9072
J. Phys. Chem. 1995,99, 9072-9079
Solvent Effects on 1,2-Dihaloethane Gauchmrans Ratios Kenneth B. Wiberg,*9la Todd A. Keithtb Michael J. Frischtb and Mark MurckolC Chemistry Department, Yale University, New Haven, Connecticut 06520; Lorentzian Inc., 140 Washington Avenue, North Haven, Connecticut 06473, and Vertex Pharmaceuticals Inc., Cambridge, Massachusetts 02139 Received: February 13, 1995; In Final Form: March 28, 1995@
The effect of solvent on the conformational equilibria for 1,2-dichloroethane and 1-chloro-2-fluoroethane was reinvestigated via IR spectroscopy and was examined theoretically via a new reaction field model. Cyclohexane solutions led to about one-third of the maximum solvent effect between the gas phase and a polar aprotic solvent. The G2(MP2) theoretical model led to trandgauche energy differences in good agreement with the gas phase experimental data. The reaction field model, using the MP2/6-31 l+G** and Becke3LYP/ 6-31 l+G** theoretical levels, reproduced the experimental solvent effects, but the latter proved to be the more successful. Geometry optimization for a relatively high dielectric constant medium was carried out at the Becke3LYP level. The changes in structure and energy were relatively small.
Introduction We have been interested in the effect on equilibrium constants and rate constants of going from the gas phase to solutions.z Here, it is important to examine solvents having both small and large dielectric constants. Reaction field theory3 suggests that about 40% of the effect of going from the gas phase to a high dielectric constant solvent will be realized on going to cyclohexane as the solvent. Is this correct? Unfortunately, there are relatively few experimental data available for testing this hypothesis, since data are needed for both the gas phase and for solutions. One of the few sets of data are for the I,Zdihaloethanes, and they will be examined in this report along with new experimental data. The results allow us to make a comparison of the observed solvent effects with those predicted using a new self-consistent reaction field model4 which is based on the Tomasi polarizable continuum modeL5 This model allows solvent effects to be calculated efficiently at the HF,MP2, QCISD, and DFT levels of theory. it also allows geometry optimization at the HF and DFT levels. The results obtained using the MP2/6-311+G** and Becke3LYP/6-31l+G** levels6 will be compared.
Experimental and Theoretical Gas Phase Energy Differences The molecule for which the largest number of gas phase studies is available is 1,2-dichloroethane. Electron diffraction studies led to AH = 1.05 f 0.10 with the trans form having the lower energy.' The temperature dependence of the IR band intensities gave A H = 1.10 f 0.05,* 1.09 f0.06? 1.03 f0.10,'O and 1.15 f 0.15 kcal/mol.ll Photoelectron spectroscopy gave 1.0 f 0.2 kcal/mol.'* It would appear that 1.10 f 0.10 is well established as the enthalpy difference. The experimental data for 1,Z-difluoroethane agree that here the gauche form has the lower energy. The origin of this preference has been explained in terms of the differences in the C-C bonds of the two conformers that result from the bond bending caused by the fluorine substituent^.'^ Electron diffraction studies gave energy differences of - 1 to -2 kcal/mol with large uncertainties.I4 A variable-temperature matrix isolation study gave an energy difference of -0.59 f 0.09 kcall mol,I5 and a gas phase NMR study gave one of -0.83 kcall @
Abstract published in Advance ACS Abstracts, May 1, 1995.
