Global Quantitation of Solvent Effects on the Isomerization

7882

J. Phys. Chem. B 2002, 106, 7882-7888

Global Quantitation of Solvent Effects on the Isomerization Thermodynamics of 1,2-Dichloroethane and trans-1,2-Dichlorocyclohexane Brian L. McClain† and Dor Ben-Amotz* Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana 47907-1393 ReceiVed: NoVember 8, 2001; In Final Form: May 17, 2002

The conformational equilibrium of the trans-gauche isomerization of 1,2-dichloroethane (DCE) and the axial, axial-equatorial, equatorial isomerization of trans-1,2-dichlorocyclohexane (T12D), both dissolved in diethyl ether, are studied using Raman spectroscopy. The C-Cl stretch band areas of the two conformers are measured as a function of temperature and pressure. The resulting area ratios, calibrated against NMR measurements, are used to globally quantitate the complete set of isomerization thermodynamic functions in solution, as well as the corresponding solvent excess contributions (by comparison with vapor-phase results). The effects of pressure on the two isomerization processes are found to be opposite in sign, as the polar isomer (gauche) of DCE is favored at high pressure and low temperature, while the more polar (equatorial, equatorial) form of T12D is driven in the opposite direction. The excess enthalpy (and energy) of reaction is negative for both reactions, while the reaction volume is negative for the DCE and positive for T12D. The results reveal the different impact of attractive (cohesive) and repulsive (cavity formation) perturbations on various thermodynamic functions.

I. Introduction Molecular conformational equilibria play an important role in many biological and industrial chemical processes. Systematic studies of the effects of solvent, temperature, and pressure on such equilibria are required in order to better understand the influence of intermolecular interactions on molecular structure and bulk properties. The conformational (isomerization) equilibria of relatively small molecules are of particular interest as these serve both as prototypes for more complex conformational processes and as benchmarks for critically testing theoretical approximations used in modeling liquids.1-6 In this work pressure- and temperature-dependent Raman spectroscopic measurements are used to globally quantitate the isomerization thermodynamics of 1,2-dichloroethane (DCE) and trans-1,2-dichlorocyclohexane (T12D), dissolved in diethyl ether. In particular, the trans-gauche (t-g) and axial, axialequatorial, equatorial (aa-ee) peak area ratios of DCE and T12D, respectively (see Figure 1), are used to measure changes in the isomerization equilibrium constant in the solution phase as a function of pressure and temperature. These are combined with vapor-phase results to determine solvent excess contributions to the complete set of reaction thermodynamic functions (∆G, ∆H, ∆S, ∆V, ∆A, ∆U) for these two systems.7 A number of previous experimental8-23 and theoretical8,24-26 studies of the t-g isomerization of DCE, both in the vapor and solution phase, have established this as an important model conformational reaction. However, despite the significant prior effort devoted to this system, no previous studies have attempted to globally quantify the effects of solvation on the thermodynamics of this isomerization in any solvent. The aa-ee isomerization of T12D was selected as a complimentary compound for this comparative study as it undergoes a similar structural change around the two chlorine atoms, but a different overall * Author to whom correspondence should be addressed. E-mail: [email protected]. † Present address: Department of Chemistry, Stanford University, Stanford, CA 94305.

Figure 1. The Newman projection of the isomerization of 1,2dichloroethane showing the two degenerate gauche isomers (top) and Kekule´ structures of the two isomers of trans-1,2-dichlorocyclohexane (bottom, the hydrogen atoms have been omitted for clarity).

molecular shape change. Thus the comparison of these two isomerization processes in the same solvent may be used to determine whether the observed solvent excess thermodynamic changes are due to interactions localized around the two chlorines or extend over the entire solvation shell around the isomerizing solute. Previous studies of the aa-ee isomerization of 1,2- and 1,4dichlorocyclohexane (T14D) have noted the preference for the aa isomer in the vapor phase.27-35 This contrasts with expectations based on the isomerization energy of monochlorocyclohexane, for which the equatorial conformer is favored by 2.5 kJ/mol.28,30 Simple additivity would thus suggest that the ee conformer of T12D or T14D should be stabilized by about 5.0 kJ/mol. The observed preference for the aa isomer of the T12D compound is thus likely due, at least in part, to the lower electrostatic repulsions between the chlorine atoms in the aa relative to the ee conformer.27 Solution-phase studies of both T12D and DCE further indicate that the preferred isomer is highly solvent-dependent, with increasingly polar solvents generally driving the equilibrium toward the more polar ee conformer.22

10.1021/jp0140973 CCC: $22.00 © 2002 American Chemical Society Published on Web 07/12/2002

