10740
J. Phys. Chem. 1992, 96, 10740-10746
Conformatlonal Analysis of 1,P-Dlhaloethanes: A Comparison of Theoretical Methods David A. Jlixon,* Nobuyuki Matsuzawa,t and Scott C . Walker The Central Research and Development Department,$Experimental Station, E. Z. Du Pont de Nemours & Company (Znc.), P.O. Box 80328, Wilmington, Delaware 19880-0328 (Received: May 15. 1992) The geometries of the gauche and trans conformers and the two transition states connecting the conformers for the 1.2dihaloethanes have k e n calculated. The methods used in this study are the AM-1 and PM-3 parametrizations of the MNDO Hamiltonian, ab initio molecular orbital (MO)SCF and MP-2 with large basis sets and local density functional (LDF). The ab initio MO and LDF results are in good agreement with each other and with the available experimental data for the energetics and structures. The semiempirical methods show much poorer agreement with both experiment and the other calculations and are often qualitatively wrong. The gauche structure is calculated to be less stable than the trans by 1.78, 1.78, and 2.32 kcal/mol for X = CI, Br, and I at the highest level of calculation in contrast to the result found for X = F where the gauche is more stable than the trans. The rotation barrier between the two gauche structures ranges from 9.55 to 9.93 kcal/mol, and the rotation barrier between the trans and the gauche ranges from 5.06 to 5.77 kcal/mol for X = C1, Br and 1 at the highest level of calculation.
Introduction
TABLE I: Ex~erimenblRelative Eaamiea (kd/mol)g
The torsion potential in simple 1,2disubstituted ethanes plays an important role in conformational analysis. Such species have the additional feature of the presence of two stable conformers, trans and gauche. Although simple steric arguments suggest that the gauche conformer of 1,2-dihaloethanes should be less stable then the trans conformer,' it is well established from both experiment2and high-level ab initio calculations3 that the gauche conformer of 1 ,2-Muoroethane is about 1 kcal/mol more stable than the transu " e r . For other halogens, the transconformer is experimentally observed to be more stable than the gauche conformer, and the relative energy difference increases with increasing halogen atomic number1 (seeTable I for the experimental results4-'). The small energy difference for the gauche-trans conformers and the reasonably large barrier due to the eclipsed halogens make these molecules a good set on which to benchmark various computational methodologies. These molecules allow us to test how various computational methods treat 1,Cnonbonded interactions which are important in sterically crowded structures. We are interested in testing two methods that we have been using in a variety of other studies. The first of these is the semiempirical MNDO method with both the AM-18 and PM-39 parametrizations. We have been using these semiempirical methods to study the nonlinear optical properties of molecules'O and to study fullerene derivatives.'I These latter molecules can have significant 1,4-nonbonded interactions which have an important effect on the relative energetics of various isomers.' IC The other method that we have been benchmarking is the local density functional (LDF) method.12J3 Density functional theory is a promising method for the calculation of molecular properties without any empirical parameters. This method includes correlation effects at all levels of the calculation and scales as lV' where N is the number of basis functions. It is also computationally efficient when implemented on vector processors. Conventional HartrerFock theory scales as M ,and the inclusion of correlation effects exhibits even worse scaling, Nm,m 1 5 . We have shown that the LDF method can be used to predict the molecular properties of a wide range of systems including molecules such as FOOFI4 which requires a high-level correlation treatment. We have applied the above two methods as well as ab initio molecular orbital theory to calculate the gauchetrans energy difference and the gauche-trans barrier for the dihaloethanes (CH2X-CH2X,X = H,F, C1, Br, I). The ab initio calculations were done with conventional basis sets as well as effective core potentials15 for Br and I.
Metbods All of the calculations were performed on a Cray YMP-4332 Resent address: SONY Corporation Rgearch Center, 174 Fujitsukasho, Hodogaya-ku, Yokohama 240,Japan. 'Contribution no. 6204.
0022-3654/92/2096-10740$03.00/0
method
G T
E-T
E'-T
X=H
IR (G)b
3.04 2.93 2.88
IR (G)C heat capacity (G)d
X=F IR and Raman (G)' NMR (G)I ED (G)8 ED (G)h
-0.9 -0.8 -0.93 -1.76
MW' M Wl
IR (G)k
IR (G)' IR (G)" IR (G)"
IR (G)" NMR (G)p ED (G)q ED (G)' Dipole (G)" PES
heat capacity (G)'
2.76 5.5 4.6
0.60 2.3 2.0
4.50
2.81
x = c1 1.09 1.14 1.03 1.14 1.10 1.3 1.5, 1.0 1 . 1 1 , 1.05 1.21 1 .o 1.38
2.76
X = Br IR (G)k IR (G)'
IR (G)" IR (G)" NMR (G)P ED (G)" dipole (G)" heat capacity (G)'
1.68 1.70 1.45 1.77 1.8 2.2 1.4 1.8, 1.9
4.7, 4.8
x-I
NMR (G)" NMR (S)w NMR (CY ED (G)' IR (S)Y
2.45 2.13 2.6 2.0 1.38
" G gas phase. S = solution phase. bRcfercnce4a. EReference 4b. dRefercnce 4c. 'Reference 2a. /Reference 2j. #Reference 2h. Reference 2g. Reference 2k. Reference 2b. Reference Sa. 'Reference 5b. "Reference 5c. "Reference 5d. "Reference 5c. p Reference 5f. +'Reference 5g. 'Reference 5h. 'Reference 5i. Reference 5j. " Reference 6a. "Reference 6b. Reference 7a. "Reference 7b. YRcfercnce 7c.