mo1.I6 A more recent analysis of the vibrational spectrum gave AH = -0.8 f0.1 kcal/mol,17and an analysis of the temperature dependence of the dielectric constant gave -1.0 f 0.3.'* We will use -0.8 f 0.1 in the following discussion. 1-Fluoro-2-chloroethanehas received less study, but a recent investigation of its vibrational spectrum found the trans form to have the lower energy, with an energy difference of 0.82 f 0.08 kcal/m01.'~ This is surprisingly close to that for the dichloride, in view of the reversed conformational preference for the difluoride. The theoretical estimates of the gauche/trans energy difference for 1,2-dichloroethane have converged on about 1.5 kcal/ mol,zo,zlwhich is significantly larger than the experimental values. In order to obtain a better estimate of the energy difference, we have carried out geometry optimization at several theoretical levels (MP2/6-31l+G**, MP2/6-3 1l++G**, and Becke3LYP/6-311+G*) and then obtained the G2(MP2) energieszzusing the MP2/6-31+G** geometry. This level of theory is known to given very satisfactory relative energies. It is essentially QCISD(T)/6-31l+G(3df,2p) plus correction for the zero point energy and a higher level correction. The latter will cancel in all comparisons in this report. The energies are given in Table 1, and the geometries are summarized in Table 2. As part of the GZ(MP2) procedure, one obtains the MP2/6-3 11+G(3df,2p) energy, and this is also given in Table 1. The energies were converted to 298 K in the usual mannerz3 using the calculated HF/6-3lG* vibrational frequencies scaled by 0.893.24 The GZ(MP2) calculated enthalpy difference between gaucheand trans-l,2-dichloroethane(1.1 1 kcal/mol) is in complete agreement with the experimental value (1.1 f 0.1 kcal/mol). This agreement required the inclusion of higher angular momentum functions (3df,2p), and smaller basis sets gave energy differences that were too large. The energy differences for 1,2-dichloroethane and 1-fluoro2-chloroethane were obtained in the same fashion. The GZ(MP2) calculated enthalpy difference between gauche- and trans- 1,Z-difluoroethanewas again in very good agreement with experiment (calc -0.81 kcal/mol, expt -0.8 f 0.1 kcal/mol). Here, all of the theoretical levels that were used gave essentially the same result. With l-fluoro-2-chloroethane,the GZ(MP2) calculated enthalpy difference, 0.47 kcal/mol, is somewhat smaller than the experimental value, 0.8 f 0.1 kcal/mol. This difference also is surprising in view of the very good agreement between calculation and experiment for the dichloro and
0022-3654/95/2099-9072$09.00/0 0 1995 American Chemical Society
1,2-Dihaloethane GaucheErans Ratios
J. Phys. Chem., Vol. 99, No. 22, 1995 9073
TABLE 1: G2/MP2 Calculated Energief AH
AG level
a
trans
MP2/6-311+G** opt MP2/6-311++G** opt Becke3LYP/6-31 l+G** opt MP2/6-3 11+G(3df,2p) ZPE (kcaymol) S” (cal/(mol K)) G2NP2
-997.683 -997.684 -999.101 -997.838 35.27 72.18 -997.913
92 53 11 75
MP2/6-311+G** opt MP2/6-31 l++G** opt Becke3LYP/6-3 11+G** opt MP2/6-311+G(3df,2p) ZPE (kcaUmo1) S‘ (caV(mo1 K)) G2NP2
-637.701 -673.702 -638.742 -637.855 36.23 70.98 -637.919
86 37 83 61
MP2/6-311+G** opt MP2/6-31 l++G** opt Becke3LYP/6-311+G** opt MP2/6-3 1l+G(3df,2p) ZPE (kcaVmo1) 5” (caV(mo1 K)) G2NP2
-277.718 -277.719 -278.383 -277.872 37.16 67.1 1 -277.925
77
98 78 71 59 37 82
gauche 1,2-Dichloroethane -997.681 66 -997.682 22 -999.098 77 -997.836 90 35.24 71.91 -997.911 87 1-Chloro-2-fluoroethane -637.701 07 -637.701 48 -638.742 04 -637.854 80 36.21 70.74 -637.919 12 1,2-Difluoroethane -271.719 99 -277.720 36 -278.384 87 -277.873 78 37.15 66.85 -277.927 01
AE 1.42 1.45 1.46 1.16
0.50 0.56 0.50 0.5 1
-0.76 -0.75 -0.80 -0.88
OK
298 K
298 K
1.39 1.42 1.43 1.13
1.32 1.35 1.36 1.06
1.40 1.43 1.44 1.14
1.19
1.12
1.20
0.48 0.54 0.48 0.49
0.42 0.48 0.42 0.43
0.49 0.55 0.49 0.50
0.54
0.48
0.55
-0.77 -0.76 -0.8 1 -0.89
-0.83 -0.82 -0.87 -0.95
-0.75 -0.74 -0.79 -0.87
-0.75
-0.81
-0.73
The energies are given to 0.01 to avoid round off errors. They are significant to 0.1 kcaUmol.
