J. Phys. Chem. 1994,98, 424-428
424
Vibrational Dephasing of Axial and Equatorial Conformers in Cyclohexyl Halides H. Abramczyk' and M. Barut Technical University. Institute of Applied Radiation Chemistry, 93-590 Lodz, Wroblewskiego 15. Poland
A. Ben Altabef Universidad Nacional de Tucuman, Facultad de Bioquimica, Quimica y Farmacia, San Lorenzo, 456-4000-San Miquel de Tucuman, Argentina
R. Escribano Cosejo Superior de Inuestigaciones Cientifcas, Instituto de Estructura de la Materia, 28006 Madrid, Calle Serrano 11 9- 123, Spain Received: July 7, 1993'
The Raman and I R spectra of the C-X stretching modes (X = C1, Br, I) in the axial and the equatorial positions of cyclohexyl halides have been measured at room temperature. The band broadening mechanisms and the differences in the rate of vibrational dephasing of the axial and the equatorial conformers have been discussed. It has been found that intermolecular long-range transition dipoletransition dipole coupling gives the main contribution to the differences in vibrational dephasing rate. This paper demonstrates that a simultaneous study of the vibrational dephasing of different conformers provides a method to isolate the individual relaxation mechanisms.
SCHEME 1
1. Introduction
U
Thevibrational dephasing in molecular liquids occurs according to a variety of relaxation mechanisms. Although significant theoretical advances in the vibrational dephasing in liquids have been made in recent years, it is very difficult to separate individual relaxation channels. The dilution in nonpolar solvents, the isotopic dilution, temperature, pressure, and density effects have been used to provide insight in dephasing dynamics. Important information about dephasing can be obtained from experiment for conformationally mobile systems.'-3 In nonrigid molecules an oscillator is perturbed not only by the environment but also by intramoleculr interactions, which are modulated with time by internal molecular motions of the molecule. The simultaneous observation of dephasing dynamics of different conformers can provide a powerful method to isolate the individual relaxation channels. In this paper we will concentrate on the conformationally mobile derivatives of cyclohexane with conformational equilibrium l a l b between axial (la) and an equatorial (lb) forms given in Scheme 1, where X = C1, Br, or I.
Raman bandwidths were obtained using the Marquardt leastsquares fit procedure assuming one Lorentz line shape function for each conformer. The uncertainties of the experimental bandwidths are estimated to be 0.5 cm-'. The vibrational correlation functions $V(t) were obtained using the usual procedure4 by applying
2. Experimental Section
where I h ( w ) is the normalized Raman isotropic band profile. The vibrational correlation times were calculated as
-
Spectrograde chlorocyclohexane, bromocyclohexane, and iodocyclohexane (Merck) were used without further purification. Raman spectra in neat cyclohexanes were measured with a Ramanor UlOOO (Jobin Yvon) at room temperature. A Spectra Physics 2017 argon-ion laser operating at 514 nm with a power of 300 mW was used as the excitation source. The slit opening of the monochromator corresponds to a spectral slit width of 1 cm-I. The IR spectra were measured with a Nicolet FTIR spectrophotometer 60 SX at a resolution of 1 cm-1 in neat cyclohexanes andataconcentrationof6.5 X 10-3mol/LinCS2. Thethicknesses of the cuvettes were 0.002 and 0.574 cm, respectively. The stretching modes C-X, where X = CI, Br, I, have been measured for the axial (la) and theequatorial (lb) forms. They are observed in the range 650-760 cm-1, and the bands of the axial and the equatorial forms are well separated. The IR and Abstract published in Aduance ACS Abstracts, December 1, 1993.