computer in a single-processor mode. Previous calculations on 1,Zdihaloethane have shown the need for geometry optimization of various conformers in order to correctly predict the relative energie~.~'These geometries were optimized at each level of 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10741
Conformational Analysis of 1,2-Dihaloethanes calculation except as discussed below for the largest ab initio MO calculations. The semiempirical calculations were done with the program MOPAC16with the AM-ls and PM-39 parametrizations of the MNDO Hami1t0nian.I~ An SCF energy convergence criteria of (PRECISE option in MOPAC) was used. The calculations of the X-X eclipsed E and trans T conformers were constrained to have C, and C2, symmetry, respectively. For the gauche G and X.-H eclipsed E’ conformers, no symmetry constraints were applied. The LDF calculations were done with the program DMol.I8 The atomic basis functions are given numerically on an atomcentered, spherical-polar mesh. The radial portion of the grid is obtained from the solution of the atomic LDF equations by numerical methods. Since the basis sets are numerical, the various integrals arising from the expression for the energy need to be evaluated over a grid, which is generated in terms of radial functions and spherical harmonics. The number of radial points NR is given as
+
NR = 1.2*14(Z 2)”j
Result9 Calculations were done on the trans (T), gauche (G), X-X eclipsed (E), and X-H eclipsed (E’) structures:
(1)
where Z is the atomic number. The maximum distance for any function is 12 au. The angular integration points No are generated at the NR radial points to form shells around each nucleus. The value of No ranges from 14 to 302 depending on the behavior of the density.I9 The Coulomb potential componding to the electron repulsion term is determined directly from the electron density by solving Poisson’s equation. The form for the exchange-correlation energy of the uniform electron gas is that derived by von Barth and HedinS2OThe geometries were optimized by using analytic gradient met hods. 8b All of the DMol calculations were done with a double numerical basis set augmented by polarization functions. This can be considered in terms of size for comparison to traditional molecular orbital calculations as a polarized double-l; basis set. However, because of the use of exact numerical solutions for the atom, this basis set is of significantly higher quality than a normal molecular orbital polarized double-l; basis set. The multipolar fitting functions for the model density used to fit the effective potential have angular momentum numbers, I , 1 greater than that of the polarization function. The ab initio calculations were performed with the program GRADSCF.21 For C2H6, the geometry optimization and force field calculations22were done with a DZ P basis set.23 For 1,2-difluoroethane,the results were taken from our previous work?‘ For l,Zdichloroethane, the geometries and force fields were calculated with a DZ + P basis set with the Cl basis set from McLean and Chandler.24 For 1,Zdibromoethane and 1,2-diiodoethane, the initial optimizations and force field calculationszzf were done with an effective core potential (ECP) on the halogen with a DZ + P valence basis setals The geometries and force fields for 1,Zdibromoethane with all electrons were done with a large This Br basis set has Br basis set derived from Dunning’s the form (1491 lp6d)/[ 10s8p3dI with the first five s orbitals, first four p orbitals, and first four d orbitals each contracted as one and with the remaining orbitals uncontracted. The d polarization exponent is 0.4504. For 1,2-diidoethane, the all electron calculations for the geometry optimizations and force fields were done with an I basis set from Huzinaga’s compilation.26The I basis set has the form (16~13p8d)/[6sSp3d],and is contracted as 433321/43321/431 following Huzinaga et al. Correlation corrections to the final energies were done at the MP-2 levelz7including all of the valence electrons. We also performed MP-2 calculations with larger basis sets at the final geometries. The final basis set for C is triple-t2*augmented by two sets of d polarization functions. Each d set is a two-term contraction of Gaussian functions29with effective Slater exponents of 2.0 for the inner d and an effective Slater exponent of 0.8 for the outer d. The basis set for C has the form (1 ls6p4d)/[5s3p2d]. For C1, the double-l; basis set used in the geometry optimization was extended by adding diffuse s and p orbitals whose exponents were obtained by geometric extension. The d functions were generated in the same way as for C with exponents of 1.9 and 0.7. For Br,
+
the basis set was extended in the same manner as the s and p orbitals were for C1 for the s, p, and d orbitals. The final Br basis set has the form (15~12p7d)/[lls9p4d]. For I, a large basis set derived from work of Dunning was used.M It was contracted very simply following the work of Gropen et al?’ The fmt five s orbitals were contracted as one and the next two s orbitals were contracted as one. The first four p orbitals were contracted as one as were the first four d orbitals. The remaining orbitals were left uncontracted. Diffuse s and p orbitals were obtained by a geometric extension and two diffuse d orbitals were added in the same fashion. The final I basii set has the form (16s12p9d)/[l ls9p6dI.
