated molecule provide a self-consistent set of results which demonstrate that 2,2'-BN exists at room-temperature as a mixture of comparable amounts of two rotamers, a trans-like one (# = 35") and a cis-like one (4==: 145").Both isomers still exist and exhibit their fluorescence properties at 90 K, a fact which clearly confirms their having very close ground-state energies. The identification of the experimentally observed rotamers with the theoretically predicted ones is based on the fact that, while the trans- and cis-like isomers have very similar 2 'A +1 'A and 1 'B +1 'A transition energies and oscillator strengths (table 3), the 2 'B ['La( -)] +1 'A transition of the cis-like rotamer is bathochromically shifted relative to the corresponding transition of the trans-like rotamer.? Thus, it should be possible to excite the cis-like conformer almost selectively by choosing excitation wavelengths at which the cis-like isomer shows the strong 2 'B +1 'A absorption, while the trans-like one can only undergo the much weaker 'L,+-'A transitions.This is indeed the interpretation that we propose for the described dependence of the fluores- cence spectrum of 2,2'-BN on A,,,. The observation that the relative contribution of emission A (the hypsochromically shifted emission) reaches a maximum at A,,, = 335 nm (onset of the La absorption band, see fig. 2 and table 1) and decreases with increasing excitation energies suggests that the experimentally observed A conformer can be identified as the cis-like one. t Such a behaviour is reminiscent of that of the 1 'B state of b~tadiene,~owing to the bond-order alternance in the naphthyls and to the absence of strong steric constraints preventing coplanarity of 2,2'-BN in the 'La(--} state.I. Baraldi et al. The 2 'B ['La(-)] state curve does not cross the 'Lb state curves at any value of 4. As a consequence, this state does not affect the photophysical behaviour of 2,2'-BN, which is thus expected to differ considerably from that of 1,l'-BN, whose torsional energy curve diagram is characterized by several crossings between the 'Lb-state curves and the curve of the low-lying 'La(-) state, which carries a large oscillator strength to the ground state.' Indeed, for 2,2'-BN we did not observe the dramatic dependence of the fluorescence spectrum and lifetimes on temperature and on solvent viscosity found for l,l'-BN.7 That the photophysical properties of the two rotamers of 2,2'-BN are completely determined by the pair of close-lying 'Lb states is confirmed by the comparable values of their fluorescence lifetimes and quantum yields (table 2).A basic condition for the experimental observability of the two rotamers (i.e. for the observation of a hexc-dependent fluorescence spectrum and of biexponential fluorescence decays) is that they do not interconvert in the fluorescent state so as to reach equilibration within their lifetimes. This amounts to saying that the interconversion rate constants of the two rotamers in the S1 states at room temperature must be much lower than the rate constants for the decay to the ground state, which are given by the reciprocals of the measured lifetimes: kA= TA' = 4.5 x lo7 s-'; kB= 7;' = 1.78 x lo7s-'. If, for the A-B interconversion processes, we assume frequency factors in the range 10'2-10'4s-', which are typical for spin-allowed processes, then we find that the energy barriers for the A-B isomerizations in the S1 states must be of the order of 7-9 kcal mol-', or larger.Our calculation gives barriers of only ca. 4.5 kcal mol-' for the S, states of the isolated 2,2'-BN molecule. Even though the isomerization barriers experienced by the molecule in solution certainly contain a contribution related to solvent viscosity, this cannot amount to 3-4 kcal mol-' in view of the low viscosity of the solvents employed." Thus, our calculation underestimates the potential-energy barriers on the 'Lb states.This