J . Phys. Chem. 1991, 95, 139-144 single band at 995 cm-' and the pair of bands a t 1099 and 1125 cm-' in phase I' correspond to the average frequencies of two bands in phase 1'. These vibrations are not assigned in ref 8. The rest of the bands shown in Figure 8 and the C-H bending vibrations in phase 1 correspond nearly one to one to sharper bands in phase 1'. IV. Summary and Conclusions We report the Raman spectra of a new solid planar phase of monohydrogenated cyclopentene-d, and perdeuterated cyclopentene-d8. This new phase is obtained at about liquid nitrogen temperature when we "quench" the sample from the high temperature plastic phase I1 only. It is stable upon cooling. The possibility of the spectra being due to the equilibrium between two puckered conformations was contemplated and discarded. This new phase I' appears as a more odered phase than phase I. It must be pointed out that cyclopentene is nonplanar if unconstrained, the barrier between up and down forms being about 0.7 kcal/mol. A priori, the existence of a crystal with molecules whose conformational energy is at a local maximum seems unlikely. Nevertheless, the present spectroscopic evidence is consistent with the hypothesis of a planar conformation of the cyclopentene ring and no other alternative explanation can be offered at the moment. We do not obtain this new phase starting from the known low temperature crystalline phase I. Furthermore, we have not observed this phase in the fully hydrogenated cyclopentene. Steric effects involving the shorter CD bonds (compared to the C H bonds) could be involved in the appearance of this phase. Indeed, the lighter isotopic derivatives were found to occupy
139
greater volumes than their heavier analogues.35 This effect has been also associated with the high frequency isotope sensitive vibrations (CH/CD) and their a n h a r m ~ n i c i t y . ~In~future experiments, we will try to obtain this phase in monodeuterated cyclopentcnes in order to investigate the importance of the number of D atoms in this phenomenon. Such difference in the phase transitions between deuterated and hydrogenated compounds have been already observed: For example, in [N(CH3).,I2MX4 (M = Co, Zn, Mn; X = CI, Br) compounds, deuteration appears as a 'pressure decrease" effect in the temperaturepressure phase diagram.37 On the contrary, the perdeuterated methane CD, may be viewed as perhydrogenated methane CH4 under pressure.38 But, no explanation was given for such a behavior. Pressure experiments are in progress with cyclopentene. Acknowledgment. We acknowledge Dr. M. Grignon of the Laboratoire de Chimie Organique du Silicium et de I'Etain (URA35), University of Bordeaux I, and Dr. M. F. Lauti6 of LASIR CNRS Thiais for their help during the synthesis of the monohydrogenated cyclopentenes-d7. We also thank Dr. J. C. Lasdgues and Dr. C. Sourisseau for helpful discussions. Registry No. CSHs, 142-29-0;D2,7782-39-0. (35) Bartell, L. S.; Roskos, R. R. J . Chem. Phys. 1965, 44, 457. (36) Kooner, Z. S.; Van hooke, W. A. J . Phys. Chem. 1988, 92, 6414. (37) Berger, J.; Benoit, J. P.; Garland, C. W.; Wallace, P. W. J . Phys. 1986, 47, 483. (38) Prager, M.; Press, W.; Heidemann, A,; Vettier, C. J . Chem. Phys. 1982, 77, 2577.
Ab Initio Molecular Orbital Calculatlons of the Internal Rotational Potential of Biphenyl Using Polarized Basis Sets with Electron Correlation Correction Seiji Tsuzuki* and Kazutoshi Tanabe National Chemical Laboratory for Industry, Tsukuba. Ibaraki 305, Japan (Received: June 15, 1990)
The molecular geometries of biphenyl in minimum-energy twisted, copolanar, and perpendicular conformations have been optimized, with D2, DZh,and Dzdsymmetry restrictions imposed, by ab initio molecular orbital calculations using polarized basis sets. In the geometry optimization, phenyl rings are kept planar. The twist angles of the conformer of minimum energy calculated at HF/6-31G* and HF/6-31GS* levels are 46.13 and 46.26", respectively, which are very close to the recently reported value of 45.41" obtained by an HF/6-31G level calculation and the value of 44.4 f 1.2' from electron diffraction experiments. The calculated bond distances and angles are also close to those from HF/6-31G calculations and those from calculated at the HF/6-31G* level are experiments. The internal rotational barrier heights at 0" (AE,) and at 90" 3.28 and 1.48 kcal/mol, respectively. Those at the HF/6-31G** level are 3.33 and 1.51 kcal/mol, respectively. They are = 1.62 kcal/mol from recent HF/6-31G level calculations. AEo and AEgOcalculated very close to AE, = 3.17 and level are 3.47 and 1.58 kcal/mol, respectively. While the PEW value from these at the MP4(SDQ)/6-31G*//HF/6-31G* calculations is close to AEW = 1.6 i 0.5 kcal/mol from electron diffraction experiments, the AEo value from these calculations is much higher than AEo = 1.4 f 0.5 kcal/mol from the same experiments. The internal rotational potential calculated level is shallow in the region near the minimum but has a steep slope in the region at the MP4(SDQ)/6-3IG*//HF/6-31G* of 4 = 0-30". The equation V ( 4 )= 1/2V2(1 - cos 24) + 1/2V4( 1 - cos 44) + C, which was used for the estimation of the internal rotational potential from the experimental measurement, has been fitted to the calculated potential in the region near the minimum. AEo estimated from the fitted equation is much lower than the value from the ab initio calculation, which shows that this equation is not appropriate to estimate AEo from the shape of the potential near the minimum, if the shape of the potential is similar to that obtained by the ab initio method.