The T and G structures for the substituted ethanes are stable conformers. The E structure corresponds to the transition state between two G structures, whereas the E’ structures corresponds to the transition state between the T and G structures. These results were confirmed by force field calculationsat the ab initio all-electron and ECP MO levels with the two minima having all real frequencies and the two transition states having one imaginary frequency. The calculated total energies are given in Table I1 and relative energies are given in Table 111. We compare molecular geometries in Table To compare to the experimental energies which are often AG values, it is neceSSary to consider thermodynamic corrections which can be derived33from the geometry and frequencies. Thermodynamic corrections at 298 K relative to the trans isomer are given in Table V for NITand -TU. The signs of the two terms are opposite and will tend to cancel. The largest corrections are for AG(T-E), and these are still no more than 0.5 kcal/mol. The two correction terms to AG(T-G) are small, on the order of 0.1 kcal/mol. Thus, in the discussion below, we did not correct the various energies by the thermodynamic correction factors. Energies. The relative energies for C2H6 and 1,2-CzH4F2 calculated with ab initio molecular orbital (MO) theory are in good agreement with the available experimental results except for the energy of the E conformer of 1,2-C2H4Fz.As discussed previou~ly,~‘ we prefer the higher calculated value for the E conformer for 1,2-CzH4F2as compared to the lower experimental values for this barrier because not enough experimental data were obtained to accurately measure this energy difference. The E’ barrier height is in good agreement with the experimental results. We note that with a large basis set, the G T energy difference is predicted quite well at the MP-2 level with the G structure more stable by 0.8 kcal/mol. For C&, the LDF calculations show good agreement with experiment for the magnitude of the rotation barrier. However both of the semiempirical methods predict barrier heights that are more than a factor of 2 too low. The G conformer for 1,2difluoroethaneis predicted to be more stable than the T conformer at the LDF level in agreement with experiment, but it is predicted to be too stable. The energy of the E conformer relative to the T conformer is predicted to be low by 0.6 kcal/mol at the LDF level as compared to the best IV.2.536932
10742 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Dixon et al.
TABLE II: Total Energie~~*~ compd C2H6 C2H6
SCF (DZ+P) -79.249 384 -79.244 552 -997.101 039 -997.097 944 -997.084 7 10 -997.092 925 -5222.849 608 -5222.845 618 -5222.832 482 -5222.840 796 -13904.178 374 -13904.1 72 945 -1 3904.1 59 8 19 -1 3904.168 609
E
C2H4C12 T C2H4C12 G C2H4C12 E C2H4C12 E’ C2H4BrZT C2H4Br2G C2H4Br2 E C2H4Br2E’ C2H412 C2H412 C2H412
E
C2H412 E’ compd
SCF (ECP)
Ab Initio MO ECP and LDF“ LDF compd -79.096 8 10 C2H4C12 E’ -79.092 353 C2H4Br2T -276.442934 C2H4Br2G -276.445 930 C2H4Br2E C2H4Br2E’ -276.432 336 -276.441 31 1 C2H412 -995.408 792 CZH4I2 G -995.407 075 C2H412 E C2H412E’ -995.394963
MP-2 (ECP)
CZH6 C2H6 E C2H4F2
C2H4F2 C2H4F2 E C2H4F2 E’ C2H4C12 T C2H4C12 G C2H4C12 E compd C2H6
C2H6
E
C2H4F2 T C2H4Fz G C2H4F2 E C2H4F2 E’
AM-1 -17.41 -16.17 -1 14.29 -113.75 -1 11.67 -1 13.52
All-Electron ab Initio MO” MP-2 (DZ+P) -79.548 723 -79.543 628 -997.661 588 -997.659 355 -997.646 188 -997.653 026 -5223.380 178 -5223.377 082 -5223.364 456 -5223.371 074 -1 3904.649 347 -13904.645 105 -13904.632478 -13904.639 172
Semiempiricalb compd AM-1 C2H4C12 T -33.81 C2H4C12 G -33.07 C2H4CI2 E -29.79 CzH4C12 E’ -32.15 C2H4Br2T -7.94 -7.56 C2H4Br2 G
PM-3 -18.14 -16.71 -100.521 -101.91 -100.19 -99.68
SCF (TZ+2D+P) -79.259 182 -79.254 292 -997.1 16 567 -997.113368 -997.100 092 -997.108 645 -5222.855 179 -5222.850 293 -5222.837 65 1 -5222.846 639 -13912.830523 -13912.825 263 -13912.812 334 -13912.821 160
MP-2 (TZ+2D+P) -79.581 948 -79.577 224 -997.726 300 -997.723461 -997.7 10 668 -997.718 192 -5223.404 121 -5223.401 258 -5223.388 660 -5223.396 062 -13913.337 547 -13913.333 790 -13913.321 459 -13913.328 353
SCF (ECP)
MP-2 (ECP)
LDF
-103.960560 -103.956 519 -103.943 477 -103.951 814 -100.405 570 -100.400 28 1 -100.387 597 -100.396 230
-104.481 845 -104.478965 -104.466 246 -104.473 126 -100.903 268 -100.899069 -100.886 841 -100.893 732
-995.401 657 -5219.106 761 -5219.103 770 -5219.091 550 -5219.098 251 -13907.158 38 -1 3907.154 34 -1 3907.142 96 -13907.148 64
PM-3 -24.68 -24.07 -21.24 -23.34 -3.41 -4.70
“pd C2H4Br2E C2H4Br2E’
AM-1 -5.10 -5.85 15.75 17.41 15.66 17.83
C2H412
C2H4I2 G CZH4I2 E C2H412E’
PM-3 -2.85 -1.77 23.31 29.36 30.93 32.07
“Calculated total energies for SCF, MP-2 and LDF are in au. bCalculated heats of formation for AM-1 and PM-3 are kcal/mol.