may be due to the adoption of a rigid torsion and of a limited CI expansion (a CI extension is expected to stabilize the quasiplanar conformations, where interaction of the napthyl groups is large, relative to the perpendicular form). In conclusion, the combined analysis of the results of our fluorescence study and CS-INDO/CI calculations on 2,2'-BN shows that: (1) this molecule exists in the ground state as a mixture of similar amounts of trans-like (+ = 35") and cis-like (4 =r 145") rotamers, characterized by slightly different spectroscopic and photophysical properties; (2) electronic excitation causes a planarization of both rotamers, with preferential stabilization of the s-cis (A) form in the 2 'B ['La (-)I state (a fact which enables photoselection of this conformer); (3) the two rotamers do not equilibrate in the S1 state during their lifetimes; (4) the torsional frequencies are almost the same in the ground and three lowest excited states, despite the relevant changes in the shape of the torsional potentials experienced by the molecule following excitation.This shows that they are mainly determined by the reduced moment of inertia. The authors are grateful to Dr Barigelletti (FRAE-CNR Bologna) for allowing us to use his program for biexponential deconvolution of decay curves. Useful discussions with Prof. F. Momicchioli are warmly acknowledged. Mr M. Bandiera is thanked for his technical assistance. This work was supported by Minister0 della Pubblica Istruzione (Roma) and by the CICAIA (Universitii di Modena).References 1 For review articles, see: Yu. B. Scheck, N. P. Kovalenko and M. V. Alfimov, J. Lumin., 1977, 15, 157; E. Fischer, J. Photochem., 1981, 17,331; J. Mol. Struct., 1982,84,219; U. Mazzucato, Pure Appl. Chem., 1982, 54, 1705. 2 G. Bartocci, F. Masetti, U. Mazzucato, A. Spalletti, I. Baraldi and F. Momicchioli, J. Phys. Chem., 1987, 91, 4733. 3 D. W. Werst, A. M. Brearley, W. R. Gentry and P. F. Barbara, J. Am. Chem. SOC.,1987, 109, 32. Rotamerism in 2,2’-Binaphthyl 4 M. Ito, J. Phys. Chem., 1987, 91, 517. 5 F. Momicchioli, I. Baraldi and M. C. Bruni, Chem. Phys., 1983, 82, 229. 6 I. Baraldi and G. Ponterini, J. Mol. Struct. (Theochern.), 1985, 122, 287. 7 I. Baraldi, G. Ponterini and F.Momicchioli, J. Chem. Soc., Furuduy Trans. 2, 1987, 83, 2139. 8 W. Nowak and I. Baraldi, J. Mol. Srrucr. (Theochem.),1988, in press. 9 F. Momicchioli, I. Baraldi and G. Berthier, Chem. Phys., 1988, 123, 103. 10 I. Baraldi, F. Momicchioli and G. Ponterini, J. Mol. Strucr. (7’heochem.),1984, 110, 187. 11 A. Almenningen, 0. Bastiansen, L. Fernholt, B. N. Cyvin, S. J. Cyvin and S. Samdal, J. Mol. Struct., 1985, 128, 59. 12 J. B. Birks, G. Bartocci, G. G. Aloisi, S. Dellonte and F. Barigelletti, Chem. Phys., 1980, 51, 113. 13 I. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules (Academic Press, New York, 1971). 14 J. N. Demas and G. A. Crosby, J. Phys. Chem., 1971, 75, 991. 15 A. E. McKinnon, A. G. Szabo and D. R. Miller, J. Phys. Chem., 1977,81, 1564. 16 A. Almenningen, 0. Bastiansen and F. Dyvik, Actu Crystullogr., 1961, 14, 1056. 17 N. Mataga and K. Nishimoto, 2. Phys. Chem., 1957, 12, 335; 1957, 13, 140. 18 J. D. Lewis, T. B. Malloy Jr, T. H. Chao and J. Laane, J. Mol. Struct., 1972, 12, 427; J. D. Lewis and J. Laane, J. Mol. Spectrosc., 1977, 65, 147. 19 K. Ohno, J. Mol. Spectrosc., 1979, 77, 329. 20 A. Gamba, E. Rusconi and M. Simonetta, Tetrahedron, 1970, 26, 871. 21 B. Tinland, Theor. Chirn. Acta, 1968, 11, 385. 22 E. M. Layton Jr, J. Mol. Spectrosc., 1960,5, 181; R. A. Friedel, M. Orchin and L. Reggel, J. Am. Chem. SOC.,1948, 70, 199. Paper 8/02576B; Received 27th June, 1988

ISSN:0300-9238    

DOI:10.1039/F29898500065

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