TABLE 2: MP2/6-31+G** and Becke3LYP/6-31+G** Calculated Structures MP2 parameter
obs
B3LYP
trans
gauche
r(C-C1) r(C-C) L(C-C-Cl) t(C1-C-C-C1)
1.782 1.515 109.2 180.0
1.777 1.514 112.1 67.3
r(C-C1) r(C-F) r(C-C) L(C-C-C1) L(C-C-F) t(F-C-C-CI)
1.779 1.393 1.515 108.3 108.8 180.0
1.778 1.388 1.509 111.5 110.2 67.3
r(C-F) r(C-C) L(C-C-F) z(F-C-C-F)
1.392 1.516 107.9 180.0
1.389 1.504 110.3 69.8
trans Dichloroethane“ 1.817 1.515 109.2 180.0 1-Chloro-2-fluoroethaneb 1.811 1.401 1.517 109.3 107.9 180.0 1,2-Diflu~roethane~ 1.399 1.519 108.0 180.0
gauche
trans
1.809 1.512 112.9 69.7
1.790(4) 1.531(4) 109.0(4) 180.0
gauche
1.811 1.394 1.508 112.5 110.8 69.6
1.787(20) 1.365(20) 1.530(20) 111.1(10) 109.7(10) 68.3(20)
1.397 1.505 110.8 72.0
1.390(3) 1.493(8) 110.6(5) 7 1.0(3)
Reference 7. Mukhtarov, I. A.; Mukhtarov, R. I. Zh. Fiz. Khim. 1968, 42, 2025. Takeo, H.; Matsumura, C.; Morino, Y. J. J . Chem. Phys.
1986, 84, 4205. difluoroethanes, along with the remarkable agreement in energy differences for the several levels of theory. One might wonder if there may be some problem with the interpretation of the experimental data. On the other hand, the difference between the calculated and experimental values is quite small (0.3 kcal/ mol). The structural parameters also are of interest (Table 2). With difluoroethane there is little difference between the MP2 and Becke3LYP geometries, and both agree very well with the observed geometry. The uncertainty in the experimental parameters for fluorochloroethane is somewhat larger, and the calculated parameters agree with the experimental values within the stated uncertainties. The C-C1 bond lengths calculated at the Becke3LYP level are systematically larger than the MP2 lengths, and the experimental values are between the two. The
agreement between experiment and theory for the dichloroethane also is satisfactory.
Conformational Free Energy Differences Determined via IR Spectroscopy
It has been found that the C-Cl stretching modes for the trans and gauche forms of 1,2-dichloroethane are well separated in the infrared spectrum (727 for the antisymmetric C-C1 stretch of the former and 669 cm-’ for the symmetric C-C1 stretch of the latter). The effect of solvent on the ratio of the sizes of these bands has been used by Oi and C ~ e t z e eand ~ ~ by El Bermani et a1.26in order to determine the relative free energy differences. However, with the equipment available at that time, it was only practical to make use of band heights, whereas the band areas provide a better measure. It is now relatively easy
Wiberg et al.
9014 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 3: Observed Energy Differences, kcaYmol medium
E
AJA,
RT In(2At/A,)
0
AGO
gas cyclohexane di-n-butyl ether tetrahydrofuran acetone acetonitrile
1,2-DichIoroethane 1.00 21.9 f 1.7 2.02 9.5 f 0.5 3.06 6.9 f 0.2 7.58 3.5 f 0.2 20.7 2.3 f O . l 36.0 2.0 f 0.1
2.24 f 0.04 1.74 f 0.03 1.55 f 0.02 1.15 f 0.04 0.90 f 0.03 0.82 f 0.03
1.20 0.70 0.5 1 0.11 -0.14 -0.22
gas cyclohexane di-n-butyl ether tetrahydrofuran acetone
1-Chloro-2-fluoroethane 1.00 2.1 f O . l 0.85 h 0.03 2.02 0.97 f 0.03 0.39 f 0.02 3.06 0.61 f 0.02 0.12 f 0.02 7.58 0.32 f 0.01 -0.26 f 0.02 20.7 0.19 f 0.01 -0.57 h 0.03
0.55 0.09 -0.18 -0.56 -0.87
.
2
0
1
1
I d
I
0.00
700
680
640
660
Frequency, cm-1
Figure 2. Expanded view of the gauche C-CI symmetric stretching mode. 1.5
-8
1.0
a E s
i t
4
0.5
B
i
750
700
650
Frequency, cm-1
3
0.c
6
Figure 1. IR spectrum of 1,2-dichloroethane showing the bands for the trans and gauche C-C1 stretching modes. 4.E 0.0
to obtain the latter using a FT-IR spectrometer. The relative areas were determined in a number of solvents and in the gas phase, and are recorded in Table 3. The solvents were chosen to give a fairly uniform distribution in the Onsager function, ((E - 1 ) / ( 2 ~ l)), and did not include aromatic or halogenated solvents. The latter are known to give larger than expected solvent effects, presumably due to their enhanced polarizabilities.*' There is fairly good agreement between the present results and those previously reported for 1,Zdichloroethane, except for the gas phase. Here, a ratio of 13.4 was foundI5 whereas an examination of the spectrum (Figure 1) suggests a significantly larger ratio. The band of interest for the gauche conformer was significantly overlapped by the antisymmetric C-C1 stretching mode at 669 cm-' (Figure 2). The relative intensity with respect to the 727 cm-' band was determined by integrating the right hand half of the band and multiplying by two. This gave an intensity ratio of 21.7 f 1.7, which should be a minimum value, since the 669 cm-' band may still have a small contribution from the other band. It should be noted that there are two equivalent gauche forms, and thus on a per molecule basis the correct ratio is 2A,/Ag. The quantities RT ln(2A,/Ag)represent the relative free energy changes, and they are compared with the Onsager function, ( E - 1)/(2~ 1) in Figure 3. There is a small amount of curvature, and cyclohexane gives about 33% of the total solvent effect, in good agreement with the prediction of reaction field theory.