Solvent Effects on the Isomerization of DCE and T12D

J. Phys. Chem. B, Vol. 106, No. 32, 2002 7883

Various theoretical and computer simulation strategies have been proposed for modeling conformational equilibria in solution.6,8,22-28,36-39 The most widely used methods are based on the dielectric continuum solvent approximation.1,2,40-42 Alternative molecular approaches to modeling solvation include those based on liquid thermodynamic perturbation theory, which represent a liquid as a reference hard body fluid plus an attractive mean field.8,36-38 In addition, a variety of classical, quantum mechanical and hybrid computational methods have been used, and are actively being developed, for modeling liquid-phase chemical processes.4,6,26 The experimental results presented in this work offer benchmarks for critically testing the predictions of various such theoretical modeling strategies and approximations (although such tests are beyond the scope of the present study). II. Experimental Procedure Spectral grade DCE (Aldrich), diethyl ether (Mallinckrodt), and T12D (TCI America) were purchased and used as received. Solutions of DCE/ether and T12D/ether (at a concentration of 20.0 ( 0.5 wt %) were loaded into a diamond anvil cell (DAC) for pressure and temperature studies. The DAC was of MerrillBasset design43 using a stainless steel gasket of 500 µm thickness and a 700 µm diameter sample chamber. Pressure measurements were performed using the pressure-dependent shift of the R1 fluorescence line from ruby chips (10-50 µm) placed inside the sample chamber and gave an estimated accuracy of (0.3 kbar.44,45 The mico-Raman system used for ruby fluorescence and Raman measurements includes a 40mW (∼15 mW at the sample) He-Ne laser (Spectra Physics model 127) operating at 632.8 nm as the excitation source. The laser was focused onto the sample using a microscope objective (Olympus 20× long working distance); the backscattered Raman signal was collected using the same microscope objective and detected using a liquid nitrogen-cooled CCD detector (Princeton Instruments LN/CCD 1152E) mounted to a spectrograph (ISA HR320 f/4.2) with a 600 groves/mm ruled grating. The exposure times of 300 s and 480 s per Raman spectrum were used for the DCE and T12D solutions, respectively. The sample temperature was controlled by immersing the DAC in a thermostated oil bath. The sample temperature was determined using a thermocouple placed in the oil bath and monitored to ensure temperature stability to within (0.5 °C. Since the frequency shift of the ruby R1 line has a temperature dependence (as well as a pressure dependence), the ruby fluorescence inside the DAC was referenced to the fluorescence spectrum of a ruby chip within the oil bath but exterior to the DAC. At each temperature and pressure, three high-pressure ruby spectra were recorded prior to and after the acquisition of three sample spectra to ensure pressure reproducibility. The nominal pressure of the DAC was increased after stepping through a series of temperatures, and the process repeated. A neon calibration spectrum was collected before and after each set of temperature and pressure measurements for wavelength calibration and to correct for instrumental drift. III. Peak Area Measurement The symmetric C-Cl stretching bands of the trans (∼754 cm-1) and gauche (∼677 cm-1) isomers of DCE and the aa (∼700 cm-1) and ee (∼738 cm-1) bands of T12D were analyzed to determine peak areas. Complete peak assignments for each molecule can be found elsewhere.10,19,29,30 Solvent subtraction methods were not required in the analysis of either DCE or T12D because the frequencies of the symmetric C-Cl modes

Figure 2. Raman spectra showing the C-Cl stretching region of (a) liquid DCE, (b) liquid T12D, (c) DCE in ether, and (d) T12D in ether. The spectra in (a) and (b) were measured at ambient pressure while the spectra in (c) and (d) were recorded at a pressure of 14.5 kbar. Note the nonzero intensity between the symmetric C-Cl bands in all the spectra. The solid horizontal line in the lower two spectra represents the baseline. The dashed curves in (c) are Voigt functions used to estimate the peak areas.

for both molecules have no significant overlapped with any solvent bands. Subtraction of the broadband background signal underlying the Raman peaks of interest (resulting from read and dark counts, amplifier offset, fluorescence and other ambient sources) was performed on all spectra before evaluating peak areas. In contrast to a subtraction method previously used in our laboratory,8 the region between the trans and gauche peaks of DCE was not assumed to be purely baseline. Although this region appears relatively flat, the nonzero intensity present in this region of the pure DCE and T12D spectra (see Figure 2a,b) illustrates that it is composed of overlapping tails of the two C-Cl peaks. A more appropriate baseline subtraction procedure used in this work was found to somewhat alter the previously reported values of the thermodynamic functions for DCE.8 Although the previous results were assumed to have an error of ( 0.5 kJ/mol, the resulting absolute values of ∆H are found to differ by as much as 1.5 kJ/mol from the present results, which are more conservatively estimated to have an accuracy of (1 kJ/mol. A linear baseline function spanning the two C-Cl bands of DCE (see Figure 2c) was used to remove the background from all DCE/ether spectra. However, a fluorescence background in the T12D/ether solutions produced a nonlinear baseline. A local third-order polynomial fit to this fluorescent background reproduced the baseline observed in neat T12D and was thus used for background subtraction with this system. Figure 2c,d shows the resulting background-subtracted spectra for both DCE/ ether and T12D/ether as well as the nonzero intensity that occurs between the t-g and aa-ee peaks of DCE and T12D. The DCE peaks were fit to a Voigt function, while peak areas for T12D were obtained by direct integration (using Igor Pro by WaveMetrics). A Voigt function fit was selected for the analysis of DCE in order to exclude the shoulder on the highfrequency side of the gauche band of DCE (which is due to the asymmetric gauche stretch9,13,16) as illustrated by the dashed line in Figure 2c. Direct integration was chosen for the T12D peak area measurements because this produced less scatter in the data compared to a Voigt fit and because no asymmetric

7884 J. Phys. Chem. B, Vol. 106, No. 32, 2002

McClain and Ben-Amotz

stretch shoulder is evident in the T12D spectra. Each peak was integrated from the midway point between the C-Cl peaks and a baseline point on either side of the gauche or trans peaks, respectively. IV. Thermodynamic Analysis Raman peak area ratios (Ig/It) are closely related to the isomerization free energy.8,22,36

( )

∆G ) -RT ln CΩ

()

