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Infrared bandshapes of intramolecularly H-bonded systems, 2,4,6-tribromophenol
CHEMICAL PHYSICS LETTERS
Volume 98, number 4
INFRARED BANDSHAPES OF INTRAMOLECULARLY
1 July 1983
H-BONDED SYSTEMS. 2,4,6-TRIBROhlOPHENOL
J.P. HAWRANEK and M_AA. BRODA Institute of Chemistry, University of Wrontaw. F. Joliot-Curie I4.50-383
Wroclnw. Poland
Received 29 April 1983
A detailed quantitative analysis of the IR bandshape of the vs(OH) vibration of 2,4,6+ribromophenol in a series of solvents of varying polarity is presented. A distinct dependence of band parameters on solvent polarity has been found. Various contributions to the bandshape are discussed.
1. Introduction Several theoretical [l-6] and experimental [7-91 studies of IR bandshapes of intermolecularly Hbonded systems have been carried out in recent years. Little attention has been paid to systems with intramolecular hydrogen bonds, although the spectral manifestations due to H-bond formation are not less spectacular in this case [lO,l l] _As for intermolecular systems, quantitative bandshape studies can be undertaken only for weak intramolecular H bonds, as for stronger ones the v,(AH) band assumes a complex form [lo,1 11. In this work we report results of a detailed bandshape analysis of the vs(OH) vibration in 2,4,6-tribromophenol (TBPh) in a series of solvents of varying polarity, with the aim of recognizing the role of various possible relaxation pathways as shaping mechanisms. A weak OH.._Br bond is present in the molecule; the solvents were selected in such a way as to prevent the breaking of this weak H bond and to avoid bifurcated interactions [ 121, which would obscure the results of the bandshape analysis.
2. Experimental The spectra were recorded with a Perkin-Elmer model 180 IR spectrophotometer. The scanning parameters were chosen in such a way as to avoid any possible mechanical, electronic and finite-slit-width distortions of the bandshape [13] _ The scan speed 0 009-2614/83/0000-OOOO/%
03.00 0 1983 North-Holland
did not exceed 5 cm-‘/min with a time constant of 1.5 s. The ratio of the spectral slit width to the halfwidth of the band was maintained well below 0.1 in all cases, thus reducing to a minimum the fmite-slitwidth distortion of the profile. The spectra were recorded in KBr cells of exactly known thicknesses in the double-beam mode, with the solvent in the reference beam. The baselines were computed by joining the flat ends of the wings with a straight line. Analytical grade 2,4,6-tribromophenol was further purified by sublimation. Good commercial grade solvents were purified and dried following standard methods and stored over freshly prepared molecular sieves. The concentration of solutions did not exceed 0.1 mole dme3, to avoid self-association of TBPh.
3. Processing of spectra The computational procedures used in bandshape analysis have been described [8,9,14,15] and only a short account is given here. The shape of the bands was analyzed in several ways. The experimental absorption curve was approximated by an asymmetric Cauchy-Gauss product function (with six adjustable parameters) [14], using a non-linear least-squares iterative procedure. This enables us to obtain profde indices, semi-half-widths, shape parameters and integrated intensities separately for both sides of the band. Independently, tie transition dipole moment autocorrelation functions were calculared from ex373
Volume 98,number4
CHEMICALPHYSICSLETTERS
lJuly1983
Table1 Bandshapeanalysis of the r+(OH) vibration of 2,4,6-tribromophenol Paraneter
Solvent C6H12
cc4
C, HClx
CHCi3
C6HSCI
CH2C12
CH2Br2