High-temperature Photoelectron Spectroscopy A Study of SiS(X ?Z+) Martin C. R. Cockett, John M. Dyke,* Alan Morris and M. Hadi Zamanpour Niavaran Department of Chemistry, The University, Southampton SO9 5NH The He I photoelectron spectrum of SiS(X ‘Z+) has been recorded and interpreted with the aid of ab initio configuration interaction calculations. Five bands associated with this molecule were observed below 2 1eV ioniz- ation energy, whereas only three are expected on the basis of Koopmans’ theorem. Consequently, SiS represents an example of the breakdown of the one-electron ionization model, and the presence of five bands in the experi- mental spectrum is rationalised in terms of an ionic-state configuration interaction mechanism. Vibrational structure has been resolved in the first and third photoelectron bands and analysis of this structure leads to values of re, c3, and D, in the X ’n and B ’C+ states of SiS+.Silicon monosulphide (SiS) is an important interstellar molecule which is distinguished by the fact that it is composed of the two least abundant atoms observed in the interstellar medium. 1-3 Although it has been the subject of several spectroscopic inve~tigations,4-~ the p.e. spectrum of this molecule has not been recorded previously and no experimental measurements of its first ionization energy appear to have been made. However, some calculations have been carried out to obtain its valence ionization For ionization from the outermost (T and n occupied valence orbitals, vertical ionization energies have been computed as 9.79 and 10.73 eV using a Green’s function method,” and as 9.98 and 9.97 eV using a6 initio ASCF configuration interaction calculations.” Both types of calculations clearly indicate that the first two vertical ionizations of SiS lie close in energy, as is observed in the p.e.spectrum of the isoelectronic molecule GeO, where vertical ionization energies corresponding to ionization from the outermost u and 7~ molecular orbitals have been measured as 11.25 and 11.40eV, respectively.” In addition the Green’s function calculations on SiS in ref. (10) indicate the presence of extra bands in the p.e. spectrum at higher ionization energy which would be forbidden on the basis of one-electron ionization of the neutral molecule.Similar behaviour is known to occur in the He I p.e. spectrum of CS,13-17 a molecule which is valence- isoelectronic with SiS. In the case of CS, four p.e. bands are observed below 21 eV ionization energy, whereas only three are expected on the basis of Koopmans’ theorem. Also, the ordering of the first two vertical ionization energies differs from that obtained by application of Koopmans’ theorem to the results of a Hartree-Fock calculation on the neutral molecule. The aim of this work was to record the U.V. p.e. spectrum of SiS and to assign the observed bands using ab initio configuration interaction calculations. Clearly, the available evidence indicates that the lowest two ionic states of SiS are expected to be close in energy and that the one-electron model of ionization is probably inappropriate for this molecule, particularly at higher ionization energy.Experimental Two methods were used to produce SiS in the vapour phase. The first involved passing CS2 vapour over heated silicon in a molybdenum furnace at 1800 f50 K6 This route 75 High-temperature P.E.S. at SiS(X 'X+) gave reproducible SiS p.e. spectra, but resulted in serious contamination of the ionization chamber of the spectrometer, thus limiting the effective time during which acceptable spectra could be recorded. Consequently a second method of producing SiS in the vapour phase was used, which involved vaporising a 2: 1 Si(s)/SiS,(s) molar mixture at 1200 *50 K from a stainless-steel furnace.Initial heating of a Si(s)/SiS,(s) mixture to ca. 800 K gave rise to p.e. bands associated with SZ1*and H2S. These bands, however, disappeared before the temperature was reached at which SiS spectra were obtained. In practice the Si(s)/SiS,(s) route produced a more stable, longer-lasting SiS source which gave more intense SiS spectra than the CS,/Si(s) route with fewer overlapping bands and negligible contamination problems in the ionization chamber. As a result, the Si(s)/SiS2(s) method was chosen as the route used to obtain most of the SiS spectra recorded in this work, although the CS,/Si(s) source proved useful in that it helped to confirm the identification of bands associated with SiS in the Si( s)/SiS,(s) evaporations. The single-detector p.e.spectrometer and r.f. induction heating method used in this work have been described previously. 