Ig Fg ) -RT ln It Ft

(1)

where ∆G represents the Gibbs free energy (chemical potential) difference between the two isomers, and the constant CΩ represents the ratio of the effective Raman cross sections (including instrumental collection and detection efficiency factors). The value of CΩ is expected to be approximately pressure- and temperature-independent since solvent-induced Raman cross-section changes should scale both the t-g (or aaee) band intensities by the same factor (particularly for vibrational modes involving similar atomic motions).46 This expectation is born out (to within experimental error) by comparison of CΩ values for the same isomerization carried out in different solvents (as described below). The experimental isomerization enthalpy (∆H) and reaction volume (∆V), which are independent of CΩ (assuming that this is a temperature and pressure independent contant), are determined from the appropriate thermodynamic derivatives of the experimental Raman band intensity ratios shown by eqs 2 and 3:

∆H ) -R

[

∆V ) -RT

]

∂ ln(Ig/It) ∂(1/T)

[

(2)

P

]

∂ ln(Ig/It) ∂P

T

(3)

The resulting ∆H and ∆V values may be combined using eq 4 to determine the change in potential energy upon isomerization:

∆U ) ∆H - P∆V

(4)

The following expressions may be used to determine ∆S and ∆A from the above thermodynamic functions:

T∆S ) ∆H - ∆G

(5)

∆A ) ∆U - T∆S

(6)

However, determination of ∆G (and thus ∆S and ∆A) requires evaluating CΩ, to convert measured area ratios to ∆G using eq 1. The way in which we have obtained these values is described below. Note that the resulting CΩ values are appropriate only for converting peak areas measured using the same procedure (and instrumental characteristics) as we have used in this work. The value of CΩ for T12D in ether was obtained by combining eq 1 with our experimentally measured integrated peak intensities and literature NMR-derived values of ∆G for T12D in CCl4 and benzene.34 These yield estimated CΩ values of 1.1 for T12D/CCl4 and 0.8 for T12D/benzene. The difference between these two values may reasonably be attributed to experimental error, since this difference corresponds to a free energy difference of less than 1 kJ/mol and thus is smaller than the typical variation in experimental thermodynamic measurements for such isomerization processes.8,36 Thus the average

of the above two CΩ values (0.95 ( 0.2) is used as an estimate of the true CΩ for T12D in any solvent (including diethyl ether). In the case of DCE, no previous solution-phase ∆G values have been reported. However, we were able to extract an experimental estimate of ∆G in two solvents from early NMR coupling constant measurements, using a method outlined by Abraham and Bretschneider.22 In particular, if M is taken to be some measured quantity that is strictly proportional to concentration (i.e., a NMR chemical shift or a coupling constant) and MA and MB are the measured quantities for the reactant, A, and product, B, states (e.g., the trans and gauche isomers of DCE), then ∆G can be determined from eq 7:

e-∆G/RT ) (M - MA)/(MB - M)

(7)

Due to the long sampling time scale for NMR, isomer peaks coalesce at temperatures above the thermal conformational barrier, and thus a convolved (mean) coupling constant is measured. Abraham et al. give coupling constants for the individual isomers of DCE (i.e., MA and MB) as well as convolved coupling constants (M in eq 7) in a variety of solvents.12 In the case of DCE, the right-hand side of eq 7 must be divided by a factor of 2 in order to take into account the two degenerate forms of the gauche isomer (while this factor need not be included in the case of T12D since both isomers are nondegenerate). The resulting NMR-derived values of ∆G for DCE solvated in CCl4 and acetonitrile, obtained using the above procedure, are ∆G ) 2.8 ( 0.3 in CCl4 (carbon tetrachloride) and ∆G ) -0.1 ( 0.3 kJ/mol in CH3CN (acetonitrile). These values are in good agreement with the values Depaepe and Rychaert calculated using Molecular Dynamics simulations.26 The NMR-derived ∆G values were again combined with eq 1 and our measured integrated peak intensities in the same solvents to yield CΩ values of 1.1 ( 0.6 for DCE/CCl4 and 0.9 ( 0.4 for DCE/acetonitrile (with error bars derived by propagation of the reported NMR coupling constant uncertainties). The small numerical difference between these values is again consistent with our assumption that CΩ is solvent-independent within the experimental error. This solvent independence is particularly striking given the large difference between the polarities of the two solvents. The average of the above two values for CΩ (1.0 ( 0.5) was thus used as a best estimate of the value for DCE in ether. The vapor-phase thermodynamic functions for T12D were obtained from previous experimental measurements.27,29 In particular, the vapor-phase values of ∆G and ∆H (at 25 °C) were combined with eqs 4-6, along with the fact that ∆V ) 0 (since there is no change in the number of solute molecules upon reaction), to determined all other gas-phase values. The extrapolation of the vapor-phase values to a temperature of 75 °C was made by assuming that the gas-phase ∆H and ∆S are approximately constant over the experimental temperature range. Determination of the corresponding DCE vapor-phase results was complicated by lack of experimental vapor-phase ∆G data. Thus, following the procedure outlined by Wiberg,27 an ab initio calculation on both isomers of DCE using the B3P86 theoretical model along with the 6-311G* basis set at a temperature of 25 °C was performed.47 From these calculations, the vapor-phase entropy difference, ∆S, was calculated. This entropy difference was then corrected by addition of ln(2) to account for the degeneracy of the two gauche states of DCE (as shown in Figure 1).11 The corrected ∆S was combined with the experimental vapor-phase enthalpy from the literature,22,23 to obtain a vaporphase ∆G. The remaining vapor-phase thermodynamic functions were then determined using eqs 4-6. Solvent excess thermo-