Ym (cm-r) 3517.0 i0.3 3514.3 kO.1 3510.6 kO.2 3508.5 +0.3 3501.9 50.1 3500.6 kO.1 3491.9 kO.1 1.50+0_01 1.44-co.o1 1.37%0.01 2.39?0.02 1.83~0.01 1.54*0.02 cmax(104 cm2 mol-') 3.6220.03 hh (cm-') 6.2 20.1 10.3 kO.1 11.9 20.1 13.9 20.1 16.6 to.1 17.8 kO.1 20.1 to.1 hy (c111-'~ 4.5 kO.1 9.0 20.1 14.7 20.1 18.2 20.2 19.5 kO.1 20.8 kO.1 25.1 50.2 bh+hc (cm-') 10.7 10.1 19.3 20.1 26.6 50.1 32.1% 0.1 36.1 20.2 38.6 20.1 45.2 +O.l L), (5) 83.5 10.8 68.6 50.5 66.2 -Cl_0 57.5 kO.5 58.6 20.6 54.6 ~2.0 50.4 22.0 Lc (5;) 95.8 11.5 80.8 +0.8 67.9 k1.0 64.2 +0_6 68.2 k1.2 61.8 21.7 62.4 k1.0 6.72t0.28 4.24+0.04 4_06+0.08 358t0.02 3.6310.03 3.4850.07 3.35AO.05 PZII 3.92kO.03 4.21*0.09 3.8250.02 9.41kO.09 5s98kO.19 4.:8+0.08 3.79io.09 P2P 131,(IO6 cmmol-*) 3.0520 07 2.89TO.01 2.5520.03 2.41~0.05 2.8220.02 2.89zO.06 3.0420.02 2.44?0.05 2.78+0.04 3.18kO.03 3.24+0.02 3.45~0.01 3.46kO.05 3.97+0.04 By (lo6 cmmot-‘) 5 (lo6 cm mol-‘) 5.49zo.10 5.6620.02 5.73~0.05 5.65+0.08 6.26+0.08 6.3.90.12 7.01+0.04 k, 0.80~0.01 0.97kO.02 1.24+0.01 1.34+0.01 1.23+0.01 1.20+0.01 1.31~0.01
perimental data according to standard formulas_ Fin.dly. the correlation times were calculated by numerical integration of the correlation functions.
5 ps; averaged values from six independent measurements are presented_ The mean deviations are quoted only to illustrate the reproducibility of the procedure; they are below the level of any physical significance_
4. Results
ci (t)I
In all solvents used in this study the vJOH) vibration of TBPh exhibits a single, smooth. structureless absorption band (not shown here). very suitable for bandshape analysis. The results of the analysis are given in table 1; the solvents are arranged in sequence of diminishing position of the band maximum, vrn _ The notation used in table 1 is as follows [15]: ema, is the molar extinction coefficient (decadic); b, and b, are the semi-half-widts of the high- and lowfrequency sides of the band. respectively; L, and L, dre the profile indices. &h and flzr the shape factors calculated from the second and fourth central moments:Bt,, B, and B denote the integrated intensities of the high- and low-frequency sides and the total intensity. respectively; k, is the asymmetry factor, given as the ratio of B, to Bl,. Mean deviations are quoted with the data, obtained from at least six measurements at various path lengths and concentrations_ The experimental correlation functions of the studied band are shown in fig. 1. In table 2 the correlation times are collected. obtained by numerical integration of the correlation functions in the limits O374
1
2
3
4 t[PSl
rj!+ 1. Experimental IR correlation functions for the ~&OH) ebmrion of 2,4,6tribromophanol:
Table 3 Analysis of the data using Buckingham’s relation
Table 2 Correlation times for the @OH) vibration of TBPh Solvent
PS
(IO”’
C6H12
cc4
C2HCl3 CHC13 CH2Ci2 C6HsCi CH2Be2
1 July 1983
CHEMICAL PHYSICS LETTERS
Volume 98, number 4
0 0 3.10 3.80 5.12 5.18 6.24
Solvent
f(a)
f(n)
“talc-vobs (cm-‘)
C6H12
0.2018 0.2251 0.3087 0.3564 0.4217 0.3775 0.4032
0.2030 0.2144 0.2197 0.2096 0.2023 0.2337 0.2385
2.1 0.4 -3.4 -2.2 1.4 -2.0 3.7
Cm) &I 1.126 0.693 0.533 0.452 0.395 0.378 0.326
2 0.01 * 0.004 + 0.003 + 0.001 f 0.002 + 0.003 f 0.002
cc4
C2 HC13 CHC13 CH2C12 C6HSCl CH2 Br2
cm ml _ The constantsa,
5. Discussion
The OH group in the TBPh molecule is practically totally H bonded via intramolecular OH...Br bonds; no equilibrium between the “free” and “bonded” OH group is visible, as only one band is observed in the vs(OH) region, shifted to ~3500 cm-l (table 1). In the series of solvents of increasing polarity, the decrease of band maximum position, vrn, is accompanied with a marked decrease of the molar extinction coefficient, Emax, and a distinct increase in half-width, ZQ + br; the integrated intensity increases only slightly_ In parallel with these changes a marked decrease of the lorentzian character of the profile takes place; this can be seen from the profile indices Lh and L, and shape factors &, and f12n, which shift gradually