+
+
0.1
0.2
0.3
0.4
0.5
Onsager function
Figure 3. Correlation between the observed free energy differences and the Onsager function for 1,2-dichIoroethane.
4
-1
Onsager function
Figure 4. Correlation between the observed free energy differences and the Onsager function for 1-fluoro-2-chloroethane.
L2-Dihaloethane Gauchemrans Ratios
J. Phys. Chem., Vol. 99, No. 22, 1995 9075
TABLE 4: Calculated (6-31+G**) and Observed Infrared Bands for 1,ZDichloroethanP trans gauche mode MP2 B3LYP obs mode MP2 A,
VI v2
v3 v4
v5 v6
A,
v7 V8 v9 VI0
B,
VI1
VI2 VI3
B"
VI4
VI5 VI6
VI7 VI8
3136 1500 1394 1101 827 315 3220(3.7) 1191(2.4) 797( 1.2) 132(6.0) 3199 1325 1054 3 144(17.8) 1497(4.6) 1312(43.2) 785(78.5) 22 l(8.4)
3097 1490 1341 1060 743 295 3175(3.3) 1149(1.1) 781(2.1) 118(6.1) 3152 1229 1013 3015(14.9) 149l(6.8) 1269(40.4) 697(112.7) 213( 10.4)
2979 1431 1310 1057 772 305 3009 1124 772 122 3001 1267 996 2983 1461 1233 727 221
A
VI
v2 v3
v4 v5 v6
v7
V8 v9 VI0
B
VII
VI2 VI3 VI4
VI5 VI6 VI7 VI8
3186( 1.4) 3125(25.2) 1483(0.1) 1393(20.8) 1266(1.4) 1086(0.7) 995(9.2) 7 13(16.2) 272(0.6) 128(0.7) 3197(4.9) 3 118(4.4) 1474(11.7) 1374(36.0) 1206(1.7) 929( 17.7) 738( 18.2) 424(6.7)
B3LYP
obs
3134(0.6) 308 l(23.4) 1470(1.O) 1349(20.0) 1234(1.1) 1047(0.9) 950( 12.0) 648(27.2) 264( 1.O) 114(0.9) 3147(4.5) 3072(3.3) 1466(13.O) 1328(44.4) 1169(1.2) 896(20.9) 670(33.0) 408(9.6)
3005 2966 1446 1315 1214 1028 950 669 263 125 3005 2957 1436 1292 1146 89 1 694 41 1
The calculated intensities (kdmol) are given in parentheses. The observed were taken from ref 9.
TABLE 5: Calculated (Becke3LYFV6-3ll+G**) and Observed Infrared Bands for 1-Chloro-2-fluoroethane" trans gauche mode calc obs mode calc
A"
a
3096( 16.1) 3063(16.5) 151l(2.6) 149l(4.2) 1409(2.7) 1289(12.4) 1069(11.0) 1017(131.3) 750(5 1.O) 376(2.8) 241 ( 13.2) 3162(8.2) 31 16(12.6) 129qO.l) 1216(0.9) 1061(1.9) 797(0.7) 126(10.9)
2984 2966 1467 1436 1397 1306 1090 1052 779 383 245 3025 3010 1258 1200 964 847 138
3143(5.6) 3099(20.1) 3081( 11.8) 3035(25.3) 1490(4.1) 1463(9.9) 1416(10.7) 1336(34.1) 1272(0.3) 1216(2.2) 1090(40.4) 1047(59.1) 969(9.5) 848( 15.4) 662(34.3) 462( 14.7) 286( 1.2) 130(2.5)
obs 3025 2988 2978 2966 1467 1436 1387 1306 1258 1200 1071 1038 964 847 688 467 286 128
The calculated intensities (kdmol) are given in parentheses. The observed values were taken from ref 19.