Solvent Effects on the Isomerization of DCE and T12D

Figure 3. Spectra of DCE at 1 atm (solid curves) showing the variation in relative peak intensities in different solvents. The corresponding solvents and dielectric constants are (a) CCl4,  ) 2.2; (b) diethyl ether,  ) 4.3; (c) liquid DCE,  ) 10.1; and (d) acetone,  ) 20.7. The dashed curve in (b) shows the spectrum in ether at 15 kbar (normalized to the same trans peak intensity).

dynamic results were obtained by subtracting the vapor-phase values from our measured solution-phase values. V. Results Some of the qualitative effects of solvation on the isomerization equilibria of DCE and T12D appear to result from the change in molecular dipole moment induced by the change in relative orientation of the two C-Cl bonds upon isomerization. In DCE, the dipole moment changes from µ ≈ 0 D for the trans isomer to µ ) 3.12 D in the gauche isomer,13,16 while the dipole moment of T12D changes by 2.35 D (µaa ) 1.39 D, µee ) 3.74 D).27 Such large dipole moment changes are expected to affect solvation as the more polar isomer is stabilized, relative to the less polar isomer, in solvents of high dielectric constant. This expectation appears to be qualitatively confirmed by the spectra in Figure 3, which show the nonpolar trans form of DCE having greater peak intensity in CCl4 ( ) 2.2) while the gauche peak is larger in acetone ( ) 20.7). Figure 4 displays a similar trend for T12D in solvents of various dielectric constants. Again the more polar ee (gauche-like) form tends to be favored in more polar solvents (with the exception of benzene, which produces a peak area ratio similar to a solvent of higher dielectric constant33,35). The dashed spectra in Figure 3b and 4c represent pressureinduced changes in the relative Raman intensities of the two conformers of DCE and T12D, respectively, in diethyl ether. The high-pressure spectra have each been normalized to have the same high frequency peak intensity. These results indicate that the more polar (gauche) form of DCE is strongly stabilized at high pressure, while in the case of T12D pressure drives the reaction strongly toward the less polar aa form. Since the solvent is the same in both case, these pressure-induced changes make it very clear that the dielectric constant of a solVent alone is not sufficient to explain all of the obserVed effects of a solVent on conformational equilibria. Table 1 contains the logarithm of experimental peak area ratios derived from spectral measurements performed as a function of temperature and pressure (as described in Sections II and III). Figure 5 shows the effect of pressure and temperature on these peak area ratios. Figure 5a,c displays the logarithm of

J. Phys. Chem. B, Vol. 106, No. 32, 2002 7885

Figure 4. Spectra of T12D at 1 atm (solid curves) showing the variation in relative peak intensities in different solvents. The corresponding solvents and dielectric constants are (a) CCl4,  ) 2.2; (b) benzene,  ) 2.6; (c) diethyl ether,  ) 4.3; and (d) liquid T12D,  ) 10.0. The dashed curve shows the spectrum at a pressure of 15 kbar (normalized to the same ee peak intensity).

TABLE 1: Experimental Raman Peak Area Ratios 1,2-dichloroethane

trans-1,2-dichlorocyclohexane

T (°C)

P (kbar)

ln(Ig/It)

T (°C)

P (kbar)

ln(Iee/Iaa)

25 25 25 25 25 25

0.001 0.6 5.2 14.6 20.2 26.4

-0.919 -0.675 -0.388 -0.115 -0.013 0.121

50 50 50 50 50 50

0.001 0.8 5.4 14.5 21.0 27.5

-0.928 -0.626 -0.320 -0.119 -0.030 0.141

75 75 75 75 75 75

0.001 1.1 5.4 14.5 21.1 27.1

-0.913 -0.609 -0.366 -0.094 0.007 0.153

100 100 100 100 100 100

0.001 1.3 6.1 15.5 20.8 25.1

-0.922 -0.566 -0.268 -0.078 0.018 0.263

20 20 20 20 20 20 20 40 40 40 40 40 40 40 60 60 60 60 60 60 60 80 80 80 80 80 80 80

0.001 3.7 5.3 8.3 14.6 20.3 26.6 0.001 4.3 5.9 8.8 15.4 20.6 26.6 0.001 4.4 6.0 9.1 15.7 20.7 26.6 0.001 4.7 6.3 9.3 15.8 20.7 26.8

-0.204 -0.285 -0.320 -0.421 -0.574 -0.706 -0.877 -0.265 -0.349 -0.370 -0.456 -0.627 -0.743 -0.857 -0.326 -0.364 -0.390 -0.504 -0.695 -0.773 -0.886 -0.378 -0.393 -0.445 -0.528 -0.716 -0.752 -0.797

the intensity ratio verses inverse temperature at six isobars. Figure 5b,d plots the intensity ratio versus pressure at four isotherms (these isotherms have each been vertically offset by 0.4 for clarity). The data in Figure 5a,c (except for the one atmosphere data) were interpolated from the raw experimental data shown in Figure 5b,d (and are not offset). The lines in Figure 5 represent linear best fits whose slopes yield the solution-phase enthalpies, ∆H, volumes, ∆V, and energies, ∆U, (see eqs 2-4). Since the results in Figure 5b appear to deviate systematically from a straight line, these have also been fit to an nonlinear (exponential) function of pressure in order to better estimate the actual ∆V at each pressure.

7886 J. Phys. Chem. B, Vol. 106, No. 32, 2002

McClain and Ben-Amotz

Figure 5. Plots of peak intensity ratios as a function of T and P, used to determine ∆H and ∆V for DCE and T12D. (a) ∆H for DCE in ether at six isobars; (b) ∆V of DCE in ether at four isotherms; (c) ∆H for T12D in ether at six isobars; (d) ∆V for T12D in ether at four isotherms.