Gj#
= G(t) @)G(‘)
orientation bandshape;
polarity of the solvent seem to indicate that the electrostatic interactions between the protonic dipole and the random local field set up by the internal modes of the solvent are of importance here [ 1.2]_ In this respect, it was interesting to find that the frequency shifts do not obey either the KBM plot [ 161 or the Bayliss relationship [ 161, but a very good fit to the Buckingbarn relation [ 173
can be obtained, with the following parameters: n = 3585.94 cm-l, b = -73.51 cm-l and c = -255.07
l.rot(*)
(2)
-
(1)
it can hardly be expected
that re-
of the molecule will contribute to the the correlation times are far too short
(table 2) to justify such a contribution; additional support is obtained for this conclusion from dielectric relaxation studies of similar molecules [19] _Furtbermore, there is no proportionality between Av1/2 and which would be expected in the case of a domiq-l, nant reorientational contribution. Thus it is reasonable to assume that Gy)rot(f) =Z 1 in the time scale considered and that the obierved decay of GIR(f) is entirely due to vibrational dephasing. The question arises which of the components of the intermolecular potential contributes most to the dephasing process. This will be discussed elsewhere for these and similar systems; we note here that, in agreement with the theoretical
+ 1)
via
In the systems studied, with TB?h being a heavy and
that, the band is distinctly more intense and more lorentzian on the low-frequency side. The distinct and systematic changes of the spectral parameters of the studied v,(OH) baud with the
1) + c(n2 - 1)/(2G
vlb
bulky molecule,
to lower values, indicating a more gaussian profile with increasing polarity of the solvent. Apart from
vm = Q + b(E - 1)/(2e+
b and c were determined
a least-squares analysis of the experimental data; the results are presented in table 3. In parallel to the effects discussed above, the decay of the correlation functions becomes faster with increasing polarity of the solvents (fig. 1); correspondingly, the correlation times diminish (table 2). As is well known, the overall IR correlation function for a non-degenerate normal mode i of a polyatomic molecule, neglecting the correlation between vibration and reorientation, is given by [18]
considerations
of Lynden-Bell
[20],
a fair
linear correlation between tF1 and I.(s2us is the dipolt moment of the solvent molecule) is observed (except for C6Hl2),
indicating that dipole-dipole
tions play an important
interac-
role in these systems. Thus 375
Volume 98. number 4
CHEMICAL PHYSICS LETTERS
dephasing due to the coupling of the fluctuating local electric field set up by solvent molecules with the protonic dipole seems to be the main relaxation pathway_
Acknowledgement The authors are indebted to Mrs. B. CzarnikMatusewicz for her help with the processing of spectra and to Professor L. Sobczyk and Professor G. Zundel for helpful discussions. This work was supported by the Polish Academy of Sciences under the MR.I.9 plan.
References ill
R. Janoschek, E.G. Weidemann and G. Zundel. J. Chem. Sot. Faraday 1169 (1973) 505.
121 N. Rdsch and MA. Ratner, J. Chem. Phys. 61 (1974) 3344.
131 S. Bratos. J Chem. Phys 63 (1975) 3499. L4I II. Rom.mowski and L. Sobczyk. Chem. Phys. 19
(1977) 361; Acfn Phys. Pal. A60 (1981) 545. I51 G.N. Robsrtson and J. Yar\rood, Chem. Phys. 32 (1978)
267.