19920 Furnace temperatures at which spectra were recorded were measured by focussing a calibrated optical pyrometer onto the hottest part of the furnace. Calibration of the experimental spectra was achieved using the He I, (21.22eV) p.e. spectra of water, carbon monoxide and nitrogen. Under the experimental conditions used to obtain He I p.e. spectra of SiS, the operating resolution was 25-30 meV as measured for argon (f.w.h.m.). Computational Details The electronic ground state of SiS(X '2+)may be written as: From the known p.e. spectrum of CS13-17 and the computed ionization energies of SiS obtained by Green's function calculations," at least four bands are expected for SiS in the He I range.These can be approximately described by the processes (3n)-', (9a)-', (9a)-'( 3n)-' (47~)+'and (8~)~'. In this work single-determinantal a6 initio SCF calculations were performed for SiS(X 'Z+) and the SiS+ states produced by these processes, and ASCF vertical ionization energies were evaluated from the difference in the computed SCF total energy of the molecule and the ionic states considered. These total energies were corrected for the effects of electron correlation in each state via configuration interaction calculations. As well as the above ionic configurations a number of other SiS+ configurations were also considered. The results of these calculations are listed in table 1.Gaussian basis sets of double-zeta plus polarization quality" were used in the SCF calculations. These were [6s4p] with added d-polarization functions with exponents Si(0.39) .and S(0.54).22The SCF calculations were carried out using the ATMOL~suite of programs23 and the configuration interaction (CI) calculations used the ATMOL DIRECT-CI method.24 All single and double excitations were considered in the configur- ation interaction procedure with the constraint that the two lowest occupied molecular orbitals were held frozen. All calculations were performed at the experimental equilibrium bond length of SiS(X 'X+)of 1.9292 k4,9 For each ionic state the converged CI calculation was used to obtain a semiquantative estimate of the corresponding p.e.band intensity by summing the squares of formally allowed contributions to the final CI wavefunction. These sums are included in table 1. As well as these calculations on SiS, analogous calculations were performed on CS (see table 2) as the assignment of the U.V. p.e. spectrum of this molecule is well established. M. C. R. Cockett et al. 77 Table 1. Computed vertical ionization energies (Ei,,/eV) of SiS'"' Koopmans' Green's ionic reference theorem ASCF ASCF+ C1 E1.V function state configuration valueb Ei.v Ei,vC Z, cf (exptl) calculationsd x 2rI 8 a29a23 w3 10.60 9.44 10.06 0.90 10.56 10.73 [10.171' A 'Z+ 8a29a '3 .rr4 10.65 10.00 10.14 0.89 10.53 9.79 [10.121' B 'Z+ 8a'9u23w4 15.65 15.09 14.69 0.86 13.88 13.28 [13.611' C 'X+ 8a29u'3.rr34~' -15.29 17.21 0.56 16.91 15.52 D 'X+ 8a'9a23.rr34.rr' -21.62 20.39 0.02 18.93 20.72 E 2Cc+ 7~'8a~9~'31~~25.77 24.1 1 22.18 0.72 -21.60 a See text for details of the calculations.'This work. 'ASCF value plus allowance for correlation energy correction by configuration interaction calculations including all single and double excita- tions in each state (CISD) Ref. (10). 