Introduction The molecular structure of biphenyl has attracted great interest due to the conformational problem. The ?r-conjugation between phenyl rings stabilizes the planar conformer, whereas the steric repulsion between ortho hydrogen atoms favors the nonplanar conformer. The molecular structure of biphenyl has been de0022-3654/91/2095-0139$02.50/0
termined by various experimental The twist angle of biphenyl depends on the state of aggregation. Recent electron (1) Almenningen, A.; Bastiansen, 0.;Fernholt, L.; Cyvin, B. N.; Cyvin, ~s 1 ~,1985,~128, 59. ~ ~ ~ , (2) Bastiansen, 0.;Samdal, S.J . Mol. Strucr. 1985, 128, 115.
s. J , ; Samdal, s. J . ~
0 1991 American Chemical Society
140 The Journal of Physical Chemistry, Vol. 95, No. 1 , 1991
diffraction studies suggest that the twist angle of biphenyl is 44.4 f 1.2' in the gas phase.',2 The twist angle of biphenyl is smaller in condensed phases than in the gas phase, which has been shown by several experimental measurement^.^-'^ Various levels of molecular orbital calculations have been employed for the estimation of the twist angle.'6-26 A recently reported HF/6-3 IG calculation with geometry optimization shows that 4 ~ " = 45.41°,24 which is very close to the value from the electron diffraction measurements. In spite of the extensive experimental studies on the molecular structure of biphenyl, little has been done experimentally to determine the internal rotational potential of biphenyl in the gas phase. Only indirect estimations of internal rotational barrier heights from the comparison of the calculated and experimental thermodynamic functions,27from electron diffraction studies1q2 and from Raman spectra of the torsional mode of biphenylZ8have been reported. The internal rotational barrier heights at ' 0 (AE,) and at 90' (AE,,) estimated from electron diffraction data are 1.4 f 0.5 and 1.6 f 0.5 kcal/mol, The barrier heights estimated from the analysis of Raman spectra and those from thermodynamic data are close to these value^.*^,^^ A molecular orbital calculation is also applied for the estimation of the internal rotational potential of biphenyl as well as for the estimation of equilibrium geometry.'6-26 Recently Hafelinger reported the ab initio calculations of the internal rotational barrier heights of biphenyl at HF/STO-3G and at HF/6-31G levels with geometry o p t i m i z a t i ~ n . ~Although ~ . ~ ~ the HF/6-31G level calculation is more precise than the HF/STO-3G level calculation, better agreement with the experimental barrier height was achieved by the cruder HF/STO-3G calculation. The AEo and AEw values at the HF/STO-3G level are 2.05 and 2.40 kcal/mol, respectively, while those at the HF/6-31G level are 3.17 and 1.62 kcal/mol, respectively. AEo at the HF/6-31G level is much higher than AEo from electron diffraction experiments. Recently the importance of the incorporation of the electron correlation energy correction using polarized basis sets in the calculation of the conformational energies was emphasized even for as simple a hydrocarbon as n - b ~ t a n e . ~A~recent . ~ calculation
(3) Suzuki. H. Bull. Chem. SOC.Jpn. 1959, 32, 1340. (4) Eaton, V. J.; Steele, D. J . Chem. SOC.,Faraday Trans. 2 1973, 69, 1601. (5) Akiyama, M.; Watanabe, T.; Kakihana, M. J . Phys. Chem. 1986,90, 1752. (6) Roberts, R. M. G. Magn. Reson. Chem. 1985, 23, 52. (7) Cheng, C. L.; Murthy, D. S. N.; Ritchie, G. L. D. J . Chem. SOC., Faraday Trans. 2 1972, 68, 1679. (8) Chau, J. Y. H.; Le Fevre, C. G.; Le Fevre, R. J. W. J . Chem. SOC. 1959, 2666. (9) Trotter, J. Acta Crystallogr. 1961, 14, 1135. (IO) Robertson, G . B. Nature 1961, 191, 593. ( 1 I ) Hargreaves, A.; Rizvi, S. H. Acfa Crystallogr. 1962, 15, 365. (12) Charbonneau, G.-P.; Delugeard, Y . Acta Crysfallogr. 1977, B33, 1586. ( 1 3) Charbonneau. G.-P.; Delugeard, Y. Acta Crystallogr. 1976, B32, 1420. (14) Bonadeo, H.; Burgos, E. Acta Crysfallogr. 1982, A38, 29. ( 1 5) Cailleau, H.; Baudour, J. L.; Zeyen, C. M. E. Acra Crystallogr. 1979, 8-75, 426. (16) Imamura, A.; Hoffmann, R. J . Am. Chem. SOC.1968, 90, 5379. (17) Tinland, B. J . Mol.Strucf. 1969, 3, 161. (18) Gropen, 0.; Seip, H. M. Chem. Phys. Lett. 1971, I / , 445. (19) Tajiri, A.; Takagi, S.; Hatano, M. Bull. Chem. Soc. Jpn. 1973, 46, 1067. (20) Janssen, J.; Liittke, W. J . Mol. Struct. 1979, 55, 265. (21) Perahia, D.; Pullman, A. Chem. Phys. Lett. 1973, 19, 73. (22) Almlof, J. Chem. Phys. 1974, 6, 135. (23) Hafelinger, G.; Regelmann, C. J . Compuf. Chem. 1985, 6, 368. (24) Hafelinger, G.; Regelmann, C. J . Compuf. Chem. 1987, 8, 1057. (25) McKinney, J. D.; Gottschalk, K. E.; Pedersen, L. J . Mol. Srrucr. 1983, 104, 445. (26) Penner, G . H. THEOCHEM 1986, 137, 191. (27) Katon, J. E.; Lippincott, E. R. Spectrochim. Acfa 1959, 15, 627. (28) Carreira, L. A.; Towns, T. G . J . Mol. Sfrucf.1977, 41, 1. (29) Raghavachari, K. J . Chem. Phys. 1984, 81, 1383. (30) Clark, T. A Handbook of Computational Chemistry; John Wiley and Sons: New York, 1985.