376
1 July 1983
[6] W_P. S&on, Chem. Phys. 55 (1981) 27. [ 7 ] J. Yarwood, R. Acroyd and G-N. Robertson, Chem. Phys. 32 (1978) 283. [S] J.P. Hawranek and T. Gostyr%ka. Acta Phys. Pal. A57 (1980) 901. [9] B. Czarnik-hMwmvicz and J.P. Ha-ek, Acta Phys. Pol. A63 (1981) 555. [lo] A. Sucharda-Sobczyk and L. Sobczyk, Bull. Acad. Pol. Sci. Ser. Sci. Chim. 26 (1978) 549. [ 111 B. Brzezinski and G. Zundel, Can. J. Chem. 59 (1981) 786; J. hlol. Struct. 72 (1981) 9; J. Phys. Chem. 86 (1982) 5133, and references therein. [ 12 ] Z. hlalarski, Advan. Mol. Relaxation Interaction Processes 11 (1977) 43. 1131 K.S. Seshadri and R.N. Jones, Spectrochim. Acta 19 (1963) 1013. [I41 J.P. Hawranek, Acta Phys. PoL A40 (1971) 811. [IS] J.P. Hawranek and R. Szostak, Acta Phys. PoL A60 (1981) 407. [ 161 H.E. Ha&m, in: Infrared spectroscopy and molecular structure, ed. hl. Davies (Elsevier. Amsterdam, 1963) p. 421. [17] A.D. Buckingham. Proc. Roy. Sot. A248 (1958) 169; Trans. Faraday Sot. 56 (1960) 753. [18] J.C. Leicknam, Y. Guissani and S. Bratos, J. Chem. Phys. 68 (1978) 3380. [ 19) M.D. hlagee and S. Walker, Trans. Faraday Sot. 62 (1966) 1748. [ZO] R.M. Lynden-Bell, (1978) 1529.
Mol. Phys. 33 (1977)
907; 36
Volume 98, number 4
INFRARED BANDSHAPES OF INTRAMOLECULARLY
1 July 1983
H-BONDED SYSTEMS. 2,4,6-TRIBROhlOPHENOL
J.P. HAWRANEK and M_AA. BRODA Institute of Chemistry, University of Wrontaw. F. Joliot-Curie I4.50-383
Wroclnw. Poland
Received 29 April 1983
A detailed quantitative analysis of the IR bandshape of the vs(OH) vibration of 2,4,6+ribromophenol in a series of solvents of varying polarity is presented. A distinct dependence of band parameters on solvent polarity has been found. Various contributions to the bandshape are discussed.
1. Introduction Several theoretical [l-6] and experimental [7-91 studies of IR bandshapes of intermolecularly Hbonded systems have been carried out in recent years. Little attention has been paid to systems with intramolecular hydrogen bonds, although the spectral manifestations due to H-bond formation are not less spectacular in this case [lO,l l] _As for intermolecular systems, quantitative bandshape studies can be undertaken only for weak intramolecular H bonds, as for stronger ones the v,(AH) band assumes a complex form [lo,1 11. In this work we report results of a detailed bandshape analysis of the vs(OH) vibration in 2,4,6-tribromophenol (TBPh) in a series of solvents of varying polarity, with the aim of recognizing the role of various possible relaxation pathways as shaping mechanisms. A weak OH.._Br bond is present in the molecule; the solvents were selected in such a way as to prevent the breaking of this weak H bond and to avoid bifurcated interactions [ 121, which would obscure the results of the bandshape analysis.