'Values in brackets are the computed vertical ionization energies obtained by application of Davidson's correctionz9 to the total energy of each state. This approximate correction was applied to the three lowest states of SiS+ and SiSX 'Z+ as the coefficient of the reference configuration in the CISD expansion was in each case greater than 0.88. Table 2. Computed vertical ionization energies (E,,,/eV) of CS" Koopmans' ionic reference theorem ASCF ASCF+ CI Ei,v &.VCstate configuration valueb Ei,v C Cf (exptl)d computed' x 'X+ 6a22.rr47a' 12.80 10.82 10.97 0.88 11.33 10.53 [10.87If A 'II 6a22.rr37a2 12.58 11.67 12.38 0.89 12.90 12.44 [12.471' B 2Z+ 6a22.rr37a'3.rr' -19.68 14.54 0.34 16.06 15.16 c 2Z+ 6a '2 .rr47 a2 18.81 18.02 17.54 0.85 18.03 17.46 (I See text for details of the calculations. 'This work." ASCF value plus allowance for correlation energy correction by configuration interaction calculations including all single and double excita- tions in each state. Ref. (15)-(17). Ref. (14). Values in brackets are the computed vertical ionization energies obtained by application of Davidson's correction (29) to the total energy of each state.This approximate correction was applied to the two lowest states of CS+ and CS X 'Z+ as the coefficient of the reference configuration in the CISD expansion was in each case greater than 0.93. Results and Discussion The He I p.e. spectrum recorded over the ionization energy range 10.0-18.0 eV from CS2passed over heated silicon is shown in fig. 1 (a). Five bands were observed in spectra recorded from the CS,/Si(s) method which were assigned to ionization of SiS. These bands were also observed from the Si(s)/SiS,(s) source [see fig. 1(6)], and their relative intensities were constant over a wide range of experimental conditions. The vertical ionization energies of these bands were measured as 10.53 f0.02, 10.56f0.02, 13.88f 0.02, 16.91f0.10 and 18.93*0.10eV, respectively. The 2ast two bands were very weak and were masked by bands associated with residual nitrogen.However, they were High-temperature P.E.S. at SiS(X I,+) N2100 n co (a)1 SiS I 1 c I m mU 33 I I I IC 18 17 16 15 14 13 12 11 10 Ei/eV SiS 30 /I SiS c I v) mU 18 I I I I I 1 I I 1 I I 19 18 17 16 15 14 13 12 11 10 EJeV Fig. 1. (a) He I p.e. spectrum obtained by passing CS2 over heated silicon at 1800k 50 K. (b) He I p.e. spectrum recorded from a Si(s): SiS,(s) 2: 1 molar mixture heated to 1200* 50 K. observed in spectra obtained from both preparative routes and hence have been assigned to ionization of SiS.By analogy with the known He I photoelectron spectrum of GeO,” and from the calculated vertical ionization energies shown in table 1, the first two bands of SiS are expected to be very close in ionization energy, with a sharp band corresponding to the outermost (7-l ionization overlapped by a broad band corresponding to the outermost T ionization. As can be seen from fig. 1 and 2, this proved to be the case. Fig. 2 M. C. R. Cockett et al. Fig. 2. He I pe. spectrum recorded in the 10.0-12.5 eV ionization energy region from a Si(s) : SiS,(s) 2: 1 molar mixture heated to 1200* 50 K. shows an expanded spectrum of the 10.0-12.7 eV ionization energy region, where a sharp band was observed at 10.53f 0.02 eV overlapped by a broad band. Unfortunately no vibrational structure could be identified associated with the band at 10.53 eV.In contrast the broad band in fig. 2, with adiabatic and vertical ionization energies of 10.38f 0.02 and 10.56 f 0.02 eV, exhibited clear vibrational structure. Measurement of the vibrational separations in this band led to a value of (3, = 700f 30 cm-' in the ionic state compared to (3, = 749.6 cm-' in SiS(X The observed decrease in vibrational constant (6,)on ionization is consistent with removal of an electron from the 37r bonding orbital in SiS and on the basis of this evidence and the calculations presented in table 1, this band is assigned to the SiS+(X 'n) +SiS(X 'C+) ionization. The band at 10.53 eV can then be assigned to the SiS+(A 2Z*) + SiS(X 'C+)ionization.As