Tsuzuki and Tanabe TABLE I: Twist Angles and Internal Rotational Barrier Heights of Biphenyl from Experiments in the Cas Phase and from Calculations" ref #)b AEoc AE,od thermodynamic data' 27 1-2 1-2 Raman spectra' 28 1.4 1.4 1. 2 44.4 (1.2) 1.4 (0.5) 1.6 (0.5) ED datag 40-43 EASh 3' extended Hiickel 16 50 5.5 0.9 0.23 12.46 extended Hiickel 17 66 90 0.0 4.9 CND0/2 18 42 19 1.8 1.6 CNDO/2 35 CND012 20 2.1 3.6 20-40 PCILO 21 0.7 2.2 4.5' 32 1.2 HF/double { 22 42 25 HF/STO-3G 2.26' 3.16 HFJSTO-3G 2.2' 43.8 26 3.2 HF/STO-3G 38.63 23 2.40k 2.05 HF/6-3 1G 45.41 3.17 24 .62k 44.74 H F/6-3 1 G .65' 24 3.23 this work 46.13 HF/6-3 1G* .48' 3.28 HF/6-31G* this work 45.63 ,541 3.34 HF/6-31G** .51' 3.33 this work 46.26 this work MP2/6-3 1G * / / H F/ .72k 3.84 6-31G* this work MP3/6-31G*//HF/ 3.45 .73k 6-31G* 3.47 MP4(SDQ)//6-3 lG*// this work .58k HF/6-31* "Angles in deg; energies in kcal/mol. bEquilibrium twist angle. c T h e internal rotational barrier height at 0'. dThe internal rotational barrier height a t 90'. 'The internal rotational barrier height is estimated from the comparison of the calorimetric entropy and the entropy calculated from observed vibrational frequencies. fThe internal rotational barrier heights are estimated from the frequency of the torsional mode obtained from Raman spectra. ZThe twist angles and the barrier heights are estimated from electron diffraction data by using a dynamic model. "The twist angle is estimated from the combined analyses of electronic absorption spectra and simple molecular orbital calculations. Bond distances and bond angles are fixed. 'Geometry is optimized under the constraint that the carbon and hydrogen atoms of each ring remain coplanar and the carbon skeleton of each ring remains a regular hexagon. t Phenyl rings are kept planar in the geometry optimization. 'The planarity restriction is not imposed in this geometry optimization.
for styrene shows that the use of a polarized basis set and the incorporation of the electron correlation correction make a substantial change in the calculated internal rotational barrier heighte3' Unfortunately, the ab initio calculation for biphenyl with electron correlation using a polarized basis set has not been reported. In this work we describe the calculation of the internal rotational potential of biphenyl using polarized basis sets with geometry optimization. Electron correlation energies are corrected for the geometries obtained by the Hartree-Fock level geometry optimization by use of the M~ller-Plessetperturbation The calculated potentials are compared with previously reported experimental and calculated potentials. Computational Technique Gaussian 8237and Gaussian 8638programs were used for the ab initio calculations on a Cray X-MP computer. The geometries (31) Tsuzuki, S.; Tanabe, K.; Osawa, E. J . Phys. Chem. 1990,94,6175. (32) Mdler, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618. (33) Binkley, J. S.; Pople, J. A. Int. J . Quantum Chem. 1975, 9, 229. (34) Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J . Quantum Chem. Symp. 1976, 10, 1.
(35) Krishnan, R.; Pople, J. A. I n f . J . Quantum Chem. 1978, 14, 91. (36) Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244. (37) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Krishnan, R.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Gaussian 82; CarnegieMellon Chemistry Publishing Unit: Pittsburgh, PA 15213. (38) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fleuder, E. M.; Pople, J. A. Gaussian 8b; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA 15213.
Internal Rotational Potential of Biphenyl were optimized at the Hartree-Fock level with 6-31G* (d functions on C)39and 6-31G** (d functions on C and p functions on H)40 basis sets. The Murtagh-Sargent analytical gradient optimization routines41 in these programs were used for the optimization. In the geometry optimization, the phenyl rings of biphenyl were assumed to be planar. D2, D2*,and Dzd symmetry restrictions were imposed for twisted, coplanar, and perpendicular conformers, respectively. The requested Hartree-Fock convergence on the density matrix was IO4 unit, and the threshold value of maximum displacement was 0.0018 A and that of maximum force was 0.000 45 hartree/bohr. The electron correlation energy was calculated for the geometries obtained by Hartree-Fock level geometry optimization by using the Mdler-Plesset perturbation energy calculation r ~ u t i n e ~in ~these - ~ ~programs.