2. Experimental The spectra were recorded with a Perkin-Elmer model 180 IR spectrophotometer. The scanning parameters were chosen in such a way as to avoid any possible mechanical, electronic and finite-slit-width distortions of the bandshape [13] _ The scan speed 0 009-2614/83/0000-OOOO/%
03.00 0 1983 North-Holland
did not exceed 5 cm-‘/min with a time constant of 1.5 s. The ratio of the spectral slit width to the halfwidth of the band was maintained well below 0.1 in all cases, thus reducing to a minimum the fmite-slitwidth distortion of the profile. The spectra were recorded in KBr cells of exactly known thicknesses in the double-beam mode, with the solvent in the reference beam. The baselines were computed by joining the flat ends of the wings with a straight line. Analytical grade 2,4,6-tribromophenol was further purified by sublimation. Good commercial grade solvents were purified and dried following standard methods and stored over freshly prepared molecular sieves. The concentration of solutions did not exceed 0.1 mole dme3, to avoid self-association of TBPh.
3. Processing of spectra The computational procedures used in bandshape analysis have been described [8,9,14,15] and only a short account is given here. The shape of the bands was analyzed in several ways. The experimental absorption curve was approximated by an asymmetric Cauchy-Gauss product function (with six adjustable parameters) [14], using a non-linear least-squares iterative procedure. This enables us to obtain profde indices, semi-half-widths, shape parameters and integrated intensities separately for both sides of the band. Independently, tie transition dipole moment autocorrelation functions were calculared from ex373
Volume 98,number4
CHEMICALPHYSICSLETTERS
lJuly1983
Table1 Bandshapeanalysis of the r+(OH) vibration of 2,4,6-tribromophenol Paraneter
Solvent C6H12
cc4
C, HClx
CHCi3
C6HSCI
CH2C12
CH2Br2
Ym (cm-r) 3517.0 i0.3 3514.3 kO.1 3510.6 kO.2 3508.5 +0.3 3501.9 50.1 3500.6 kO.1 3491.9 kO.1 1.50+0_01 1.44-co.o1 1.37%0.01 2.39?0.02 1.83~0.01 1.54*0.02 cmax(104 cm2 mol-') 3.6220.03 hh (cm-') 6.2 20.1 10.3 kO.1 11.9 20.1 13.9 20.1 16.6 to.1 17.8 kO.1 20.1 to.1 hy (c111-'~ 4.5 kO.1 9.0 20.1 14.7 20.1 18.2 20.2 19.5 kO.1 20.8 kO.1 25.1 50.2 bh+hc (cm-') 10.7 10.1 19.3 20.1 26.6 50.1 32.1% 0.1 36.1 20.2 38.6 20.1 45.2 +O.l L), (5) 83.5 10.8 68.6 50.5 66.2 -Cl_0 57.5 kO.5 58.6 20.6 54.6 ~2.0 50.4 22.0 Lc (5;) 95.8 11.5 80.8 +0.8 67.9 k1.0 64.2 +0_6 68.2 k1.2 61.8 21.7 62.4 k1.0 6.72t0.28 4.24+0.04 4_06+0.08 358t0.02 3.6310.03 3.4850.07 3.35AO.05 PZII 3.92kO.03 4.21*0.09 3.8250.02 9.41kO.09 5s98kO.19 4.:8+0.08 3.79io.09 P2P 131,(IO6 cmmol-*) 3.0520 07 2.89TO.01 2.5520.03 2.41~0.05 2.8220.02 2.89zO.06 3.0420.02 2.44?0.05 2.78+0.04 3.18kO.03 3.24+0.02 3.45~0.01 3.46kO.05 3.97+0.04 By (lo6 cmmot-‘) 5 (lo6 cm mol-‘) 5.49zo.10 5.6620.02 5.73~0.05 5.65+0.08 6.26+0.08 6.3.90.12 7.01+0.04 k, 0.80~0.01 0.97kO.02 1.24+0.01 1.34+0.01 1.23+0.01 1.20+0.01 1.31~0.01
perimental data according to standard formulas_ Fin.dly. the correlation times were calculated by numerical integration of the correlation functions.