can be seen from fig. 2, two components were observed on the low-ionization- energy side of the first band which were assigned to ionization of vibrationally excited SiS. This assignment was made because the intensities of these features relative to the vibrational components at higher ionization energy were not constant over the range of experimental conditions used and their positions were not consistent with vibrational components associated with the SiS+(X 'II), vr+SiS(X '2,) v" = 0 series. In fact from the spectroscopic constants of SiS(X and the separation of these 'hot-band' features from the first adiabatic ionization energy, these components were assigned to the SiS+(X'II), zl' = 0 +SiS(X 'Z+), vr'= 2 and SiS+(X 'II), v' = 0 + SiS(X 'Z+), vr'= 1 ionizations.The third band of SiS, shown in fig. 3, has adiabatic and vertical ionization energies of 13.73 f 0.03 and 13.88 f 0.02 eV, respectively. This band exhibited resolved vibrational structure and measurement of the component separations gave (3, = 655 f30 cm-' in the corresponding ionic state, a value which is lower than 0,in the neutral molecule ground state. This result was initially somewhat surprising as the 80-molecular orbital in SiS is formally antibonding in character. However, a decrease in (3, on ionization has also been observed in both the third and fourth bands in the p.e. spectrum of CS."-" In the CS case the reduction of the vibrational constant, O,, on ionization may be ration- alised in terms of interaction between the configurations 6~~2~~70'3V' and 6u12r47u2 in both the B 2Z+ and C 2Zf ionic states.I4 In neutral CS, which can be represented as 6a227r47u23~0,the 27r and 7a molecular orbitals are formally bonding in character, 80 High-temperature P.E.S.at SiS(X 'Z+) 1 !h', IS 1L 13 12 E,/eV Fig. 3. He I p.e. spectrum recorded in the ionization energy region 12.5-16.0 eV, from a heated Si(s) :SiS,(s) 2 : 1 molar mixture at 1200 f50 K. whereas the 3~ and 6a molecular orbitals are antibonding. Hence although a (6~)~' ionization from neutral CS is expected to increase 6,in the ion, the (7~)-'(27r)-'(37r)+' process applied to neutral CS will lead to a reduction in 6,in the ionic state. On this basis, the observed reduction of 6,in the third band of SiS may well be symptomatic of a similar configuration interaction process.As in the first band of SiS(X 'X+),some evidence of ionization of the vibrationally excited neutral molecule was obtained from this band (see fig. 3), as one component was observed to the low-ionization-energy side of the adiabatic component which was not part of the main vibrational series. Two other bands associated with SiS were also observed at higher ionization energies (see fig. 4). Both bands were broad, weak and partially masked by nitrogen bands. Unfortunately no vibrational structure was resolved in these bands. Their band maxima were measured as 16.91f0.10 and 18.93f0.10 eV, respectively, and the corresponding band onsets were measured as 16.50f 0.10 and 18.37* 0.10 eV.In the case of the SiS bands which did show vibrational structure, it was possible to derive values of the ionic equilibrium bond length associated with each state by computing the vibrational envelopes at various trial ionic equilibrium bond lengths and comparing these with the experimentally observed envelope. Using experimental band envelopes which showed the smallest 'hot-band' contributions these Franck-Condon calculations led to a value of 2.05 f0.01 A for re in both the ground state and the second excited state of SiS'. Full details of the procedure used to obtain these bond lengths .have been described else~here.