la
lb
where IIR(W)is the normalized IR absorption band profile, or
3. Results
The Raman and IR spectra of the axial ( l a ) and the equatorial ( l b ) conformers of bromocyclohexane at room temperature are depicted in Figure 1. The maximum peak positions E"& and the bandwidths FQ of the axial and the equatorial conformers in cyclohexyl halides are given in Table 1. As we can see from Table 1, the most striking effect is the difference in dynamics of the axial and the equatorial conformers for all the cyclohexyl halides. Indeed, we observethe remarkable differencein the bandwidths of the axial and the equatorial conformers both in Raman and IR spectra in neat solutes. These differences nearly disappear at low concentration, and the bandwidths become similar in nonpolar solvent CS2. This trend is supported by the time
0022-3654/94/209~-0424~04.50/0 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 425
Vibrational Dephasing of Conformers
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Figwe 1. IR absorption and Raman spectra of the axial (la) and equatorial (lb) conformers in bromocyclohexane at room temperature: (a) Raman in neat bromocyclohexane, (b) IR in neat bromocyclohexane, (c) IR bromocyclohexanc at concentration 6.5 X mol/L in CSz, (d) Raman in neat iodocydohe xane, (e) IR in neat iodocyclohexane, (0 IR iodocyclohexane at concentration 6.5 X l e 3 mol/L in CS2.
TABLE 1: Maximum Peak Positions W & and the BdMtb (fwhh) Of the A f i (8X) and Equatorial (eq)Codormerb of Cyclobexyl Halides by IR and Ramn Measurements
w$
~~
Raman (neat) ax C1-cyclohexane Br-cyclohexane I-cyclohexane
684.8 658.1 639.0
Cl-cyclohexane Br-cyclohexane I-cyclohexane
4.9 3.3 2.9
IR (neat)
ea ax V&(cm-1) 730.7 686.0 654.5
684.4 658.0 639.1
V$(cm-9 1 .O 8.9 7.8
6.4 4.7 3.3
IR (in CSz)
e4
ax
e4
730.9 686.2 654.9
684.4 658.5 638.0
731.9 687.6 655.0
11.1 13.0 10.1
5.8 5.7 4.6
5.8 5.5 4.9
equatorial position relaxes much faster than the conformer with the axial C-Br. This difference disappears when CsHllBr is diluted in CS2. In the Table 2 we have shown the vibrational correlation times T ~which , are related to the dephasing times T2 through 7"-1
evolution of the vibrational correlationfunctions&(r), In Figure 2 we have shown the IR vibrational correlation function for the axial and the equatorial conformers in neat bromocyclohexane and at low concentration in CS2 solution. As we can see, in neat bromocyclohexane the conformer with the C-Br band in the
3:
q-1
+$-I
(3)
If vibrationallyinelastic processes characterized by TI are slower than elastic processes Tz,the relaxation is dominated by elastic, pure dephasing effects and 7, is equal to the dephasing time T2. As we can see from Table 2, the IR vibrational correlation times 7. are thesame for the both conformersdiluted in CS2, while they are much shorter for the equatorial form than for the axial form in neat cyclohexyl halides. To study possible electrostatic interactions, we have calculated the integral absorptions B, the molar extinctioncoefficients e, and the transition dipolemoments ac(/aQ. The molar extinction coefficient was calculated for the concentration 6.5 X 10-3 mol/L. The transition dipole moments
Abramczyk et a].
426 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
pathway for thevibrational dephasing. Many experimental results can be interpreted by assuming that pure dephasing represents rapid vibrational frequency fluctuations from interacting with its environment via the repulsivepart of the intermolecularpotential. The most frequently applied description introduces the Enskog hard-sphere collision mode146 and was successfully used to fit many experimental data.”-20 In the framework of this model, the following expression is given for pure dephasing bandwidth 6ph in a two-component system
1
I
I
I
I
05
in
15
7.0
I tlpsl
where the subscript i denotes the component under study,jdenotes the second one, and xi is the mole fraction. The bandwidth (6,& is expressed as
Figure 2. IR vibrational correlation functions of the axial (la) and the equatorial (lb) conformers in bromocyclohexane: in neat bromocyclohexane, (- -) (la), (-) (lb); at concentration 6.5X lO-’mol/L in CSz, (X) (la) and (0)(lb).