5 ps; averaged values from six independent measurements are presented_ The mean deviations are quoted only to illustrate the reproducibility of the procedure; they are below the level of any physical significance_
4. Results
ci (t)I
In all solvents used in this study the vJOH) vibration of TBPh exhibits a single, smooth. structureless absorption band (not shown here). very suitable for bandshape analysis. The results of the analysis are given in table 1; the solvents are arranged in sequence of diminishing position of the band maximum, vrn _ The notation used in table 1 is as follows [15]: ema, is the molar extinction coefficient (decadic); b, and b, are the semi-half-widts of the high- and lowfrequency sides of the band. respectively; L, and L, dre the profile indices. &h and flzr the shape factors calculated from the second and fourth central moments:Bt,, B, and B denote the integrated intensities of the high- and low-frequency sides and the total intensity. respectively; k, is the asymmetry factor, given as the ratio of B, to Bl,. Mean deviations are quoted with the data, obtained from at least six measurements at various path lengths and concentrations_ The experimental correlation functions of the studied band are shown in fig. 1. In table 2 the correlation times are collected. obtained by numerical integration of the correlation functions in the limits O374
1
2
3
4 t[PSl
rj!+ 1. Experimental IR correlation functions for the ~&OH) ebmrion of 2,4,6tribromophanol:
Table 3 Analysis of the data using Buckingham’s relation
Table 2 Correlation times for the @OH) vibration of TBPh Solvent
PS
(IO”’
C6H12
cc4
C2HCl3 CHC13 CH2Ci2 C6HsCi CH2Be2
1 July 1983
CHEMICAL PHYSICS LETTERS
Volume 98, number 4
0 0 3.10 3.80 5.12 5.18 6.24
Solvent
f(a)
f(n)
“talc-vobs (cm-‘)
C6H12
0.2018 0.2251 0.3087 0.3564 0.4217 0.3775 0.4032
0.2030 0.2144 0.2197 0.2096 0.2023 0.2337 0.2385
2.1 0.4 -3.4 -2.2 1.4 -2.0 3.7
Cm) &I 1.126 0.693 0.533 0.452 0.395 0.378 0.326
2 0.01 * 0.004 + 0.003 + 0.001 f 0.002 + 0.003 f 0.002
cc4
C2 HC13 CHC13 CH2C12 C6HSCl CH2 Br2
cm ml _ The constantsa,
5. Discussion
The OH group in the TBPh molecule is practically totally H bonded via intramolecular OH...Br bonds; no equilibrium between the “free” and “bonded” OH group is visible, as only one band is observed in the vs(OH) region, shifted to ~3500 cm-l (table 1). In the series of solvents of increasing polarity, the decrease of band maximum position, vrn, is accompanied with a marked decrease of the molar extinction coefficient, Emax, and a distinct increase in half-width, ZQ + br; the integrated intensity increases only slightly_ In parallel with these changes a marked decrease of the lorentzian character of the profile takes place; this can be seen from the profile indices Lh and L, and shape factors &, and f12n, which shift gradually
Gj#
= G(t) @)G(‘)
orientation bandshape;
polarity of the solvent seem to indicate that the electrostatic interactions between the protonic dipole and the random local field set up by the internal modes of the solvent are of importance here [ 1.2]_ In this respect, it was interesting to find that the frequency shifts do not obey either the KBM plot [ 161 or the Bayliss relationship [ 161, but a very good fit to the Buckingbarn relation [ 173
can be obtained, with the following parameters: n = 3585.94 cm-l, b = -73.51 cm-l and c = -255.07
l.rot(*)
(2)
-
(1)
it can hardly be expected
that re-
of the molecule will contribute to the the correlation times are far too short