TABLE III: Relative Energies (kcal/mol) of 1,2-DihrloethPne Isomers DZ+P C2H6 C2H6
E
PM-3 1.43 0 0.33 0.84 -1.39
C2H6F2 Eb C2H6F2 E’b CzH6F2 Gb 0 C2H6F2 T b C2H6C12 E 3.45 CzH6CI2 E’ 1.34 0.61 CzH6C12 G C2H6C12 T 0 C ~ H ~ EB ~ Z 0.56 C2H6Bf2 E’ 1.64 C2H6Br2 G -1.29 C2H6Br2 T 0 C2H612 E 7.61 C2H612E’ 8.76 C2H612 6.04 CZH612 T 0
AM-1 1.25
0 2.62 0.77 0.54 0 4.02 1.66 0.74 0 2.84 2.09 0.38 0 1.66 2.08 -0.08
0
LDF 2.80
SCF 3.03
0
0
6.65 1.02 -1.88
0 8.68 4.47 1.08 0 9.55 5.34 1.88
0 9.68 6.11 2.54 0
7.71 2.77 -0.13
0 10.25 5.09 2.53
0 10.75 5.54 2.50
0 11.64 6.14 3.41
0
MP-2 3.20
0 8.41 2.54 -0.67 0
9.66 5.37 1.40
0 9.87 5.72 1.94 0 10.58 6.39 2.66 0
TZ+2D+P SCF MP-2 3.07 2.96 0 0 7.52 7.28 2.71 2.33 -0.33 -0.77 0 0 9.81 10.34 4.97 5.09 2.01 1.78 0 0 10.82 9.55 5.36 5.06 3.01 1.78 0 0 11.22 9.93 5.88 5.77 3.25 2.32 0
0
ECP SCF
MP-2
expt4 2.9-3.0
0
10.72 5.49 2.53
0 11.28 5.86 3.32 0
9.79 5.47 1.81
0 10.30 5.98 2.63 0
4.6-5.5 2.0-2.3 -0.8 to -0.9 0 4.5 2.8 1.0-1.2 0 4.7-4.8 1.7-1.9
0 2.0-2.6 0
“Typical experimental values from Table I. bSCF and MP-2 values from ref 3f.
ab initio M O calculations. The G-G barrier height (AI? = E(E)
- E(G)) is high by 0.5 kcal/mol at the LDF level and the G-T
barrier height (AI? E(E’)- E(G)) is low by 0.2 kcal/mol as compared to the ab initio results. Thus, the agreement between the ab initio MO and LDF results within 1.0-1.2 kcal/mol is quite good. However, the semiempirical results do not show as good agreement with the ab initio results for 1,2-difluoroethane. The G conformer is predicted to be more stable than the T conformer by 1.4 kcal/mol at the PM-3level in reasonable agreement with experiment but the E conformer is only 0.3 kcal/mol above the
trans, clearly different from the ab initio MO or LDF results. In fact, the E‘ conformer is less stable then the E conformer. At the AM- 1 level, the T conformer is predicted to be more stable than the G conformer and the E and E’ conformers are still too stable. For l,Zdichloroethane, the best ab initio MO calculations predict the T conformer to be the most stable with the G conformer less stable by 1.8 kcal/mol. Experimentally, the T conformer is more stable than the G conformer by 1.0-1.2 kcal/mol. The G-G and G-T rotation barriers are both predicted to be higher than
Conformational Analysis of 1,2-Dihaloethanes the same barriers in 1,2-difluoroethane. Our results are in good agreement with those of Wiberg who used the 6-31 1G** basis set at the MP-3 level.3d The LDF method predicts the energy difference between the T and G conformers to be essentially the experimental value. The G-G rotational barrier is 0.4 kcal/mol below the ab initio value. These differences between LDF and ab initio MO are about the same as found for the 1,Zdifluoroethane comparison. In both cases, the G conformer is apparently stabilized at the LDF level as compared to the T conformer. The semi-empirical methods predict the T conformer to be more stable than the G conformer, although the energy difference is too small by about 0.5 kcal/mol as compared to experiment. The E and E' conformers are predicted to be of too low energy by at least a factor of 2 as compared to the ab initio MO values. The ab initio MO results for 1,2-dibromoethaneare in good agreement with each other independent of the basis set and of whether an ECP is used or not. There is a reasonable correlation correction to the T-G energy difference with correlation making the energy difference smaller. The T conformer is more stable and the calculated value is in good agreement with the experimental values. The energy differences between the T and E and E' conformers are comparable in magnitude to the energy differences predicted for 1,Zdichloroethane. The LDF values are in extremely good agreement with the ab initio MO values for the G, E, and E' conformers relative to the T conformer. The semiempirical MO values are in poor agreement with the experimental value for the T-G energy difference. At the PM-3 level, the G conformer is more stable than the T structure by 1.3 kcal/mol whereas the T is only 0.4 kcal/mol more stable than the G at the AM-1 level. Furthermore, the E and E' conformers are too close in energy to the T conformer with both semiempirical methods. At the PM-3 level, E' is surprisingly higher in energy than E. The T-G energy difference is predicted to be largest for 1,2diiodoethane at the ab initio MO level. The ECP result is in good agreement with the DZ P basis set value, and at the MP-2 level, both predict a AE about 0.3 kcal/mol above the value with the largest basis set. The best ab initio MO value is in good agreement with the experimental values.' The energy of the E conformer shows a somewhat larger dependence on the basis set with the beat MP-2 value 0.2-0.7 kcal/mol below the smaller basis set and the ECP values. The energy of the E conformer relative to the T conformer is within 0.6 kcal/mol of the result for 1,2-dibromoethane. The LDF values are in good agreement with the best ab initio MO values. The semiempirical values again are not in good agreement with the other calculated values. Although the energy of the E conformer relative to the T conformer at the PM-3 level is in better agreement with the ab initio value than found for the other substituents, the energy of the G conformer is too high relative to the T conformer by more than a factor of 2. Also, the E' conformer is higher in energy than the E conformer. The AM-1 values are in complete disagreement with experiment with the G and T conformers having essentially the same energy and the energies of the E