TABLE 2: Solution, Vapor, and Excess Thermodynamic Functions for 1,2-Dichloroethane and trans-1,2-Dichlorocyclohexane 1,2-dichloroethane 1 atm thermodynamic functions a ∆Gl ∆Gg ∆Gx ∆Hl ∆Hg ∆Hx T∆Sl T∆Sg T∆Sx ∆Vl ∆Vg ∆Vx ∆Ul ∆Ug ∆Ux ∆Al ∆Ag ∆Ax

(kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (Å3) (Å3) (Å3) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol)

15 kbar

25 °C

75 °C

25 °C

75 °C

2.3c 3.7 -1 0.0 5.0g -5 -2.3 1.3i -4 -4.1j 0 -4j 0.0 5.0 -5 2.3 3.7 -1

2.6c 3.5e -1 0.0 5.0g -5 -2.6 1.5e -4 -4.8j 0 -5j 0.0 5.0 -5 2.6 3.5 -1

0.3 3.7 -3 0.9 5.0g -4 0.6 1.3i -1 -1.2 0 -1 2.0 5.0 -3 1.4 3.7 -2

0.3 3.5e -3 0.9 5.0g -4 0.7 1.5e -1 -1.3 0 -1 2.1 5.0 -3 1.4 3.5 -2

trans-1,2-dichlorocyclohexane 1 atm

15 kbar

25 °Cb

75 °Cb

25 °Cb

75 °Cb

0.4d 1.9f -1.5 -2.5 3.0h -5.5 -2.9 1.1 -4 1.0j 0 1j -2.5 3.0 -5.5 0.4 1.9 -1.5

0.9d 1.7e -1 -2.5 3.0h -5.5 -3.4 1.3e -5 1.1j 0 1j -2.5 3.0 -5.5 0.9 1.7 -1

1.3 1.9f -1 -0.8 3.0h -4 -2.1 1.1 -3 1.0 0 1 -1.7 3.0 -5 0.4 1.9 -1.5

1.9 1.7e 0 -0.8 3.0h -4 -2.7 1.3e -4 0.9 0 1 -1.6 3.0 -5 1.1 1.7 -1

a Note that the superscripted lettering on the thermodynamic functions in the left-most column refers to liquid (l), gas (g), and excess (x) properties. b ln K data was linearly interpolated to the temperature in the table. c Determined using an averaged CΩ value of 1.0. d Determined using an averaged CΩ value of 0.95. e Values were calculated by assuming the ∆H and ∆S values do not change significantly over the small temperature range. f Value was calculated in ref 25. g Values taken from ref 22. h Experimentally determined value from ref 27. i Calculated using Gaussian 98 with the B3P86/6-311* method and adding a factor of R ln(2) to the entropy difference calculated. j Values obtained from an exponential fit to ∆Gl versus pressure, extrapolated to 1 atm.

Table 2 summarizes the resulting globally quantitated isomerization thermodynamics of DCE and T12D dissolved in diethyl ether. The values for the thermodynamic functions are given at two temperatures for each pressure and are each estimated to have an accuracy of (1 kJ/mol (the solvent excess functions are rounded to the nearest kJ/mol while the liquid and gas values are reported to the first decimal place). In the case of T12D, the data in Table 2 was interpolated to 25 °C and 75 °C from the raw data.

The solution-phase isomerization free energy, ∆Gl, results for DCE (see Table 2) clearly indicate the more polar gauche isomer is increasingly favored (∆Gl decreases) with increasing pressure. For T12D, on the other hand, our solution-phase ∆Gl values indicates the less polar aa isomer is increasingly favored with increasing pressure (∆Gl increases). In addition, ∆Gl values for both isomers show a very slight temperature dependence at constant pressure. The differences between the ∆Gl values in the two solutes are primarily the result of difference between the internal free energies of the corresponding isomers, and are reflected in the vapor-phase, ∆Gg, results. The solvent excess contribution to the isomerization free energy, ∆Gx, for both molecules are negative, indicating that in each case the more polar isomer is stabilized by the solvent (relative to the less polar isomer). The experimental enthalpy for DCE/ether at ambient pressure, ∆Hl ) 0 ( 1 kJ/mol, does not agree with the enthalpy of 2.9 kJ/mol reported by Abraham and Bretschneider.22 However, it should be pointed out that ref 22 lists the isomerization enthalpy of the pure liquid as 1.3 kJ/mol in contrast with the reported value of 0.0 kJ/mol given by several other sources.19-21,48 Although no other previously reported values of ∆H for DCE solvated in ether have been found, our measured value at ambient pressure is in reasonable agreement with solvent dielectric constant-dependent trends in ∆Hl for DCE dissolved in various solvents.22 Given the variance of literature values for the enthalpies of such reactions, we believe that few, if any, reported enthalpies have an absolute accuracy of better than (1 kJ/mol (at best). It is also pertinent to note that even highlevel quantum calculations are not expected to predict vaporphase isomerization enthalpies with an accuracy of better than several kJ/mol. Our experimentally determined value of ∆H for T12D/ether is -2.5 kJ/mol. Although no previously published values were found for comparison, this value is generally consistent with the trend found by Ul’yanova, Ostrovskii, and Pentin, which shows a decrease in ∆H with increasing solvent dielectric constant.29 In particular, Ul’yanova et al. present data that show the enthalpy decreasing from 3.2 kJ/mol in n-C7H16 ( ) 1.92) to 0.8 kJ/mol in CS2 ( ) 2.65). They also report a value of -2.5 kJ/mol for the pure liquid ( ) 10.0, estimated).29 These results were obtained from direct peak integration (by weighing peak cutouts) rather than peak fitting and functional integration. The reaction potential energy change, ∆Ug, is positive for both reactions in the vapor phase,22 and is identical to ∆Hg (since P∆Vg ) 0 for such one-to-one reactions in the vapor phase). This indicates that the more polar isomer, which is also the one in which the two chlorine atoms are closest to each other, has an intrinsically higher potential energy in the absence of a solvent. In solution, ∆Ul may differ from ∆Hl if P∆Vl is nonzero (eq 4). At ambient pressure, P∆Vl is invariably much smaller than the experimental error in ∆Hl, and so ∆Ul and ∆Hl are effectively equivalent. In contrast, at high pressure the magnitude of P∆Vl is large enough to produce a significant difference between ∆Ul and ∆Hl, as evident in both the DCE and T12D high-pressure results. The solvent excess isomerization potential energy change, ∆Ux, is negative for both isomerization reactions. This is again consistent with the expectation that the more polar isomer should be stabilized by its interaction with the polar ether solvent. If the observed increase in ∆Ux with increasing pressure for both reactions are considered to be outside of experimental error, then these suggest the influence of subtle changes induced by rearrangement of solvent molecules around each isomer, as discussed in Section VI.