1-Chloro-2-fluoroethane was studied in the same fashion (Table 3). The band ratios are in good agreement with those previously reported, including the gas phase data. Here, the bands were not overlapped, and the integrals were easily obtained. A plot of RT 1n(2A,/Ag)against the Onsager function is shown in Figure 4. The data show a small degree of curvature, and again cyclohexane gives about 30% of the total solvent effect. The relative free energies derived from the intensity ratios differ from the correct free energies as a result of the difference in the absorbancy indices for the bands being compared. The latter are not known, but if the calculated gas phase free energies are taken as correct, the relative energies may be converted to the free energy differences via a constant factor (Table 3). It is not, however, clear if this is completely correct, for it assumes that the ratio of absorbancy indices for the two bands remains constant on going from the gas phase to a polar solvent. Even if it were to vary somewhat, it would be expected to respond to the polarity of the solvent in the same fashion as the conformational energy difference. Thus, at worst, the relative free energies in the Table might need to be scaled linearly. Solvent effects on the 1,2-difluoroethane conformers have been studied via NMR making use of the change in coupling
constants.** However, the interpretation of the results made use of a classical reaction field model, and they cannot be considered as purely experimental data.
Calculated Infrared Spectra It might be possible to examine the question as to whether or not polar solvents will affect the relative intensities of the infrared bands making use of the reaction field model. But, first, it is necessary to see how well calculations reproduce the gas phase spectra. The vibrational transitions for both transand gauche- 1,2-dichloroethane were calculated using MP2/63 1+G** and Becke3LYFV6-31+G** levels of theory. The MP2 level of theory gives vibrational frequencies in much better accord with the experimental values than RHF,29 density functional theory (DIT) calculations might be expected to do equally The results are shown in Table 4 and are compared with the observed f r e q u e n c i e ~ . ~ ~ The observed transitions are fairly well reproduced at the MP2 level of theory, but the Becke3LYP level gives a significantly better fit. Leaving out the CH stretching modes, which are considerably shifted due to anharmonicity, the root mean square (rms) deviation between the calculated and observed transitions is only 25 cm-' without scaling the calculated frequencies.
9076 J. Phys. Chem., Vol. 99, No. 22, 1995
Wiberg et al.
TABLE 6: Calculated Solvent Effects, MP2/6-311+G** (0) E
trans
fi
1.o 2.02 3.06 20.7 47.0
-997.689 -997.690 -997.690 -997.691 -997.691
17 09 52 47 58
1.o 2.02 3.06 20.7 47.0
-637.711 -637.712 -637.713 -637.714 -637.714
29 68 30 59 74
1.o 2.02 3.06 20.7 47.0
-277.703 -277.705 -277.706 -277.708 -277.708
82 79 64 38 57
gauche
1,2-DichIoroethane 0.000 -977.687 02 0.000 -997.688 38 0.OOO -997.689 05 0.000 -997.690 55 0.000 -997.690 72
fi
2.686 2.904 3.014 3.267 3.298
1-Chloro-2-fluoroethane 0.213 -637.710 56 2.86 0.244 -637.712 47 3.09 0.253 -637.713 37 3.193 0.266 -637.715 32 3.435 0.267 -637.715 55 3.464 1,2-Difluoroethane 0.000 -277.705 10 3.082 0.000 -277.707 77 3.307 0.000 -277.708 98 3.409 0.000 -277.711 55 3.633 0.000 -277.711 85 3.659
AE
1.35 1.07 0.92 0.58 0.54
AG'
1.20 0.92 0.77 0.43 0.39
0.55 0.46 0.13 0.22 -0.04 0.05 -0.46 -0.37 -0.51 -0.42 -0.80 -1.24 -1.46 -1.99 -2.06
-0.73 -1.17 - 1.39 - 1.92 - 1.99 MP2 energy differences
TABLE 7: Calculated Solvent Effects, Becke3LYP/ 6-311+G** (6D) . . E
trans
iu
1.o 2.02 3.06 20.7 47.0 47.0"
-999.103 -999.105 -999.105 -999.107 -999.107 -999.107
53 02 68 07 23 28
1.o 2.0 3.06 20.7 47.0 47.0"
-638.745 -638.747 -638.747 -638.749 -638.749 -638.749
45 37 99 58 53 83
1.o 2.02 3.06 20.7 47.0 47.0"
-278.386 59 278.388 65 -278.389 54 -278.391 34 -278.391 54 -278.391 64
gauche
1,2-Dichloroethane 0.000 -999.101 04 0.000 -999.103 15 0.000 -99.104 14 0.000 -999.106 32 0.000 -999.106 58 0.000 -999.106 68
p
2.920 3.243 3.358 3.685 3.726 3.815
1-Chloro-2-fluoroethane 0.078 -638.744 75 3.002 0.062 -638.747 20 3.266 0.054 -638.748 33 3.391 0.044 -638.750 78 3.675 0.043 -638.751 07 3.710 0.061 -638.751 25 3.847 1,2-Difluoroethane 0.000 -278.387 92 3.021 0.000 -278.390 71 3.243 0.000 -278.391 97 3.347 0.000 -278.394 67 3.577 0.000 -278.394 98 3.605 0.000 -278.395 24 3.796
AE
Figure 5. Relationship between solvent effects calculated at the MP2/ AG'
1.56 1.17 0.97 0.47 0.41 0.38
1.20 0.8 1 0.61 0.1 1 0.05 0.02
0.44 0.1 1 -0.21 -0.75 -0.97 -0.89
0.55 0.22 -0.10 -0.64 -0.86 -0.78
-0.83 -1.29 -1.52 -2.09 -2.16 -2.26
-0.73 -1.19 - 1.42 - 1.99 -2.06 -2.16
a These energies were calculated at the E = 47 optimized geometries. The other entries were calculated using the gas phase geometries.