and E' conformers relative to the T are too small. Geometries. The ab initio MO calculated geometry of CzHs is in good agreement with the experimental results. The C-C bond is predicted to lengthen by 0.014 A going from the T to the E conformer. The LDF C-C bond is -0.02 A shorter than the 'experimental value and the ab initio MO value. The LDF C-H bonds are longer than the ab initio values and than experiment. The C-C bond shows a similar lengthening for the E conformer at the LDF level as found at the ab initio MO level. The semiempirical methods predict the C-C bond length to be shorter than the experimental values by 0.025-0.04 A and the bond length increases only slightly (0.003-0.004 A) in the E conformer. For l,Zdifluoroethane, the LDF C-C bond is less than the ab initio MO value and is 0.01-0.02 A shorter than experiment. Whereas the ab initio MO C-F bond lengths are shorter than experiment, the LDF values are slightly longer than experiment. The only real difference from experiment or the ab initio MO
+
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10743 values at the LDF level is the value of r(F-C-C-F) for the G conformer which is 9' larger than the experimental value and 10' larger than the ab initio value. The semiempirical geometries behave in a different way. Whereas substitution of two fluorine is predicted to decrease the C-C bond as observed experimentally as compared to C,&, the semiempirical methods predict a longer C-C bond. Both parametrizations predict the C-F bond to be too short with the largest error found for the PM-3 parametrimuon. As found for c,&,neither AM-1 nor PM-3 predicts much change in the C-C bond on eclipsing. The AM-1 method predicts T(F-C-C-F) for the G conformer to be too large by 10' whereas the PM-3 method predicts the torsion to be too small by 14'. The C-C-F bond angles in the E and E' conformers are predicted to have values similar to those of the G conformer and increase as compared to the T conformer by all of the computational methods. The ab initio MO value for r(C-C) in 1,2-dichloroethaneis shorter than the experimental value by 0.01 1 A and the LDF value is -0.02 A shorter than the ab initio MO value. The ab initio MO and LDF results for the C-CI bond are in good agreement with the experimental value. The semiempirical methods behave as discussed above, but the AM-1 method predicts the C-CI bond to be shorter than does the PM-3 method and both are shorter than the experimental value. The calculated CI-C-C-Cl torsion angles for the G conformer are in good agreement with each other as well as with the ab initio value. The C-C-Cl bond angle is predicted to significantly increase in the E conformer as compared to the T by all of the methods. For 1,2-dibromoethane, the ab initio all-electron and ECP MO results agree with each other with the only differences being the C-Br bond length where the ECP predicts the bond to be 0.009 A longer and the Br-C-C-Br torsion for the G conformer to be 1.3' smaller. Both calculated C-Br bond lengths are slightly longer than experiment. The C-C bond is predicted to be 0.01 A too long at the ab initio MO level. The LDF method predicts the C-C bond to be shorter than experiment by 0.019 A and shorter than the ab initio MO value by 0.029 A. The C-Br bond length is predicted to be essentially the same as the ab initio MO value and is only 0.008 %r. longer than the experimental value. The LDF value for the Br-C-C-Br torsion angle in the G conformer is '7 less than the ab initio MO value. The semiempiricalmethods behave as found for 1,2-dichloroethane. However, the PM-3 torsion angle for the G conformer is now only 43', 28' less than the ab initio MO value and 30' less than experiment. The AM-1 value for this torsion is only too small by 10'. For the E' conformer, the AM-1 result for the Br-C-C-Br torsion angle differs most from the other values. The C-C-Br bond angle is predicted to significantly increase in the E conformer as compared to the T by all of the methods. However, the C-C-Br angle in the E conformer at the PM-3 level is quite small because the angle in the T conformer is only 104'. The ECP bond length for the C-I bond in 1,Zdiiodoethane is 0.019 A less than the all-electron value. The ECP value is in excellent agreement with the experimental value, whereas the ab initio MO value is 0.015 A too long. The experimental value for r(C-C) is surprisingly short as compared to the ab initio MO values but has a large standard deviation. The experimental estimate of the torsion is larger than the calculated ab initio MO values, but again there is a large standard deviation. The remaining values are all in agreement with each other except for the I-C-C-I torsion in the E' conformer for which the values differ by 5.5'. The LDF values are in reasonable agreement with the ab initio MO results except for 7(I-C-C-I) for the G conformer which is predicted to be 9-10' less than the ab initio MO values. These calculations all predict a shortening of the C-I bond in the G conformer as compared to the T conformer. The semiempirical methods do not predict the C-I bond length at all well with differences from the ab initio MO values of up to 0.15 A. The PM-3 method is clearly worse than the AM-1 method for iodine. The C-C-I angle increases significantly in the E conformer as compared to the T conformer for all of the calculations. The largest increase is predicted by the LDF calculations. The smallest increase is at the PM-3 and AM-1 levels. Again the PM-3 C-C-I
10744 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Dixon et al.