Solvent Effects on the Isomerization of DCE and T12D The isomerization entropies in solution, ∆Sl, are significantly different from those in the vapor phase, ∆Sg, because of the important role of solvent structure associated with cavity formation and cohesive solute-solvent interactions. The resulting solvent excess entropy changes are invariably negative. This suggests that cohesive interactions between the solvent and the more polar isomer (g or ee) tend to restrict the mobility of the solvent cage. However, the observed isomerization entropies undoubtedly are not exclusively cohesive in origin, as discussed in Section VI. The isomerization volumes, ∆V, in both systems reflect changes in the volume of the solvation shell around each solute upon isomerization. Since the number of molecules in the product and reactant is the same, ∆Vg ) 0. However, this is not the case in solution where the structure of the solvent shell changes upon isomerization. Therefore the liquid and excess partial molar volume changes are identical, ∆Vl ) ∆Vx. In DCE, which does not possess a bulky ring structure, ∆Vx is negative indicating that the solvent packs more tightly around the more polar gauche form. For T12D, on the other hand, ∆Vx is positive, indicating that the solvent packs more efficiently around the less polar aa form. An electrostatic argument can be made for solvent contraction in the DCE/ether system based on the large dipole moment of the gauche form drawing the solvent in. However, the more polar ee (gauche-like) form of T12D has a larger partial molar volume than the aa conformer. These differences between DCE and T12D thus again reflect subtle structural changes in the solute-solvent complex, as discussed in Section VI. The value of ∆Vl (and ∆VX) for DCE at 1 atm is obtained from a nonlinear extrapolation of the high-pressure data. The resulting value of about -5 Å3 is significantly larger than the -1 Å3 value obtained from a linear fit to all the high pressure, but is smaller than the value of -13 Å3 obtained from a linear fit to only the two lowest pressure ∆Gl data points. These two estimates of ∆Vl for DCE at 1 atm are consistent with the value of -9 Å3 reported by Seki, Choi, and Takagi; although this literature value was determined in the pure liquid.11 The significant difference between the low- and high-pressure ∆Vl values is believed to be significant, as this behavior suggests pressure-dependent changes in reaction volumes and partial molar volumes, as has been observed and theoretically predicted to occur in other systems,8,49-51 and is discussed further below. VI. Discussion and Conclusions The above global thermodynamic results reveal some obvious and some not so obvious ways in which solvation can influence conformational equilibria. All of these may be viewed as resulting from the balance of competing attractive and repulsive solute-solvent interactions. This balance is much the same as that which determines the equilibrium density of an ambient liquid as that density at which the cohesive intermolecular interactions, which attract molecules to each other, exactly balance the repulsive interactions, which prevent molecules from interpenetrating. Similarly, it is the difference between the cohesive and cavity formation energies of the product and reactant isomers that dictate the equilibrium concentrations of the two isomers in a given solvent (at a given temperature and pressure). Since DCE and T12D undergo a very similar structural change in the neighborhood of the two chlorine atoms, any differences between the observed excess isomerization thermodynamic functions must reflect the degree to which the entire solvent-solute complex, rather than just the local solvent