Results and Discussion Torsional Angle. As mentioned in the Introduction, the twist angle of biphenyl has been measured by various experimental methods.'-I5 The twist angle from electron diffraction studies in the gas phase is 44.4 f 1 .2'.]s2 The twist angle from the interpretation of electronic absorption spectra in the gas phase is 40-43' and in heptane solution is 19-26°.3 The twist angle from the analysis of vibronic spectra in the molten state and in solution is 32 f 2:' and that in carbon disulfide solution is 37 f 20e5 The analysis of the chemical shifts for solution I3CNMR spectra gave a twist angle of 26 f 5°.6 The planarity of biphenyl was concluded from the analysis of magnetic anisotropy' and of the Kerr constant8 in carbon tetrachloride. X-ray crystallography showed that biphenyl was planar in the crystalline state at room temperature.*I2 However, the planarity of biphenyl was claimed in X-ray crystallography studies at 1 IO K, which showed that the biphenyl molecule had large-amplitude torsional motion about the C-C bond between phenyl rings and that the molecular geometry determined by crystallography at this temperature did not correspond to the equilibrium g e ~ m e t r y . ' ~At, ~lower ~ temperature, biphenyl crystals show a phase t r a n ~ i t i o n . ~A~twisted geometry of perdeuteriobiphenyl was found from a neutron diffraction study of a crystal at 22 K.I5 Various levels of molecular orbital calculations have been applied for the estimation of the twist angle. The calculated twist angles are listed in Table I . The twist angles from extended Huckel calculations are a little larger than the experimental v a l ~ e . ' ~The , ' ~ twist angle from a CND0/2 calculation with fixed geometry is 90°, which fails to reproduce the experimental twist angle.I8 The change of the bond distance between phenyl rings improved the agreement of the twist angle with the experimental v a l ~ e . ' The ~ . ~ twist ~ angle from a PCILO calculation is close to the experimental value.2' The first ab initio calculation of biphenyl was reported by Almlof using a double-{-quality Gaussian basis set.22 McKinney et al. reported an HF/STO-3G level cal~ulation.~~ They calculated the twist angles to be 32 and 42', respectively, by using fixed bond distances and angles. Penner reported the HF/STO-3G level calculation of the internal rotational potential of biphenyl by imposing the restriction that phenyl rings remain regular hexagons.26 From this potential the equilibrium twist angle was estimated to be 43.8'. Recently Hafelinger et al. reported the full geometry optimization of the twisted conformer of biphenyl at H F/STO-3G and HF/6-3 1G level^.^^,^^ The calculated twist angle at the HF/STO-3G level is 38.63'. The twist angle of 45.41' from the HF/6-31G level calculation is very close to that from electron diffraction experiments. We optimized the twisted geometry of biphenyl at the HF/631G* level by imposing D2 symmetry and assuming planarity of the phenyl rings. The calculated twist angle is 46.13', which is very close to the value from the HF/6-31G level calculation and ~~
~
~~
(39) Hariharan, P. C.; Pople, J . A. Chem. Phys. Lett. 1972, 16, 217. (40) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (41) Murtagh, B. A,; Sargent, R. W. H. Comput. J. 1970, 13, 185. (42) Hochstrasser, R . M.; McAlpine, R. D.; Whiteman, J. D. J. Chem. Phys. 1973, 58, 5078.
The Journal of Physical Chemistry, Vol. 95, No. I, 1991 141 H5
\C5
H6
H 6'
H 5'
H2
H 2'
H3
C6/
H3
Figure 1. The numbering of the atoms of biphenyl.
that from electron diffraction work. The removal of the planarity restriction does little to change the calculated twist angle of the HF/6-31G level calculation. The twist angle obtained by further optimization after removing the restriction is 45.63'. The addition of the polarized basis set on hydrogen atoms does little to affect the calculated twist angle. The twist angle of 46.26' is obtained by HF/6-3 IG** level optimization with the planarity restriction imposed. Bond Distances and Angles. The bond distances and angles of the twisted, coplanar, and perpendicular conformers of biphenyl obtained from HF/6-31G* and HF/6-31G** level calculations are very close to those from the HF/6-3 1G level c a l c ~ l a t i o n , ~ ~ as shown in Table 11. The deviations of the bond distances and angles from the HF/6-31G values are less than 0.003 A and 0.2', respectively. Torsional Potential. The internal rotatinal barrier height of biphenyl was first estimated at 1-2 k ~ a l / m o by l ~ the ~ comparison of the calorimetric entropy and the entropy estimated from observed vibrational frequencies. The internal rotational barrier height in the gas phase was also estimated from electron diffraction measurements and Raman spectra. A E O and AEw were estimated to be 1.4 f 0.5 and 1.6 f 0.5 kcal/mol, respectively, from electron diffraction analysis.1,2 The analysis of the Raman spectra of the torsional mode assuming a twist angle of 45' showed that AEo and AEgOwere both 1.4 kcal/mo1.28 The internal rotational barrier heights were also measured in solution. The internal rotational barrier heights of 4,4'-dideuteriobiphenyl in methylcyclohexane solution, in chloroformcarbon tetrachloride solution, and in carbon disulfide solution obtained from measurements of the temperature dependence of the chemical shifts in proton NMR spectra are 0.44 f 0.05,0.7, and 1.10 f 0.25 kcal/mol, re~pectively.~~ The barrier height estimated from the measurement of the spin-lattice relaxation time of perdeuteriobiphenyl in dimethyl sulfoxide is 3.5 1 kcal/mol.s Various levels of molecular orbital calculations were also applied for the estimation of the internal rotational barrier height of biphenyl. The calculated barrier heights are summarized in Table I. The barrier heights from semiempirical molecular orbital calculations show considerable scatter. AEo is overestimated by extended Huckel ~ a 1 c u l a t i o n . lThe ~ ~ ~barrier ~ height at 0' from C N D 0 / 2 calculations with fixed geometry is also higher than that from electron diffraction work.l8 Tajiri et al. and Janssen et al. reported that improved agreement with the experimental barrier heights was achieved by changing the bond distance between phenyl The barrier height at 0' from the PCILO calculation is lower than the barrier height from electron diffraction experimentS2l Almlof and McKinney reported the ab initio calculations of the internal rotational barrier heights using a fixed g e ~ m e t r y . ~ ~ . ~ ~ The overestimated AEg0 value of 4.5 kcal/mol was given by Almlof. The AEo value of 3.76 kcal/mol from the HF/STO-3G calculation by McKinney is higher than that from electron diffraction work. Recently the importance of geometry optimization in the calculation of the internal rotational barrier height was e m p h a ~ i z e d . ~Thus ~ the disagrement of these calculations with ~~
(43) Kurland, R. J.; Wise, W. B. J. Am. Chem. Sac. 1964, 86, 1877. (44) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986.