TABLE I V Geometry Parameters for Conformers of 1,2-Dihaloethnnes" X = H geometries for T (trans) PM-3 LDF 1.505 1.513 1.098 1.106 111.6 111.5 107.2 107.4
AM- 1 1.500 1.117 110.7 108.2
4C-C) r(C-H) O(CCH) O(HCH)
DZ+P 1.53 1 1.086 111.1 107.8
exptb 1.536 1.09 1 110.9
exptC 1.543 1.102 109.4 109.2
geometries for E (eclipsed) AM-1 1.503 1.117 111.1 107.9
r(C-C) r(c-Hj O(CCH) O(HCH)
PM-3 1.509 1.098 112.0 106.9
LDF 1.526 1.105 111.8 107.1
DZ+P 1.545 1.085 111.6 167.3
X = Fd
G-C) r(C-X) r(C-H)c r(C-H)' e(ccx) O(CCH)' O(CCH)' O(HCH) O(HCX)' O(HCXy T(XCCX)
AM-1 1.544 1.379 1.124
geometries for T (trans) PM-3 LDF DZ+P 1.546 1.501 1.519 1.357 1.395 1.369 1.102 1.106 1.082
110.6 109.5
110.7 111.5
107.9 111.2
108.1 111.1
108.8 109.2
108.4 107.3
109.2 108.7
109.6 108.4
180
180
180
180
expt8 1.535 1.394 1.126
expth 1.503 1.389 1.103
expt' 1.504 1.386 1.116
108.3 108.3
110.3 111.0
110.8 110.3
108.5 107.9 74.4'
71.3'
71.7'
expt'.' 1.493 1.390 1.093 1.099 110.6 111.3 108.4 109.1 107.8 109.6 71.0
geometries for E (eclipsed) r(C-C) r(C-X) r(C-H)' r(C-H)m e(ccx) O(CCH)' O(CCH)"' O(HCH) O(HCX)' O(HCX)m r(XCCX)
AM-1 1.547 1.377 1.125
PM-3 1.548 1.355 1.101
LDF 1.531 1.385 1.106
DZ+P 1.544 1.360 1.083
112.2 109.3
112.6 111.2
110.6 111.0
110.8 110.8
108.6 108.7
108.3 106.7
108.6 107.8
109.0 107.6
0
0
0
0
AM-1 1.508 1.754 1.117
geometries for PM-3 1.494 1.790 1.102
AM-1 1.547 1.380 1.125 1.124 111.3 109.6 109.4 108.0 109.0 108.6 119.8
geometries for AM-1 PM-3 1.543 1.540 1.379 1.356 1.125 1.101 1.124 1.102 111.9 111.0 108.5 110.6 109.5 111.8 109.4 108.9 108.5 107.5 108.9 106.9 81.3 57.3
G (gauche) LDF 1.484 1.396 1.108 1.108 111.2 109.7 110.3 109.5 108.1 108.0 79.8
geometries for E' (eclipsed) PM-3 LDF 1.549 1.503 1.357 1.397 1.103 1.108 1.102 1.106 111.4 110.5 112.3 108.4 111.1 113.2 108.3 109.7 106.8 108.3 106.7 106.9 123.0 122.1
DZ+P 1.506 1.368 1.084 1.083 110.4 109.4 110.8 109.9 108.1 108.1 69.4
DZ+P 1.526 1.372 1.081 1.082 109.8 109.4 112.0 109.8 108.5 107.2 123.7
x = c1 r(C-C) r(C-X) r(C-H)' r(C-H)' e(ccx) O(CCH)' O(CCH)' B(HCH) O(HCX)c O(HCX)' T(XCCX)
r(C-C) r(C-X) r(C-H)' r(C-H)"'
e(ccx) O(CCH)' O(CCH)"' O(HCH) O(HCX)' O(HCX)"'
T(xccx)
T (trans) LDF 1.496 1.790 1.104
DZ+P 1.517 1.795 1.077
expt" 1.528 1.796 1.120 108.9 113.0
110.4 111.5
108.8 111.7
108.5 11 1.6
109.1 11 1.3
109.6 106.9
109.3 107.6
109.5 107.7
109.7 107.7
180
180
180
180
AM- 1 1.513 1.746 1.118
geometries for E (eclipsed) PM-3 LDF 1.512 1.532 1.772 1.778 1.102 1.105
78.2k DZ+P 1.550 1.784 1.078
116.4 109.8
112.5 111.0
115.7 110.6
117.4 109.3
109.1 105.8
106.6 107.7
108.5 105.6
108.6 106.0
0
0
0
0
AM-1 1.507 1.751 1.118 1.117 112.6 109.6 111.5 109.7 106.5 106.8 71.5 AM-1 1.511 1.755 1.118 1.118 111.8 112.2 110.7 109.3 106.4 106.3 120.2
geometries for G (gauche) PM-3 LDF 1.503 1.494 1.776 1.784 1.104 1.105 1.105 1.103 109.3 112.4 111.2 109.9 111.7 111.3 107.5 109.1 108.5 107.0 108.6 107.0 67.5 70.7 geometries for E' (eclipsed) PM-3 LDF 1.509 1.512 1.779 1.789 1.106 1.102 1.104 1.103 109.6 112.0 112.1 111.3 111.8 111.5 107.1 109.0 108.2 106.8 108.0 106.1 120.2 118.2
DZ+P 1.517 1.788 1.080 1.077 1 12.4 109.4 111.1 109.3 106.8 107.7 71.2 DZ+P 1.534 1.796 1.076 1.078 111.9 111.6 110.8 109.3 106.7 106.3 118.5
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10745
Conformational Analysis of 1,2-Dihaloethanes
TABLE IV (Continued) X = Br
geometries for G (gauche)
geometries for T (trans) r(C-C) r(C-X) r(C-H)' r(C-H)' e(ccx) O(CCHy O(CCH)' O(HCH) O(HCX)' O(HCX)' T(XCCX)
AM-1 1.500 1.928 1.116
PM-3 1.481 1.954 1,101
LDF 1.487 1.958 1.101
DZ+P 1.516 1.953 107.7
ECP 1.516 1.962 1.077
expt"
112.0 111.4
103.9 113.7
107.9 112.4
109.5 111.9
109.5 111.9
109.5 110.0
109.1 106.3
108.8 108.3
110.5 106.7
110.1 106.6
110.1 106.6
180
180
180
180
180
AM-1 1.500 1.922 1.117 1.116 114.0 109.5 111.3 108.9 106.4 106.6 62.7