*~~~~ The dissociation energy (DG)in SiS+(X 'II) can be derived from the first adiabatic ionization energy of SiS(X 'E+) determined in this work.Assuming that SiS(X 'Z+) dissociates to Si(3P) and S(3P), and that SiS+(X 'n) dissociates to Si+(2P) and S(3P), the first adiabatic ionization energy of SiS(X 'Z+) of 10.38f0.03 eV can be combined with Dg of SiS(X 'X+)of 6.39f0.13 eV26 and the first ionization energy of Si(3P) of 8.15 eV" to give D: in SiS'(X 'n) of 4.16 k0.16 eV. An analogous calculation for the A 'Z+ state of SiS+ yields a value of DG of 4.01 * 0.16 eV. In the case of the third ionic state of SiS, it is difficult to derive a value for the dissociation energy as the dissociation products are not known. However, assuming that this state dissociates to Si+(*P) and S('S), the energetically most reasonable limit, then Dg can be derived as 3.56 * 0.16 eV for this state.The spectroscopic parameters derived for the first three states of SiS+ observed in this work are presented in table 3. As can be seen from fig. 2 and 3, some evidence of ionization from vibrationally excited SiS(X 'Z+) was obtained from the structure in the first and third bands. From spectra which showed maximum vibrational excitation, the relative intensities of the M. C. R. Cockett et al. n 01 I I I I I I 19 I8 17 16 15 11 Ei Fig. 4. He I p.e. spectrum recorded in the ionization energy region 14.0-19.5 eV, from a heated Si(s) :SiS2(s) 2 :1 molar mixture. Table 3. Physical constants of SiS+ derived in this work' electronic state Do/ eV re/ o,/ cm-' SiS X 'E+ 6.39f0.136 1 .9292'3d 749.6' SiS+ x 'II 4.16 f0.16 2.05 f0.01 700 f30 SiS+ A *Zf 4.01 f0.16 --SiS+ B *Z+ 3.56f0.16 2.05 f0.01 655 f30 a See text for details of how these parameters were obtained and the assignment of the SiS photoelectron bands.Ref. (26). Ref. (4). Ref. (9). u' =0 +-u" = 1 and u' =0 tu" =0 components were measured for each band and were combined with the corresponding computed Franck-Condon factors to derive a value of the vibrational temperature at the point of photoionization of 910*50 K. This is somewhat lower than the furnace temperature of 1200*20 K, indicating that some collisional deactivation of the SiS molecules between the furnace and the point of ionization had occurred. Similar behaviour has been observed in a p.e.s.study of AlF,28 a molecule which is isoelectronic with SiS. Although the assignment of the first two SiS photoelectron bands could be achieved relatively easily by comparison with p.e. spectra of valence-isoelectronic molecules where the assignment is well established, the assignment of the higher SiS bands could not be achieved in this way and reference had to be made to the results of the configuration interaction calculations shown in table 1. As stated earlier, analogous calculations were also performed on CS as this molecule provides a useful reference against which the results of the SiS calculations could be compared since the p.e. spectrum of CS has been studied in some detailI5-l7 and the assignment is well e~tab1ished.l~ In the CS case, the configuration interaction calculations show that in the neutral X 'X+ state, the 6u22.rr47a2configuration is the dominant configuration, whereas in the CS+ X 'X+ and A211states the configurations 60~2~~70' are the main contributors in and 60~27~~7~~ each case.The B 'Z+ and C 2C+ states of CS' cannot, however, be described in terms High-temperature I? E.S. at SiS(X 'Z+) of a single configuration and both contain significant contributions from the configur- ations 6a227r37a'37r'and 6u127r47u2.On the basis of the calculations performed in this work, which are summarised in table 2, an approximate assignment of the third CS band would be that it arises from a 70-' ionization followed by a 27r to 37r excitation.This gains intensity by an ionic state configuration interaction mechanism at the expense of the fourth band which formally arises from a 6u-'ionization. This explanation is in agreement with a previous assignment of the p.e. spectrum of CS13,14obtained from Green's function calculations. Similar behaviour was found in the configuration interac- tion calculations performed in this work for SiS+, in that the 'Z+ SiS+ states which lie in the region 3.0-10.0 eV above the SiS' ground state are best represented at the neutral equilibrium bond length in terms of a linear combination of a number of determinants rather than just by a single determinant. For example, the B 2Z+,C 'Z+ and D 'Z+ states listed in table 1 have appreciable contributions from the determinants,..8a19a237r4, . . . 