J. Phys. Chem. B, Vol. 106, No. 32, 2002 7887 structure around the Cl atoms, influences the isomerization equilibrium. Although the scope of the present work does not extend to the development and testing of a detailed theoretical model for this balance of solvation interactions, our results do offer evidence for the effect of such a balance on different thermodynamic functions. Our observation that the excess isomerization energy, ∆Ux, and enthalpy, ∆Hx, are invariably negative suggests that cohesive interactions, which favor the more polar product isomer, predominate in determining these excess functions. The fact that the magnitude of ∆Ux in T12D is slightly larger than in DCE, although T12D has a slightly smaller change in dipole moment upon isomerization, may indicate the influence of dispersive and/or multipolar cohesive solute-solvent interactions. An elegant set of previous studies of the isomerization of 1-chloropropane, 1,2-dichloroethane (DCE), and 1-chloro2-fluoroethane in the gas phase and in rare-gas solutions offers further evidence regarding the magnitudes of different cohesive interaction mechanisms.22,23 The solvent excess values of ∆Hx ) ∆Ux for DCE in rare-gas solvents are of the order of -2 kJ/mol and thus are somewhat smaller than those of DCE in diethyl ether of about -5 kJ/mol. This difference may approximately reflect the relative importance of dipole-dipole or multipolar interactions as opposed to inductive and dispersive interactions. Furthermore, in rare-gas solvents the ∆Ux for 1-chloropropane is about 10 times smaller than that of DCE in rare gases.22 This implies that dipole-induced dipole interactions are much larger than dispersive contributions to the isomerization of DCE. The reason for this is that 1-chloropropane has virtually the same structure and polarizability as DCE, but does not undergo a significant change in dipole moment upon isomerization. This conclusion is supported by previous comparisons of 1-chloropropane and DCE in diethyl ether, which again reveal that ∆Ux of 1-chloropropane is 10 times smaller than that of DCE.8 The fact that the excess isomerization volumes are opposite in sign for the two isomerization reactions undoubtedly reflects a balance of attractive and repulsive contributions. This offers the clearest evidence that excess isomerization thermodynamic functions are not dictated by the local solute and solvent structure around the solute chlorine atoms, but are sensitive to the structure of the entire solute-solvent complex. For DCE the product species has both a larger dipole moment and a smaller excluded volume.8 Thus both cohesive and cavity formation contributions are expected to produce a decrease in partial molar volume upon isomerization, as observed experimentally. In the case of T12D, cohesive interactions are still expected to contribute a volume decrease upon isomerization to the more polar product state. Thus the fact that the observed reaction volume is positive suggests that in this case there is an increase in excluded volume upon isomerization, and that increase is large enough to overcome the opposing effect of cohesive forces. Our excess entropy results can again be understood by considering the balance of attractive and repulsive interactions. The negative sign of the excess entropy for both reactions suggest that the larger dipole moment of the product isomer serves to constrain the structure of the ether solvation shell so as to decrease its entropy relative to the solvation shell around the less polar reactant state. This decrease in entropy can either be the result of a constriction of the solvation shell to a lower volume (and thus a lower entropy), or the result of restricted orientational mobility of the solvent surrounding the more polar isomer.

7888 J. Phys. Chem. B, Vol. 106, No. 32, 2002 The excess Gibbs (and Helmholtz) free energies are both smaller in magnitude than the entropic and enthalpic (and energetic) contributions into which the free energies may be decomposed. This is suggestive of what has been termed “enthalpy-entropy compensation”53-55sa phenomenon which results from the undisputable fact that solvent molecules in the solvation shell around a solute are in equilibrium with bulk solvent molecules, and so must have the same chemical potential (but not necessarily the same entropy or enthalpy/energy) as bulk solvent molecules. The fact that the resulting compensation is not perfect indicates that this solvent chemical potential balance is not the sole factor responsible for the excess effects of the solvent on such chemical processes. In summary, the effects of pressure and temperature on the isomerization of DCE and T12D dissolved in diethyl ether were studied using Raman spectroscopy. The experimental values of ∆H, ∆V, and ∆U, when combined with literature values for ∆G, allowed the first reported global thermodynamic quantitation of any isomerization reaction.7 The results reveal that temperature plays a less significant role than pressure in shifting isomerization equilibria. In DCE, the polar gauche isomer is favored at high pressure. The opposite is true for T12D where the less polar axial-axial (aa) increases in population at high pressure. The results are qualitatively interpreted as resulting from the delicate balance of repulsive (cavity formation) and attractive (cohesive energy) contributions. It is hoped that future studies will go beyond the present work in using these experimental global thermodynamic results to critically test and refine both theoretical and numerical predictive liquid modeling strategies. One such theoretical analysis, using the perturbed hard fluid (PHF) model, is currently in progress. Acknowledgment. Support for this work from the National Science Foundation (Grant CHE-0092580) is gratefully acknowledged. References and Notes (1) Cramer, C. J.; Truhlar, D. J. Chem. ReV. 1999, 99, 2161. (2) SolVent Effects and Chemical ReactiVity; Tapia, O., Bertran, J., Eds.; Kluwer-Dordrecht: New York, 1996. (3) Fawcett, W. R. J. Phys. Chem. B 1999, 103, 11181. (4) Pratt, L. R.; Laviolette, R. A. Mol. Phys. 1998, 94, 909; Pratt, L. R.; Rempe, S. B. In Simulation and Theory of Electrostatic Interactions in Solution; Pratt, L. R., Hummer, G., Eds.; American Institute of Physics: New York, 1999. (5) Lazaridis, T. J. Phys. Chem. B 2000, 104, 4964. (6) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471. Parrinello, M. Solid State Commun. 1997, 102, 107. (7) Gift, A. D.; Ben-Amotz, D. J. Phys. Chem. A 2000, 104, 11459. (8) Melendez-Pagan, Y.; Taylor, B. E.; Ben-Amotz, D. J. Phy. Chem. B 2001, 105, 520. (9) Kato, M.; Abe, I.; Taniguchi, Y. J. Chem. Phys. 1999, 110, 11982. (10) Bernstein, H. J. J. Chem. Phys. 1949, 17, 258. (11) Seki, W.; Choi, P.-K.; Takagi, K. Chem. Phys. Lett. 1983, 98, 518. (12) Abraham, R. J.; Pachler, K. G. R.; Wessels, P. L. Z. Phys., Chem. Neue Folge 1968, 58, S. 257-267, 17. (13) Taniguchi, Y.; Takaya, H.; Wong, P. T. T.; Whalley, E. J. Chem. Phys. 1981, 75, 4815. (14) Kuratani, K.; Miyazawa, T.; Mizushima, S.-I. J. Chem. Phys. 1953, 21, 1411. (15) Nomura, H.; Murasawa, K.; Ito, N.; Iida, F.; Udagawa, Y. Bull. Chem. Soc. Jpn. 1984, 57, 3321. (16) Takaya, H.; Taniguchi, Y.; Wong, P. T. T.; Whalley, E. J. Chem. Phys. 1981, 75, 4823.