The calculated relative intensity for ~ 1 of7 the trans conformer and Y8 of the gauche conformer is 4.1 at the DFT level of theory and 4.8 using MP2. The observed intensity ratio, based on the data in Table 2, is 5.8. Although the DFT level of theory gives a ratio that is somewhat too small, it should be able to give a reasonable estimate of the change in ratio on going from the gas phase to solution. Using the SCRF model described in the next section, the dipole moment derivatives for the antisymmetric C-Cl stretching symmetry coordinate (AS = 0.14) of the trans conformer and the symmetric C-Cl stretching symmetry coordinate of the gauche form were calculated for both the gas phase and for a solvent having E = 20.7 (acetone). The dipole moment derivatives for the trans conformer were 4.815 and 5.993 for E = 1 and 20.7, respectively, and the corresponding values for the gauche conformer were 2.623 and 3.420. Since IR intensities are proportional to the dipole moment derivatives squared, the calculated intensity ratio for the gas phase is 3.4 and that for acetone solution is 3.1. This will result in a change in AG
6-31 1+G** and Becke3LYP/6-31l+G** theoretical levels. The slopes are 1.32 for dichloroethane, 1.21 for chlorofluoroethane, and 1.00 for difluoroethane.
of 0.05 kcal/mol for acetone solution. This is probably within the uncertainty of the calculations and may be considered to be negligible. The vibrational spectra of 1-chloro-2-fluoroethane also were examined using density functional theory. The calculated and observed frequenciesI8 are compared in Table 5. Here, the rms deviation between observed and calculated frequencies was only 18 cm-' for the gauche form but 40 cm-' for the trans form (31 cm-' overall). The unusually large deviation between the calculated and observed values for Y16 of the trans form suggests that it may have been misassigned and may be under the strong band at 1071 cm-' of the gauche form. The gas phase observed intensity ratio and the assigned AG value imply that the band used for the trans form absorbs more strongly than that for the gauche form, with a ratio of 1.7. The calculated intensities are in accord with this order, and the calculated ratio (Table 5, ~9 for trans and ~ 1 for 5 gauche) is close to the observed ratio (1S ) . The effect of solvent on the ratio of intensities for the two conformers was estimated as described above. The calculated ratio increased from 1.8 in the gas phase to 2.0 in acetone solution. This will again lead to only a small change in the AG values and may be considered to be negligible.