(table 2) to justify such a contribution; additional support is obtained for this conclusion from dielectric relaxation studies of similar molecules [19] _Furtbermore, there is no proportionality between Av1/2 and which would be expected in the case of a domiq-l, nant reorientational contribution. Thus it is reasonable to assume that Gy)rot(f) =Z 1 in the time scale considered and that the obierved decay of GIR(f) is entirely due to vibrational dephasing. The question arises which of the components of the intermolecular potential contributes most to the dephasing process. This will be discussed elsewhere for these and similar systems; we note here that, in agreement with the theoretical
+ 1)
via
In the systems studied, with TB?h being a heavy and
that, the band is distinctly more intense and more lorentzian on the low-frequency side. The distinct and systematic changes of the spectral parameters of the studied v,(OH) baud with the
1) + c(n2 - 1)/(2G
vlb
bulky molecule,
to lower values, indicating a more gaussian profile with increasing polarity of the solvent. Apart from
vm = Q + b(E - 1)/(2e+
b and c were determined
a least-squares analysis of the experimental data; the results are presented in table 3. In parallel to the effects discussed above, the decay of the correlation functions becomes faster with increasing polarity of the solvents (fig. 1); correspondingly, the correlation times diminish (table 2). As is well known, the overall IR correlation function for a non-degenerate normal mode i of a polyatomic molecule, neglecting the correlation between vibration and reorientation, is given by [18]
considerations
of Lynden-Bell
[20],
a fair
linear correlation between tF1 and I.(s2us is the dipolt moment of the solvent molecule) is observed (except for C6Hl2),
indicating that dipole-dipole
tions play an important
interac-
role in these systems. Thus 375
Volume 98. number 4
CHEMICAL PHYSICS LETTERS
dephasing due to the coupling of the fluctuating local electric field set up by solvent molecules with the protonic dipole seems to be the main relaxation pathway_
Acknowledgement The authors are indebted to Mrs. B. CzarnikMatusewicz for her help with the processing of spectra and to Professor L. Sobczyk and Professor G. Zundel for helpful discussions. This work was supported by the Polish Academy of Sciences under the MR.I.9 plan.
References ill
R. Janoschek, E.G. Weidemann and G. Zundel. J. Chem. Sot. Faraday 1169 (1973) 505.
121 N. Rdsch and MA. Ratner, J. Chem. Phys. 61 (1974) 3344.
131 S. Bratos. J Chem. Phys 63 (1975) 3499. L4I II. Rom.mowski and L. Sobczyk. Chem. Phys. 19
(1977) 361; Acfn Phys. Pal. A60 (1981) 545. I51 G.N. Robsrtson and J. Yar\rood, Chem. Phys. 32 (1978)
267.
376
1 July 1983
[6] W_P. S&on, Chem. Phys. 55 (1981) 27. [ 7 ] J. Yarwood, R. Acroyd and G-N. Robertson, Chem. Phys. 32 (1978) 283. [S] J.P. Hawranek and T. Gostyr%ka. Acta Phys. Pal. A57 (1980) 901. [9] B. Czarnik-hMwmvicz and J.P. Ha-ek, Acta Phys. Pol. A63 (1981) 555. [lo] A. Sucharda-Sobczyk and L. Sobczyk, Bull. Acad. Pol. Sci. Ser. Sci. Chim. 26 (1978) 549. [ 111 B. Brzezinski and G. Zundel, Can. J. Chem. 59 (1981) 786; J. hlol. Struct. 72 (1981) 9; J. Phys. Chem. 86 (1982) 5133, and references therein. [ 12 ] Z. hlalarski, Advan. Mol. Relaxation Interaction Processes 11 (1977) 43. 1131 K.S. Seshadri and R.N. Jones, Spectrochim. Acta 19 (1963) 1013. [I41 J.P. Hawranek, Acta Phys. PoL A40 (1971) 811. [IS] J.P. Hawranek and R. Szostak, Acta Phys. PoL A60 (1981) 407. [ 161 H.E. Ha&m, in: Infrared spectroscopy and molecular structure, ed. hl. Davies (Elsevier. Amsterdam, 1963) p. 421. [17] A.D. Buckingham. Proc. Roy. Sot. A248 (1958) 169; Trans. Faraday Sot. 56 (1960) 753. [18] J.C. Leicknam, Y. Guissani and S. Bratos, J. Chem. Phys. 68 (1978) 3380. [ 19) M.D. hlagee and S. Walker, Trans. Faraday Sot. 62 (1966) 1748. [ZO] R.M. Lynden-Bell, (1978) 1529.
Mol. Phys. 33 (1977)
907; 36