McClain and Ben-Amotz (17) Ikawa, S.; Whalley, E. J. Chem. Phys. 1984, 81, 1620. (18) Piercy, J. E. J. Chem. Phys. 1965, 43, 4066. (19) Tanabe, K. Spectrochim. Acta 1972, 28A, 407. (20) Rank, D. H.; Kagarise, R. E.; Axford, W. E. J. Chem. Phys. 1949, 17, 1354. (21) Bernstein, H. J. J. Chem. Phys. 1950, 18, 897. (22) Abraham, R. J.; Bretschneider, E. In Internal Rotation in Molecules; Orville-Thomas, W. J., Ed.; Wiley-Interscience: New York, 1974; Chapter 13. (23) Herrebout, W. A.; van der Veken, B. J. J. Phys. Chem. 1996, 100, 9671. (24) Wiberg, K. B.; Keith, T. O.; Frisch, M. J.; Murcko, M. J. Phys. Chem. 1995, 99, 9072. (25) Wong, M. W.; Frisch, M. J.; Wiberg, K. B. J. Am. Chem. Soc. 1991, 113, 4776. (26) Depaepe, J.-M.; Ryckaert, J.-P. Chem. Phys. Lett. 1995, 245, 653. (27) Wiberg, K. B. J. Org. Chem. 1999, 64, 6387. (28) Richardson, A. D.; Hedberg, K.; Wiberg, K. B. J. Phys. Chem. A 1999, 103, 7709. (29) Ul’yanova, O. D.; Ostrovskii, M. K.; Pentin, Yu. A. Zh. Fiz. Khim. 1970, 44, 562. (30) Kozima, K.; Sakashita, K.; Maeda, S. J. Am. Chem. Soc. 1954, 76, 1965. (31) Abraham, R. J.; Rossetti, Z. L. J. C. S. Perkin II 1973, 582. (32) Kozima, K.; Sakashita, K. Bull. Chem. Soc. Jpn. 1958, 31, 796. (33) Abraham, R. J.; Siverns, T. M. J. C. S. Perkin II 1972, 1587. (34) Buys, H. R.; De Vries, H. J. A.; Hageman, H. J.; Altona, C. Recueil 1970, 89, 245. (35) Altona, C.; Buys, H. R.; Hageman, H. J.; Havinga, E. Tetrahedron 1967, 23, 2265. (36) Hu, M.-H. A.; de Souza, L. E. S.; Lee, M.-R.; Ben-Amotz, D. J. Chem. Phys. 1999, 110, 249. (37) Pratt, L. R.; Hsu, C. S.; Chandler, D. J. Chem. Phys. 1978, 68, 4202. Chandler, D.; Pratt, L. R. J. Chem. Phys. 1976, 65, 2925. Chandler, D. Faraday Discuss. Chem. Soc. 1978, 66, 184. (38) Chandler, D.; Weeks, J. D.; Andersen, H. C. Science 1983, 220, 787. (39) Jorgensen, W. L. J. Phys. Chem. 1983, 87, 5304. (40) Florian, J.; Warshel, A. J. Phys. Chem. B 1999, 103, 10282. (41) Rashin, A. A.; Bukatin, M. A. Biophys. Chem. 1994, 51, 167. (42) Luo, H. Q.; Tucker, S. C. J. Phys. Chem. 1996, 100, 11165. (43) Merrill, L.; Bassett, W. A. ReV. Sci. Instrum. 1974, 44, 290. (44) Forman, R. A.; Piermarini, G. J.; Barnett, J. D.; Block, S. Science 1972, 176, 284. (45) Barnett, J. D.; Block, S.; Piermarini, G. ReV. Sci. Instrum. 1973, 44, 1. (46) Nestor, J. R.; Lippincott, E. R. J. Raman Spectrosc. 1973, 1, 305. (47) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; HeadGordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.9; Gaussian, Inc.: Pittsburgh, PA, 1998. (48) Kuratani, K.; Miyazawa, T.; Mizushima, S. J. Chem. Phys. 1953, 21, 1411. (49) Ben-Amotz, D. J. Phys. Chem. 1993, 97, 2314. (50) Ben-Amotz, D.; Omelyan, I. P. J. Chem. Phys. 2001, 115, 9401. (51) Ravi, R.; de Souza, L. E. S.; Ben-Amotz, D. J. Phys. Chem. 1993, 97, 11835. (52) Widom, B. Science 1967, 157, 375. Longuet-Higgins, H. C.; Widom, B. Mol. Phys. 1964, 8, 549. (53) Ben-Naim, A. Biopolymers 1975, 14, 1337; Ben-Naim, A. J. Phys. Chem. 1978, 82, 874. (54) Grunwald, E.; Steel, C. J. Am. Chem. Soc. 1995, 117, 5687. (55) Lee, B. Biophys. Chem. 1994, 51, 271.