142 The Journal of Physical Chemistry, Vol. 95, No. 1. 1991
Tsuzuki and Tanabe
TABLE II: Calculated Geometric Parameters and Energies for the Twisted, Coplanar, and Perpendicular Conformers of Biphenylu** distances, HF/STO-3GC HF/6-3 lGd HF/6-31G* HF/6-31G** angles, and energies (1985) (1987) (this work) (this work) expe Twisted Conformer1 38.63 45.405 46.13 46.26 44.4 (1.2) 48 CI-CI' 1.5074 1.4918 1.4887 1.4915 1.509 (4) CI-C2 1.3946 1.3950 1.3927 1.3925 1.406 (4) C 2-C 3 1.3850 1.3866 1.3847 1.3844 1.397 (5) c3-c4 1.3862 1.3873 1.3853 1.3850 1.398 (5) C2-H2 1.0819 1.102 (20) 1.0731 1.075 1 1.0755 C3-H3 1.0755 1.0733 1.0759 1.0826 1.102 (20) C4-H4 1.0824 1.0754 1.0730 1.0757 1.102 (20) H2.*H2Ih 2.3462 2.4982 2.4808 2.4989 C2-CI-C6 118.34 1 18.340 119.4 (4) 118.302 118.359 CI-C2-C3 120.84 120.848 119.9 (4) 120.877 120.836 c2-c3-c4 120.240 120.254 120.247 120.20 120.9 (5) c3-c4-c5 119.57 119.483 119.0 (6) 119.436 119.476 1 19.67 119.535 C 1-C 2-H 2 119.8 119.566 119.559 C2-C3-H 3 119.76 1 19.695 119.688 119.675 119.8 C3-C4-H4 120.22 120.259 120.282 120.5 120.262 601.207 01 602.1 37 78 602.498 41 602.623 07 Erepi -454.648 46 -460.095 76 -460.253 85 -460.271 75 El02 k -0.245 31 -0.302 40 -0.300 16 -0.300 17 Ehomo 0.227 27 0.11572 0.1 17 21 0.11705 Ehol 48
CI-CI' c 1- c 2 C2-C3 c3-c4 C2-H2 C3-H3 C4-H4 H2.9H2' C2-C 1 -C6 c 1-c2-c3 c2-c3-c4 c3-c4-c5 C I -C2-H2 C2-C3-H3 C3-C4-H4 Erspl ElOlJ Ehomt
Elumol 49
CI-CI' CI-C2 C2-C3 c3-c4 C2-H2 C3-H3 C4-H4 H 2. *H2' C2-C I -C6 c I -c2-c3 c2-c3-c4 c3-c4-c5 C I -C2-H2 C2-C3-H3 C 3-C4-H 4 Erspi
El02 Ehomb
Elumol
0.0 1.5142 1.3980 1.3843 1.3830 1.0794 1.0825 1.0823 1.9539 117.10 121.50 120.46 119.57 120.37 119.49 120.47 600.461 88 -454.645 19 -0.237 63 0.21531
Coplanar Conformer"' 0.0 0.0 1.4983 1.501 1 1.3982 1.3962 1.3857 1.3838 1.3857 1.3836 1.0697 1.0718 1.0733 1.0756 1.0728 1.0752 1.9608 1.9669 1 16.934 116.791 121.598 121.677 120.487 120.528 1 18.896 I 18.799 120.601 120.66 1 1 19.393 119.312 120.552 120.601 601.437 30 601.727 48 -460.090 70 -460.248 63 -0.291 87 -0.289 50 0.100 47 0.101 77
0.0 1.5012 I .3961 1.3836 1.3834 1.0721 I .0759 1.0756 1.9663 116.805 121.662 120.539 1 18.792 120.668 119.310 120.604 601.767 21 -460.266 43 -0.289 54 0.101 39
90.0 1.5158 1.3923 1.3861 1.3861 1.0827 1.0827 1.0824 3.5481 1 18.80 120.6 1 120.16 1 19.68 1 19.59 119.81 120.21 600.142 10 -454.644 64 -0.276 57 0.267 31
Perpendicular Conformer" 90.0 90.0 1.4962 1.4987 1.3930 1.3907 1.3876 1.3858 1.3873 1.3854 1.0734 1.0755 I .0756 1.0733 1.0757 1.073I 3.5297 3.5300 118.737 118.720 120.657 120.670 1 20.156 120.174 1 19.673 119.591 119.398 119.439 1 19.745 119.768 120.164 120.204 601.275 1 1 601.691 02 -460.093 22 -460.251 50 -0.331 21 -0.327 97 0.13360 0.13455
90.0 I .4987 1.3906 1.3855 1.3851 1.0759 1.0760 1.0760 3.5294 1 18.725 120.660 120.183 119.588 119.423 119.733 120.206 601.748 93 -460.269 34 -0.328 04 0.1 3401
0.0 1.497 (3) 1.398 (2) 1.387 (2) 1.379 (3) 0.980 (2) 0.990 (2) 1.000 (2) 2.056 117.4 (2) 121.2 ( I ) 120.4 ( I ) 119.5 (2) 118.7 ( 1 1 ) 119.5 ( 1 1 ) 120.3
'Distances in A; angles in deg; energies in hartrees. *The numbering of atoms is shown in Figure I . CFrom ref 23. dFrom ref 24. eThe experimental geometric parameters for the twisted conformer are the ro values from electron diffraction experiments.'*24 Those for the coplanar conformer are taken from X-ray diffraction work.I0 'The D2 symmetry constraint is imposed and the phenyl rings are kept planar in the geometry optimization. 8Twist angle. "Distance between the H2 and H2' atoms. 'Nuclear repulsion energy. )Total energy. kEnergy of the highest occupied molecular orbital. 'Energy of the lowest unoccupied molecular orbital. "'The Dlh symmetry constraint is imposed in the geometry optimization. "The D2d symmetry constraint is imposed in the geometry optimization. t h e experiments m a y be explained by t h e lack of geometry optimization. Recently Hafelinger et al. reported calculations of the internal rotational barrier heights with geometry ~ p t i m i z a t i o n . * ~T *h ~e ~
AEo and AE90values obtained a t t h e H F / S T O - 3 G level by assuming the planarity of phenyl rings a r e 2.05 and 2.40 kcal/mol, respectively, and those a t t h e H F / 6 - 3 1 G level are 3.17 a n d 1.62 kcal/mol, r e s p e ~ t i v e l y . ~While ~ AEPoa t the H F / 6 - 3 1 G level is