1.506 1.950 1.108
73.0k
geometries for E (eclipsed) @-C) r(C-X) r(C-H)' r(C-H)"' e(ccx) O(CCH)' O(CCH)"' O(HCH) B(HCX)' O(HCX)" r(XCCX)
PM-3 1.484 1.950 1.101 1.101 103.4 114.1 113.6 108.8 108.9 107.7 43.3
LDF 1.487 1.950 1.105 1.102 113.3 109.5 112.7 109.7 105.4 105.8 63.7
DZ+P 1.517 1.944 1.080 1.077 113.4 109.0 111.8 109.6 105.8 106.9 71.1
ECP 1.515 1.951 1.080 1.077 113.6 108.5 112.0 109.6 106.2 106.8 69.8
geometries for E' (eclipsed)
AM-1 1.506 1.918 1.117
PM-3 1.489 1.945 1.103
LDF 1.524 1.947 1.100
DZ+P 1.546 1.949 1.077
ECP 1.546 1.941 1.077
117.2 109.8
108.6 113.0
117.5 110.7
119.1 109.4
119.0 109.4
108.5 105.5
107.7 107.0
109.0 103.9
108.7 104.9
108.7 105.0
0
0
0
0
AM-1 1SO4 1.927 1.116 1.117 113.4 113.4 110.4 108.4 105.8 106.0 113.4
0
PM-3 1.484 1.956 1.103 1.102 106.6 114.5 113.4 108.1 106.9 106.9 119.5
LDF 1.508 1.954 1.101 1.101 112.0 112.5 111.9 109.5 105.5 105.0 118.4
DZ+P 1.533 1.95 1 1.075 1.077 112.3 112.4 110.9 109.4 105.7 105.8 118.5
ECP 1.534 1.960 1.075 1.078 112.3 112.5 110.9 109.4 105.8 105.7 117.0
X=I
geometries for T (trans) 4C-C) r(C-X) r(C-H)' r(C-H)' e(ccx) O(CCH)' O(CCH)' O(HCH) O(HCXy O(HCX)' r(XCCX)
geometries for G (gauche) exptp
AM-1 1.492 2.071 1.115
PM-3 1.485 2.033 1.104
LDF 1.487 2.180 1.101
DZ+P 1.512 2.181 1.076
ECP 1.513 2.169 1.076
1.479 0.033 2.166 & 0.015
112.2 111.5
105.8 112.8
107.7 113.2
109.9 112.6
110.1 112.4
110.2 112.4
* 4.0 1.2
108.7 106.4
108.2 108.5
110.6 105.8
110.3 105.5
110.1 105.7
105.2
4.7
180
180
180
180
180
79 & 16'
geometries for E (eclipsed) 4C-C) r(C-X) r(C-H)' r(C-H)"' e(ccx) O(CCH)' O(CCH)m @(HCH) O(HCX)' @(HCX)" r(XCCX)
AM-1 1.493 2.065 1.116 1.115 113.6 109.9 111.3 108.2 106.9 106.9 57.0
PM-3 1.488 2.030 1.104 1.104 105.1 113.4 112.9 108.4 109.1 107.7 42.2
LDF 1.492 2.162 1.105 1.102 114.1 110.1 113.2 109.6 103.9 105.5 61.7
DZ+P 1.518 2.168 1.079 1.077 114.3 109.2 112.5 109.7 104.6 106.1 73.2
ECP 1.519 2.153 1.080 1.077 114.5 109.0 112.3 109.4 104.9 106.1 72.4
geometries for E' (eclipsed)
AM-1 1.498 2.063 1.116
PM-3 1.491 2.024 1.106
LDF 1.520 2.166 1.099
DZ+P 1.541 2.168 1.077
ECP 1.541 2.155 1.077
116.0 110.3
110.1 112.5
120.0 111.2
121.4 109.5
121.1 109.4
107.9 106.0
107.1 107.2
108.2 102.6
108.9 103.4
108.6 103.8
0
0
0
0
0
AM-1 1.497 2.069 1.115 1.116 113.4 112.3 110.5 107.9 106.0 106.3 120.4
PM-3 1.487 2.036 1.105 1.107 109.3 114.3 112.2 107.3 106.9 106.4 118.0
LDF 1.509 2.171 1.100 1.102 112.4 113.3 112.2 109.0 104.9 104.4 119.8
DZ+P 1.532 2.173 1.074 1.078 112.9 113.4 110.9 109.3 104.8 105.0 117.4
ECP 1.533 2.157 1.075 1.078 113.2 113.2 110.7 109.1 105.0 105.2 111.9
'Units: lengths in angstroms, angles in degrees. bReference32a. 'Reference 32b. dDZ+P calculated values obtained from ref 3f. 'G values for H,.fGvalues for H 8Reference 2d. *Reference2g. 'Reference 2h. /Reference 2k. li Values for the gauche conformer. 'E' values for H eclipsed with F. "E' values for H eclipsed with H. "Reference 5g. OReference 6f. PReference 7b. angle in the E conformer is small due to a small angle in the T conformer. Msclrssion The ab initio MO results suggest that the conformational energies can be calculated quite accurately if a good basis set with an estimate of the correlation energy is used together with a set of optimized geometries. The largest error is found for 1,2-dichloroethane where the best calculated value is about 0.5-0.8 kcal/mol above the experimental T-G energy difference. The experimental results are quite consistent for a variety of measurements, so it suggests that there is some deficiency in the