-
TABLE 2 IR Vibrational Correlation Times ‘I,(ps) of the Axial (ax) and Equatorial (eq)Conformers in Neat Cyclohexyl Halides CsHiiCl neat inCS2
ax 1.65 1.83
eq 0.95 1.83
CsHiiBr ax 2.25 1.86
eq 0.82 1.93
CsHllI ax 3.2 2.30
eq 1.05 2.16
were evaluated from the IR spectra according to the formula (4)
where Mis the reduced mass of the oscillator and N Ais Avogadro’s number. The results are compiled in Table 3. The molar extinction coefficients z were obtained using the concentrations of the axial (Cax)and the equatorial (C,) conformers calculated from the conformational free energy values A G O by ’H-NMR and 13C-NMR spectral data AGO = -RT In K,
(5)
where
Ke = Cq/Cax (6) The ratio Cq/Caxat 233 Kin CS2 (5% solution) is given in Table 4.
where M is the reduced mass of the oscillator with frequency o; reduced mass of the colliding molecules i and j ; 7 is an amplitude factor; Lijmeasures the range of interaction of colliding molecules; ut, = ( q+ uj)/2, wher e u, and uj are the hard-sphere diameters; p is the number density of the binary solution; and gu is the radial distribution function at contact distance. For the axial and the equatorial conformers, the hard-sphere parameters uu, Ltj,gij, and are the same. The ratio of the bandwidths of the equatorial and the axial ;6 conformers obtained from eqs 7 and 8 is
pi] is the
63
(9) where wq and wax are the frequencies of the equatorial and the axial conformers, respectively. The values of are given in Table 4. If we compare the 62/6; values with the experimental ratio of the bandwidths in neat solutes, we see that the hard-sphere collision dephasing model fails completely to describe theexperimental data. It suggeststhat the bandwidth of the axial formshould be a littlelarger than that oftheequatorial one, which is in significant disagreement with experiment. It means that dephasing via the repulsive part of the interactions is not able to explain the observed differences between the bandwidths of the axial and the equatorial forms. Similar arguments apply for the mechanism of resonant transfer via repulsive potential (mechanism ii). In this case, eq 7 is modified to the following expression:
63/69
fi2/#72
4. Discussion
The main goal of most papers dealing with vibrational dephasing is to isolate the individual relaxation channels. A variety of mechanisms are possible:1.4-616(i) pure dephasing, (ii) resonant energy transfer between quantum mechanically indistinguishable molecules, and (iii) vibrational energy relaxation. Each of these mechanisms may occur via the repulsive part or the attractive part (dispersion, induction, dipoledipole, or transition dipole transitiondipolecoupling)of the intra- or intermolecular potential. Mechanisms (ii) and (iii) may occur through coupling to other vibrational modes (V-V), rotational (V-R), and translational (V-T) motions. In cyclohexyl halides the bandwidths of the axial and the equatorial conformers are the same when diluted in nonpolar CS2 (Table 1). It means that the CHllllX gauche interactions in cyclohexyl halides (see Scheme 1) affect the conformational equilibrium5 and have little effect on the band broadening. Additionally, the effect of significant narrowing of the IR bands upon dilution in CS2 indicates that vibrational dephasing in these systems is dominated by intermolecular interactions, and mechanisms (i)-(iii) occurring via intramolecular interactions play a negligible role. A number of theoretical and experimental studies seem to have established that the pure dephasing (i) is the most significant
where ~ R is T the resonant intermolecular contribution (ii); is the nonresonant (pure dephasing) contribution (i), given by eqs 7 and 8; and xl is the mole fraction of component i. Equation 10 shows that only the resonant intermolecular contribution depends on the conformational equilibrium, Le., varies with the concentraction of the axial (C.J and the equatorial (C,) conformers. It has been shown in the literature4 that resonant transfer via short-range coupling leads to the expression a