8u29a'37r347r'and . . .8~'9u~3~~47r'.The third band can be viewed as an (8a)-' ionization, whereas the fourth and fifth bands can be thought of as a (9a)-' ionization plus a 37r --* 47r excitation and a (8a)-'ionization plus a 37~--* 4~ excitation, respec- tively. The fourth and fifth bands, although formally forbidden on the basis of a one-electron ionization selection rule, gain intensity through configuration interaction in the ionic states. In contrast to the 2Xc+states of SiS+, configuration interaction in the low-lying SiS' 211 states, at the neutral molecule equilibrium bond length, was found to be small and no 211ionic states are expected to contribute to the 11.O-21 .O eV ionization energy region of the experimental spectrum. The computed vertical ionization energies of SiS obtained in this work are summarised in table 1.Apart from the fifth ionic state, the values computed at the most sophisticated level of theory used, are all within 0.5 eV of the corresponding experimental values and allow unambiguous assignment of the five observed SiS photoelectron bands to be made. It is interesting that the ordering of the first two vertical ionization energies is incorrectly calculated at the ASCF level. It is also incorrectly computed when configuration interaction is allowed for in each state, at the single and double excitation level, although the computed separation of the vertical ionization energies is reduced. It is only when Davidson's for quadruple excitations is applied to each state that the correct ordering is obtained.Also, as can be seen from tables 1 and 2, in CS and SiS the experimental ordering of the first two vertical ionization energies differs from that obtained by application of Koopmans' theorem and in this respect CS and SiS behave like N2 rather than CO, with which they are valence-isoelectronic. In this present work, five electronic states of SiS+ have been observed for the first time. With this in mind it is instructive to look back at the spectroscopic studies that have been made on the low-lying electronic states of CS'. The p.e. spectrum of CS was recorded in 197215-" and within the next ten years spectroscopic studies were made of the CS+B 2Z+--* X 2Z+, B 2Z+---* A 211and A 'II -+X 2Zc+transition^.^'-^^ This led to an improvement in the spectroscopic constants and term values for the X, A and B states from those obtained in the earlier p.e.measurements. The p.e. data proved important in that they identified energy regions in which electronic emissions occur and the spectroscopic parameters derived from the p.e. measurements assisted in the assignment of the electronic emission spectra. In the case of SiS', the separation of the zeroth vibrational levels in the B 2Z.'-A 'Z+ and B 2Zc'-X 211 transitions are expected at 3.20* 0.05 and 3.35*0.05 eV, respectively, and it is hoped that this investigation of SiS by p.e. spectroscopy will stimulate further studies of the electronic states of SiS+ by higher-resolution spectroscopic methods.The authors gratefully acknowledge the S.E.R.C. for financial support for this research and a research studentship (to M.C.R.C.).M.H.Z.N. also thanks the Iranian government for support. M. C. R. Cockett et al. 83 References 1 A. P. C. Mann and D. A. Williams, Nature (London), 1970, 283, 721. 2 D. F. Dickinson and E. N. Rodriguez-Kuiper, Astrophys. J., 1981, 247, 112. 3 M. Morris, W. Gilmore, P. Palmer, B. 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ISSN:0300-9238    

DOI:10.1039/F29898500075

出版商:RSC    

年代:1989

数据来源: RSC