calculation, and we would expect this to be the basis set. The correlation corrections for this set of conformational energies are not large but need to be included in order to compare to the experimental quantities. The ECP results for Br and I are in extremely good agreement with the all-electron calculations with a comparable basis set. The results from the local density functional calculations are in quite good agreement with the ab initio MO results with the largest differences found for 1,Zdifluoroethane. Not surprisingly, this is the substituted system with the smallest number of elecuons. The predictions of the LDF method are also in good agreement with the available experimental results. This suggests that the
10746 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 TABLE V Thermodynamic Corrections (kcal/mol) to Relative Energies" G E E' atom AHT AHT AHT -TU -TU -TU H 0.45 -0.29 0.15 F -0.08 -0.49 0.95 -0.49 0.57 C1 -0.09 0.05 -0.49 0.89 -0.51 0.60 Br -0.08 0.08 -0.51 0.95 -0.56 0.76 I -0.14 0.14 -0.53 0.96 -0.59 0.88
" Relative to trans structure. LDF method will be good for predicting torsional potentials for these types of systems, especially if the substituentsare from second or higher rows of the periodic table. Also, the LDF method should also be good for studying sterically hindered systems involving the halogens. The above results show that the semiempiricalmethods can not be used to predict the torsional potentials in these simple model ethanes. The interactions between the halogens are simply not repulsive enough. Not only are the results for the energies quantitatively in error but the results are often qualitatively in error. There are also serious problems in predicting the geometries of structures containing Br and 1. This leads in the eclipsed structure to X-X interactions that are too far short at the PM-3 level. There is also a significant error in the C-I bond length at the semiempirical level with both methods predicting the bond to be shorter than the C-I bond in CH31 ( r = 2.132 As3). The barriers to rotation exhibit some interesting trends. We discuss these with respect to their height relative to the trans. The HQ-Xeclipsing barrier (AE(E') = E(E') - E(T))decreases from H to F by 0.7 kcal/mol and then increases by 2.1 kcal/mol for C1 and Br. The barrier for X = I is an additional 0.7 kcal/mol higher. The X-X eclipsing barrier (AE(E) = E(E) - E(T)) is higher by 4-5 kcal/mol as compared to AE(E'). The value of AE(E) for X = F is about 2.5 kcal/mol less than the values for X = C1, Br, and I, which are all essentially identical. The energies of the G conformer relative to the T for X = C1, Br and I are all predicted to be similar with the energy for X = I about 0.5 kcal/mol above the other values. Thus,the conformationalenergy surfaces for X = Cl, Br, and I are all very similar even though the steric size of the atoms differs considerably. The conformational surface for F is different not only with the global minimum being the G conformer but also with lower values for the barriers. Reghtry No. CI(CH2)2CI,107-06-2; Br(CH,),Br, 106-93-4; I(CHJ21, 624-7 3-1.
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(24) McLean, A. D.; Chandler, G. S . J . Chem. Phys. 1980, 72, 5639. (25) Dunning, T. H., Jr. J . Chem. Phys. 1977, 66, 1382. (26) Huzinaga, S.;Andzelm, J.; Klobukowski, M.; Radzio, J.; Sakai, Y.; Takasaki, H. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (27) (a) Meller, C.; Plesset, M. S.Phys. Reu. 1934, 46, 618. (b) Pople, J. A,; Binkley, J. S.; Seeger, R.Inr. J. Quantum Chem. Symp. 1976, I O , 1. (28) Dunning, T. H., Jr. J. Chem. Phys. 1971, 55, 716. (29) Stewart, R. F. J. Chem. Phys. 1969, 50, 2485. (30) Dunning, T. H., Jr., private communication. (31) Stromberg, A.; Gropen, 0.;Wahlgren, U. J . Compur. Chem. 1983, 4 , 181. (32) (a) The values are the ones tabulated in Stewart, J. J. P. J. Comput.-aided Mol. Design 1991, 4 , 1. (b) Hansen, G. E.; Dennison, D. M. J . Chem. Phys. 1952, 20, 313. (33) McQusrrie, D. A. Statistical Mechanics: Harper & Row: New York, 1976.