exp(-aa)(da3/2
+ ~a~/21’/~w-’
(1 1)
where a is the short-range potential parameter. Considering two-limit cases we obtain
or
SZ/Sr
The values of for the contributions via repulsive potential are given in Table 4. Comparing them with the experimental
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 421
Vibrational Dephasing of Conformers
TABLE 3 Int d Absorptions B, Molar Extinction Coefficients e, and Transition Dipole Moments arc/@ for the C-X Bands of Cyclobexyl Ha% at Room Temperature in Carbon Disulfide Solutions (6.5 X mol/L) integral molar extinction absorption B (cm-1) coefficient e (L mol-' cm-2) acc/aQ @/A) ax eq ax eq ax eq CI-cyclohexane 0.26 1.14 161.9 513.3 0.97 1.74 Br-cyclohexane 0.55 2.64 335.4 1262.5 1.79 3.47 I-cyclohexane 0.68 2.76 432.1 1397.4 2.26 4.06 TABLE 4 Ratio of Concentrations C,/C, in Cyclohexyl Halides; Ratios of the Experimental IR Bandwidth Theoretical Bandwidths FJS;, and S&/St;a*
Q/e,
wt"f2/ q2; and
V2IV2 COqlCPX
Cl-cyclohexane Br-cyclohexane I-cyclohexane
qJv2
1.36 1.26 1.25
neat 1.73 2.76 3.01
in CS2 1.oo
0.96
1.07
values in neat solutes, we can state the same as for pure dephasing via a short-range repulsive interaction: a hardsphere collision resonant transfer mechanism fails to describe the experimentaldata. A more specific description of intermolecular collisionstaking into account the symmetry of the mode in different configurationslike the mode-matching models16would not change our conclusions. In Figure 3 we have shown the van der Waals surface of the axial and the equatorial conformers of chlorocyclohexane, where the shaded surfaces are active for collisions. As we can see they are approximately the same for the both conformers. An additional way toverify the above conclusionscoming from the difference in the bandwidths of the axial and the equatorial conformers is to study the dependence of the bandwidth on the substituent in the cyclohexyl halides series. As we can see from eq 8 for the dephasingvia hard collision interactions,the bandwidth strongly depends on the reduced mass M of the oscillator, which significantly increases in the order I > Br > C1. We have calculated the bandwidths bph from eqs 7 and 8 and the results are given in Table 5 . The results were obtained for the parameters given in Table 2. The radial distribution functions gi, were calculated from the Percus-Yevick equation.2l The amplitude factor y was taken to be 1.0. If we compare the results from Table 5 with the experimental IR and Raman bandwidths in neat cyclohexyl halides (Table l), we can state that the 8ph values decrease much faster than we observe in the experiment. Some comment is needed for the bandwidth obtained from IR and Raman spectra. Assuming that one is looking at the same mode, the difference may come from rotational broadening and/or collective many-particle correlation effects. We have found that the differences which we observe in IR and Raman spectra are due to rotational broadening. From the comparison of the anisotropic Zanh and isotropic Zi, Raman profiles, we have found the reorientational effect to be of second order 1.2 cm- for the equatorial and 0.4 cm-' for the axial conformer in neat bromocyclohexane. It gives, approximately for the IR broadening as for the firstorder process, 3.6 and 1.2 cm-' assuming a model of rotational diffusion. Elimination of pure dephasing and resonant transfer via short-rangerepulsive interactionsand the significantnarrowing of the bands upon dilution in nonpolar solvent seem to suggest mechanisms (i) and/or (ii)-(iii) via long-range attractive interactions. Since both conformers in the cyclohexyl halides have, to a first approximation (ideal chair forms), the same dipole moments, the differences in dynamics between them cannot be explained by dipoldipole coupling. However, as we can see from Table 3, the values of transition dipoles moments ap/aQ of both conformers are significantly different and may contribute to pure dephasing or resonant transfer via transition dipoletransition dipole coupling. The pure dephasing via transition dipoletransition dipole coupling leads to the bandwidth (in the