Calculated Solvent Effects Reaction field theory3 provides a means of estimated solvent effects for cases where the solvent does not give a specific interaction with the solute, such as hydrogen bonding. In this model, the solute is placed in a cavity in the solvent which is taken as an unstructured dielectric continuum. The electric moments of the solute lead to reflection moments in the solvents that are aligned to give an attractive interaction, reducing the energy of the solute. In the case of the dihaloethanes, even though the trans isomers have no dipole moments, they have fairly large quadrupole moments. As a result, both the gauche and trans conformers will have their energies reduced on going from the gas phase to solution. Thus, the simple spherical cavity/dipole model is not adequate. The use of an elliptical cavity and considering higher electric moments is an impr~vement.~' However, even
1,ZDihaloethane G a u c h e h m s Ratios
J. Phys. Chem., Vol. 99, No. 22, 1995 9077 TABLE 8: Effect of Solvent on Structures, BeckeJLYP/ 6-311+G**, E = 47.0
1.o
/
J
I
trans €=I
€=l
€=47
1.512 1.810 112.9 69.9 2.92 1.56
1SO5 1.820 112.8 68.6 3.82 0.38
z(F-C-C-Cl) P E(re1)
1-Chloro-2-fluoroethane 1.517 1.516 1.508 1.401 1.411 1.395 1.813 1.817 1.811 110.9 107.9 107.6 109.2 108.9 112.5 70.0 180.0 180.0 0.073 0.137 3.00 0.44 0.00 0.00
1.505 1.408 1.822 110.6 112.2 67.4 3.85 -0.89
r(C-C) r(C-F) LC-C-F t(F-C-C-F) iu E(re1)
1,2-Difluoroethane 1.519 1.518 1.399 1.409 108.1 107.6 180.0 180.0 0.00 0.00 0.0 0.0
1.501 1.411 110.3 69.4 3.80 -2.26
r(C-C) r(C-CI) LC-C-C1 t(C1-C-C-Cl) iu E(re1) r(C-C) r(C-F) r(C -Cl) LC-C-F
c-c-c1 -0.5
0.0
0.5
1.0
1.5
Observed energy difference, kcal/mol
gauche €=47
1,2-Dichloroethane 1.515 1.514 1.818 1.824 109.2 108.9 180.0 180.0 0.000 0.000 0.00 0.00
1.505 1.396 110.9 71.8 3.02 -0.83
where A(rJ is the outward normal vector at r,. The solute Hamiltonian in solution is given by
-0.8 4
-1
I 1
0
Observed energy difference, kcal/mol
Figure 6. Comparison of calculated and observed solvent effects. The slopes of the lines are (a) 0.82 for dichloroethane and (b) 0.85 for chlorofluoroethane.
this approximation is not fully adequate. Therefore we have developed a new self-consisting reaction field model,4 based on Tomasi' s polarizable continuum (PC) modeL5 In this model, a solute molecule is placed in a cavity within the solvent, which is treated as a simple dielectric characterized by its bulk dielectric constant ( E ) . The electric field EOfrom the solute charge distribution indcues a dipole density distribution P within the solvent
P(r) = (1 - €)E@)= (1 - E ) ( Z 0 ( T )
+Ep@))
where g ( r ) is the total electric field at point r in the solvent, including that from P itself, Ep(r). Taking advantage of Gauss' law, the potentia! from solvent polarization appears in the solute Hamilitonian H in terms of a distribution of charge density, UP, over the solute cavity surface. At a point rs on the cavity surface u p is given by
op(rs)= - [ ( E - 1)/4n~IE(r,).iz(r,)=
where $O) is the corresponding gas phase Hamiltonian, the first summation is the operator for the interaction between electrons and the solvent, and the second summation is the operator for the interaction between the nuclei and the solvent. The solute wave function Y and the energy E are thus modifi$d in the presence of the solvent. It should be_noted that since H depends on the solute wave function (via EO),proper application of a PC model must lead to self-consistencybetween Y and P. The (electrostatic) solvation free energy AGsol within a PC model is given by the difference between the expectation value of the solute Hamiltonian in solution, E, and in the gas phase, Po),plus the free energy required to polarize the solvent, EPl, which is assumed to be minus one-half of the interaction energy between the solvent and s01ute.~ In the general case, one must also consider the energy of forming the cavity, and the dispersive interaction between solvent and s01ute.~However, for the conformational processes described herein, these terms would be expected to be essentially the same for the two conformers and can be neglected. For general solute charge distributions and/or general cavity shapes, the potential integrals from u must be calculated numerically, Le., as a sum of contributions from a finite number of points on the cavity surface each with an appropriate position and weight. The solute electronic contribution to u p at the relatively large number of surface grid points (typically -4000) is calculated very efficiently using the PRISM algorithm.32The calculations may be efficiently carried out at the RHF, MP2, QCISD, and D I T levels of theory. As an example, RHF energy calculations require only 20-50% more computer time than the standard gas phase calculations. W e have chosen to define the solute cavity explicitly in terms of a property of the solute, an isosurface of its electron distribution, which is generally considered to provide a reason-
Wiberg et al.