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 143
Internal Rotational Potential of Biphenyl close to AE90 = 1.6 f 0.5 kcal/mol from electron diffraction experiments, AEo a t this level is much higher than AEo = 1.4 f 0.5 kcal/mol from the same experiments. Strangely, hEoobtained by cruder HF/STO-3G calculations is closer to AEo from electron diffraction experiments. Recently the importance of electron correlation and the use of a large basis set in the calculation of conformational energy was rep~rted.~~JO Thus, one possible explanation of the disagreement between AEo values obtained from the HF/6-31G calculation and from electron diffraction work is that this level of calculation is not accurate enough to reproduce the experimental internal rotational barrier height. Thus, we have calculated the barrier heights by using polarized basis sets and incorporating the electron correlation correction. The AEo and AE90 values obtained by HF/6-31G* level calculations with geometry optimization imposing the constraint that phenyl rings remain planar are 3.28 and 1.48 kcal/mol, respect i ~ e l y . ~Those ~ at the HF/6-31G** level are 3.33 and 1.51 kcal/mol, respectively. The barrier heights calculated at the HF/6-31G* and HF/6-31G** levels are close to those obtained by HF/6-31G calculation^.^^ AEo at the HF/6-31G* level and that at the HF/6-31G** level do not agree with hEofrom electron diffraction work.'S2 Electron correlation energies were calculated by the MdlerPlesset method using the 6-31G* basis set on the geometries obtained by HF/6-31G* optimization. AEo increased due to the incorporation of the electron correlation correction. The calculated AEo values with MP2, MP3, and MP4(SDQ) level electron correlation corrections are 3.84, 3.45, and 3.47 kcal/mol, respectively, and the calculated AEw values are 1.72, 1.73, and 1.58 kcal/mol, respectively.'" The use of the polarized basis sets and the incorporation of electron correlation corrections do not improve the agreement between AEo values from electron diffraction work and from calculation. The internal rotational potential of biphenyl was estimated from electron diffraction measurements and Raman spectra under the assumption that the potential can be described by eq 1.1-2,28 The
V ( 4 ) = '/2[ V*(1 - COS 24)
+ Vd( 1 - COS 44)] + C
(1)
V2 and V4 parameters which appear in eq 1 were optimized to reproduce the experimental measurements. Then the internal rotational barrier heights were calculated from this potential by using the optimized parameters. The information about the potential function from these experimental measurements is essentially for the region around the minimum. Thus the curvature of the potential at the minimum is determined with some degree of accuracy, while the barrier heights depend to a great extent on the mathematical expression selected to describe the potential. This deficiency has already been mentioned by Bastiansen and SamdaLz One possible reason for the disagreement between the experimental AEo value and that from the calculations is the inappropriateness of the mathematical expression for the internal rotational potential that is used to analyze the potential from the experimental measurements. Penner has reported the internal rotational potential at the HF/STO-3G level. He has claimed that eq 1, which has the second and fourth terms of the Fourier series, is not adequate to express his HF/STO-3G potential and the sixth term is necessary.26 In order to understand the details of the shape of the internal rotational potential of biphenyl, we calculated the potential at the MP4(SDQ)/6-3lG*//HF/6-3 1G* level. The geometries are optimized at the HF/6-31G* level by imposing the constraint of planarity of the phenyl rings and fixing the twist angle at 0, 15, (45) The restriction of lanarity of the phenyl rings does little to affect the calculated barrier height4 (46) Removal of the planarity constraint for the twisted geometry gave little change in the calculated barrier heights. Both barrier heights increased only 0.06 kcal/mol on removal of the constraint at the HF/6-31G* level. (47) The calculated energies for the minimum-energy twisted conformer at the MP2, MP3, and MP4(SDQ) levels are -461.76644, -461.81036, and -461.822 85 hartrees, respectively.