67/6::, 0.87
0.92 0.95
82/62 (neat) 1.27
1.20 1.22
(neat)
6.&,e/6.&e
1.46
1.71 1.67
static limit) proportional to1.4
where the subscript i denotes the component under study and j denotes the second component. The reduced mass of the both conformers is assumed to be the same. We can estimate the ratio of the bandwidths of the axial and the equatorial conformers for this mechanism, which can approximately be expressed as
where R = xq/xaX. We have taken the values of and e,, from Table 3 to calculate b ~ p l e / 8 ~ & e The . values are given in Table 4. As we can see from Table 4, the agreement with the experimental data W72/W& is much better than that for the dephasing via short-range repulsive potential. The resonant transfer via transition dipole coupling leads to an expression4
The ratios calculated for this mechanism are much larger (4.3 1, 4.74,4.04, respectively) than for the pure dephasing via the longrange, transition dipole-transition dipole interaction. It has been shown in many papers4J2that the resonant transfer mechanism contributes no more than 10-20% to the dephasing rate in the neat liquids, but it can make the ratio b&,,e/b&,le from Table 4 higher and in M t e r agreement with experiment. So, the results from Table 4 show that the bandwidths in the neat cyclohexylhalides are predominantly determined by nonresonant dephasing via transition dipole-transition dipole coupling. Similarly as for the pure dephasing via repulsive interaction, we can verify the conclusions by studying the dependenceof the bandwidth on the substituent in the cyclohexyl halides series. For the transition dipole-transition dipole mechanism the bandwidth depends on the reduced mass of the oscillator like for the dephasing via collisions, but its does not depend on the collision parameters pi/, uii, gij, and Lip According to eq 14, we have calculated the bandwidth bdipolc normalized to the bandwidth in neat chlorocyclohexane, and the results are given in Table 6. If we compare the results from Table 4 with experimental IR bandwidth in neat
428 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
Abramczyk et al. diameter of CS2 in comparisonwith cyclohexyl halides. However, we can see that the IR experimental bandwidths (see Table 1) are nearly the same for all the cyclohexyl halides while for the hard collision repulsive mechanism it should decrease about 4 times with the increasing reduced mass M of the oscillator M I > MB,> Mcl. Thus, the results in diluted CS2 suggest that like in neat solutes the dephasing via repulsive, hard collision interaction is negligible or is are compensated by the other important mechanisms. The results presented in this paper show that for the neat cyclohexyl halides the transition dipole-transition dipole interaction is dominant. The mechanism for diluted solutions is less evident, but it seems that long-range attractive interactions are more important than the dephasing via hard, repulsive collisions.
a
5. Conclusions
Figure 3. van der Waals surface of the conformer with the axial C-CI bond (a) and the equatorial C-CI bond (b) for chlorocyclohexane. The shaded surface is active for collisions.
TABLE 5: Theoretical Values of the Vibrational Dephasing Widths (a,), and the Dephasing Parameters in Neat Cyclohexyl Halides MX Mir 10” (g) Mi) X 10” (8) CI 4.128 9.8 Br 6.766 13.5 I 8.342 17.4
u,, = ~j
L,, =
(A) 4,j(A)
6.22 6.37 6.57
67
grr
0.345 0.353 0.365
gr/ :6 22.42 5.8
16.21 11.70
5.08 1.90 1.74 1.03 0.98
TABLE 6 Theoretical Values of the Bandwidths ddpk in Cyclohexyl Halides of the Axial (ax) and Equatorial Conformers (eq) 6dipOlc(cm-l)
CI Br I
ax 6.4 5.2 4.2
(cm-1) eq
9.35 8.89 7.01
ax 6.4 4.7 3.3
eq
11.1 13.0 10.1