9078 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 9: Effect of Basis Set and Volume on Calculated Solvent Effect for l&Dffluoroethane basis MP2/6-3 1+G* MP2/6-311+G*
e”
volb
E
0.0004 0.0004 0.0004 0.0004 0.0005 0.001
56.3 56.3 56.2 56.2 53.2 44.7
1 20.7 1 20.7 20.7 20.7
cis
AE
-277.549 34(3.091)c -271.555 gl(3.640) -217.705 lO(3.082) -277.71 1 55(3.633) -277.71 1 98(3.659) -277.713 B(3.742)
0.51 1.77 0.80 1.99 2.01 2.06
trans -277.548 -271.552 -271.103 -217.708 -217.108 -217.710
52 99 82 38 77 30
AAEd 1.26 1.19 1.21 1.26
a The value of charge density chosen to define the cavity size. Calculated molar volume, mL/mol. Dipole moment, D. The change in AE on going from E = 1 to E = 20.7.
able definition of “molecular shape”. We have found that the molar volumes defined by the 0.0004 au isosurface are in good correspondence with the experimentally measured liquid molar volumes. For example, the calculated molar volumes of 1,2dichloroethane, 1-chloro-2-fluoroethane, and 1,2-difluoroethane are 85.5,73.3, and 58.7 mL and the observed volumes are 84.2, 70.2, and 61.8 mL, respectively. In the solvent effect calculations, both MP2/6-3 11+G** and Becke3LYP/6-31l+G** theoretical levels were used, giving the results shown in Tables 6 and 7. The dielectric constants used correspond to cyclohexane, di-n-butyl ether, acetone, and a larger value (DMSO, which proved not to be suitable for the IR study). The calculated gas phase values are somewhat different than the G2(MP2) values due to deficiencies in basis set and correction for electron correlation (cf. Table 1). However, the changes in energy with solvent depend only on the charge distribution, and it will not change much as long as reasonably good theoretical levels are used. Thus, to facilitate comparisons, the energies have been shifted (AG’) so that the gas phase values agree with the G2(MP2) calculations. The two sets of calculated energy changes are linearly related (Figure 5 ) with slopes close to unity. Since the Becke3LYP level was the more satisfactory for the vibrational spectra calculations, the solvent effects calculated at this level will be used in the following discussion. The calculated and observed solvent effects are compared in Figure 6. Using the experimental AG values and the solvent effects calculated at the gas phase geometries, the slope is 0.82 for dichloroethane and 0.85 for chlorofluoroethane. It can be seen that there is a good agreement between experiment and theory.
Geometry Optimization in the Presence of a Solvent It is readily possible to carry out geometry optimizations for compounds in solution at the HF and Becke3LYP levels of theory using analytical gradients including the partial derivatives with respect to the ~ a v i t y .The ~ Becke3LYP should be the more satisfactory theoretical level and was used with the 6-3 1l+G** basis set to give the results shown in Table 8. There are some systematic changes in structure, but they are not large. Similarly, the changes in the calculated solvent effects are quite small (Table 7). Effect of Cavity Size The question of the appropriate cavity size for these calculations has been raised many times.5 We have chosen the most conservative approach, making it as close to the observed molar volumes as possible. How large an error may result from this choice? This question is explored for the present case in Table 9. It can be seen that a fair range of volumes gives essentially the same effect. It will be of interest to see if this is generally the case. Experimental Section The IR spectra were obtained using a Midac FT/IR spectrometer. The resolution was 0.5 cm-’ for the gas phase spectra
and 1.0 cm-’ for the solution spectra. The gas phase spectra were obtained using a 10 cm gas cell and 20-40 mm of gas pressure. The spectra were repeated bringing the pressure to -760 mm with nitrogen, and no significant change in intensity or ratio of intensities was observed, suggesting that pressure broadening with higher pressures was not needed. The solution spectra were obtained using a 0.1 mm solution cell and 2% concentrations and were repeated using new solutions. The band ratios were in some cases checked with 4% solutions, and no significant change in ratio was observed. The band areas were obtained using the integration software, and the reported values are the averages of the experimental ratios. The baseline was essentially zero in all cases. Band overlap was not a problem except for the gas phase spectrum of 1,2-dichloroethane. Here, the band for the gauche conformer was integrated from the center of the band toward lower frequencies and the integral was multiplied by two before taking the ratio with respect to the trans conformer. The latter integration was carried out using a cut and weight procedure. Calculations. The ab initio calculations were carried out using Gaussian 93.33
Conclusions The difference in energy between the trans and gauche forms of the 1,2-dichaloethanes (X = C1, F) was reproduced at the G2(MP2) level of theory. The solvent effects on the gauche/ trans ratio determined by IR spectroscopy could be reproduced satisfactorily via self-consistent reaction field theory using a newly developed method at the Becke3LYP/6-31 l+G** theoretical level. Calculations of the vibrational frequencies at this level were in good agreement with the experimental frequencies.
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