TABLE 111: Calculated Internal Rotational Potential of Biphenyl
torsional" angle, deg 0 15 30
45 60
75 90
HF 3.271
2.385 0.757 0.0 0.381 1.126 1.472
re1 energy! kcal/mol MP2 MP3 3.848 3.461 2.478 2.772 0.845 0.728 0.0 0.483
1.350 1.727
0.0
0.509 1.365 1.734
MP4 3.475 2.508 0.766 0.0 0.442
1.237 1.579
"Geometries are optimized at the HF/6-31G* level by fixing the torsional angle and assuming palanarity of the phenyl rings. Energies are calculated by using the 6-31G* basis set with the electron correlation correction by the Maller-Plesset perturbation treatment for the geometries obtained by the HF level geometry optimization. The calculated energies for the 45' twisted geometry at HF, MP2, MP3, and MP4(SDQ) levels are -460.253 84, -461.76644, -461.810 37, and -461.822 85 hartrees, respectively. 30, 45, 60, 75, or 90°. A Moller-Plesset fourth-order correction of the electron correlation energy was made for the optimized geometries. The calculated potential is very shallow in the region near the minimum but has a steep slope in the region of 4 = 0-30°, as shown in Table 111. The calculated torsional potentials of biphenyl were fitted by eq 2, which has the sixth term. The
V(4) =
Y2[ V2(1 - cos 24) + V4(1 - cos 44) +
- COS 64)] + C (2) HF/6-31G* and MP4(SDQ)/6-31G*//HF/6-31G* potentials can be fitted by V(4) = 1/2[-1.45(1 -cos 24) - 2.38(1 -cos 44) - 0.35( 1 - cos 64)J + 3.26 and V ( 4 ) = 1/2[-1 .48( 1 - cos 24) 2.54(1 - cos 44) - 0.42(1 - cos 64)] + 3.46 (kcal/mol), reV6( I
spectively. The sixth term is not negligible in either potential. In order to examine whether eq 1 is appropriate to estimate AEo from the shape of the potential near the minimum, the parameters of the equation were optimized to fit the MP4(SDQ)/6-3lG*//HF/6-3lG* potential in the region of 4 = 30-90°. In this region the energy of the conformer differs from that of the minimum conformer by less than 2.0 kcal/mol. A large fraction of the molecules in this region exist in conditions corresponding to those in experimental measurements. The optimized V2and V4 parameters and constant C are -0.72, -1.91, and 2.35 kcal/mol, respectively. The AEo and AEgOvalues derived from this equation are 2.29 and 1.57 kcal/mol, respectively. AEo obtained from this equation is lower than the correct value from the MP4(SDQ)/6-3lG*//HF/6-31G* potential by as much as 1.18 kcal/mol. These calculations lead to the following conclusion: Equation 1 is not appropriate to describe the potential obtained by the MP4(SDQ)/6-3 IG*/HF/6-3 lG* calculation; the sixth term is necessary to fit the potential satisfactorily. AEo estimated from the shape of the MP4/6-31G*//HF/6-31G* level potential in the low-energy region by use of eq 1 is much lower than the correct value. AEo obtained from the analysis of electron diffraction measurements1q2or of Raman spectra2*using eq 1 would be underestimated if the shape of the experimental internal rotational potential of biphenyl is close to the potential shape obtained from the ab initio calculation. This underestimation can partly be the cause of the disagreement between the experimental AEo value and those from a recent HF/6-31G calculation and from our calculations. the energy Orbital Energy. According to Koopmans' of the highest occupied molecular orbital (HOMO) is equal to the first ionization potential. The calculated energy levels of the HOMO are shown in Table 11. The energy levels of the HOMO for the twisted and perpendicular conformers are lower than that for the planar conformer by 0.01 and 0.04 hartree, respectively, at each level of calculation. The experimental value of the first ionization potential is 0.30 hartree.49 The HF/STO-3G calcu(48) Koopmans, T. Physica 1934, I , 104. (49) Watanabe, K.; Motte, J. R. J . Chem. Phys. 1957, 26, 1773.