cyclohexyl halides we can see a good agreement for the axial conformer and fairly good for the equatorial one. This trend for the cyclohexyl halides series supports the conclusions obtained from studying the differences in the bandwidths of the axial and the equatorial conformers that the predominant mechanism of the IR band broadening in neat cyclohexyl halides occurs via transition dipoletransition dipole coupling. A comment is necessary for the IR results in diluted solutions in CSz. As we stated above (see Table l), thedifference in the bandwidths of the axial and the equatorial conformers disappears in diluted solutions. The bandwidth of the equatorial conformer becomes much lower (because the mechanism of the transition dipole-transition dipoledisappears) but the bandwidth of the axial form becomes even larger in diluted solution in comparison with the neat bromocycloehexane and iodocyclohexane. This trend would suggest that the dephasing via hard collisions becomes important in solutions because the collision rate increases significantly (about 10 times) due to the smaller hard-sphere
A major emphasis of this work has been put on the role of short-range repulsive and long-range, usually attractive, interactions, on vibrational dephasing mechanisms in nonrigid, conformationally mobile molecules. We have found that a significant role is played by long-rangetransition dipole-transition dipole interactions for the systems studied in this paper. We have measured the dephasing rate of the C-X stretching modes (X = C1, Br, I) in the axial and the equatorial positions in cyclohexylhalides. We have found that the C-X oscillator in the equatorial position relaxes much faster than that in the axial position. At low concentration in nonpolar solvent this difference disappears and the relaxation rate is nearly the same for both conformers. We haveshown that the collision models with shortrange repulsive potential are not able to explain the observed differences in vibrational dynamics of the conformers. The intermolecular long-range transition dipole-transition dipole coupling has been found to give the main contribution to these differences in vibrational relaxation of the axial and the equatorial conformers. The intramolecular interaction, which mainly determines the conformational equilibrium, is negligible as a pathway for vibrational dephasing. This paper demonstrates that the simultaneous studying of the dephasing rate of different conformers, in this case the axial and the equatorial ones, helps to eliminate some of relaxation channels and provides a powerful method to isolate the individual relaxation mechanisms. References and Notes (1) Abramczyk, H. Mol. Physics 1988, 64, 315. (2) Reimsch[issel, W.; Abramczyk, H.; Michalak, J. PhosphorusSul/ur 1988,36,201. (3) Abramczyk, H.; Michalak, J. Chem. P h p . 1988,122,317. (4) Rothschild,W. G.DyMmicsofmolecularIlquidr,Wilcy: New York, 1984. (5) Schrooten,R.; Borremans, F.; Anteunis, M.Spectmhim. Ada 1977, 34A, 291. (6) Fischer, S. E.; Laubereau, A. Chem. Phys. Lerr. 1975, 35, 6. (7) Lynden-Bell, R. Mol. Phys. 1977, 33,907. (8) Wertheimer, R. K. Chem. Phys. Le?? 1977,52,224. (9) Ttmkin, S. I.; Burshtein, A. I. Chem. Phys. Le??.1979, 66, 52. (10) Brueck, S . R. J. Chem. Phys. Le??.1977,50, 516. (11) Schweizer, K.S.;Chandler, D. J . Chem. Phys. 1982, 76,2296. (12) Knapp, E. W.; Fiacher, S . F. J. Chem. Phys. 1901, 74, 89. (13) Logan, D.E. Mol. Phys. 1986,58,91. (14) Chesnoy, J.; Gale, G . M. Ann. Phys. (Parts) 1984, 9.893. (15) Geimaert, M.;Gale, G. Chem. Phys. 1984,86,205. (16) Miklavc, A.; Fischer, S . F. J. Chem. Phys. 1978, 69, 281. (17) Abramczyk, H. Chem. Phys. Le??.1983,100,287. (18) Abramczyk, H.; Marcinek, A.; Reirmchussel,W. Chem. Phys. Le??. 1983. - - - - , -108. - -, -245. .-. (19) Abramczyk, H.; Rtimschuasel, W.; BaraLka, H.; dabudzinska, A. Chem. Phys. 1985, 94,435. (20) Abramczyk, H.; Samios, D.; Dorfmuller, Th.J. Mol. Llquids 1987, -36. -, 211. - . .. (21) Lebowitz, J. L.; Helfand, E.;Praestgard, E.J. Chem.Phys.1965,43, 114. (22) Fickenscher, M.;Purucker, H.-G.; Laubereau, A. Chem. Phys. Let?. 1992, 191, 182.