144 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 TABLE IV: Mulliken Total Electron Densities and Total Overlap Populations' HF/STO-3Gb HF/6-31Gc HF/6-31G* HF/6-31G1* Electron Densities Coplanar Conformer 5.996 9 I 6.022 27 CI 5.978 a3 5.99641 c2 6.064 IO 6.19857 6.21992 6.14976 6.1 5075 c3 6.063 22 6.20271 6.19869 c4 6.19136 6.201 a5 6.063 20 6.149~ 0.85129 H2 0.937 36 0.793 46 0.793 67 0.799 24 0.798 44 0.937 12 H3 0.850 1 5 H4 0.936 29 0.798 43 0.797 a9 0.849 a3
c2 c3 c4 H2 H3 H4
5.99603 6.065 08 6,06296 6.063 a2 0.93690 0.936 74 0.936 78
Twisted Conformer 6.030 ao 5.988 47 6.19580 6.21542 6.20067 6.19849 6.19691 6.20292 0.79006 0.79244 0.799 67 0.798 46 0.799 a8 0.798 97
6.013 19 6.149 19 6.147 12 6.151 52 0.845 56 0.850 27 0.851 03
CI c2 c3 c4 H2 H3 H4
5.99490 6.065 93 6.062 35 6.064 91 0.936 66 0.936 61 0.937 06
Perpendicular Conformer 6.065 74 6.015 65 6.181 82 6.203 86 6.19867 6.19807 6.19702 6.201 60 0.787 a9 0.790 a4 0.799 97 0.798 a2 0.800 54 0.799 58
6.042 ao 6.13752 6.14597 6.15032 0.843 55 0.85065 0.851 52
CI-c2 C2-C3 c3-c4 CI-CI' CZ-HZ C3-H3 C4-H4
Total Overlap Populations Coplanar Conformer 1.007 83 1.021 I I 1.12754 1.02591 0.997 I 7 I .oaa 04 1.017 73 1.03967 1.10952 0.798 79 0.659 20 0.797 98 0.791 ao 0.746 19 0.75282 0.791 17 0.747 a7 0.767 52 0.79067 0.747 39 0.765 46
1.12350 1.095 50 i.ioa30 0.766 16 0.785 00 0.788 36 0.788 26
CI-cz C2-C3 c3-c4 CI-CI' C2-H2 C3-H3 C4-H4
I ,009 05 1.023 68 1.01835 0.799 84 0.789 92 0.79048 0.79065
Twisted Conformer 1.02an 1.12640 I ,004 1 2 I ,082 90 1.041 36 1.11074 0.623 49 0.728 68 0.747 76 0.759 90 0.746 72 0.764 94 0.75004 0.766 56
1.123 62 1.086 16 1.11090 0.712 70 0.78644 0.786 52 0.789 70
CI-c2 C2-C3 c3-c4 CI-CI' C2-H2 C3-H3 C4-H4
Perpendicular Conformer 1.01091 1.02873 1.14026 I ,00558 I .079 62 1.02090 1.01938 I ,042 24 I .I I 1 aa 0.799 54 0.603 72 0.688 oa 0.789 40 0.748 74 0.762 i o 0.746 36 0.764 10 0.790 15 0.790 69 0.750 5 1 0.766 66
c1
1.I37 24
1.082 16 1.112ia
0.681a2 0.787 a4 0.785 94 0.789 70
#The geometry of each conformer is given in Table 11. The numbering of atoms is shown in Figure 1. From ref 23. From ref 24.
lation fails to reproduce this experimental value.23 The calculated HOMO energy levels from our HF/6-31G* and HF/6-31G** level calculations are close to those from an HF/6-31G level c a l c ~ l a t i o n The . ~ ~ HOMO energy level for the twisted conformer
Tsuzuki and Tanabe obtained from an HF/6-3 lG* calculation agrees with the experimental value. Mulliken Population Analysis. Mulliken electron densities and total overlap population^^*^^ for biphenyl calculated at HF/631G* and HF/6-31G** levels are compared with those calculated at HF/STO-3G and HF/6-31G levels, as shown in Table IV. The electron densities calculated at HF/6-31G* and HF/6-31G** levels are close to those calculated at the HF/6-31G The calculated electron density on Cl is smaller than those on other carbon atoms. The increase of the twist angle causes the decrease in the difference between the electron density on CI and those on other carbon atoms. The overlap populations calculated at HF/6-3 lG* and HF/ 6-31G** levels are larger than those at the HF/6-31G level. This difference is large especially for bonds between carbon atoms. The increase of the twist angle causes the decrease of the overlap population of the bond between phenyl rings. The change of the overlap population of this bond is larger at HF/6-31G* and HF/6-31G** levels than that at the HF/6-31G level. The decreases in the overlap population from the planar conformer to the perpendicular conformer calculated at HF/6-3 1 G, HF/631G*, and HF/6-31G** levels are 0.055, 0.110, and 0.084, respectively. Conclusion
The bond distances, valence angles, and twist angle of biphenyl obtained at HF/6-31G* and HF/6-31G** levels well reproduced the experimental values as well as the recently reported values from an HF/6-3 1G level calculation. The internal rotational barrier heights of biphenyl at 0 and 90' obtained at HF/6-31G* and HF/6-31G** levels were close to those from the HF/6-31G level calculation. The calculated barrier heights at 90' were close to the value from electron diffraction experiments, whereas those at 0' were higher than that from electron diffraction experiments. The electron correlation correction by the Moller-Plesset perturbation treatment further increased the barrier height at 0' . The use of the polarized basis sets and the incorporation of the electron correlation correction did not improve the agreement between the calculated barrier height at 0' and that from electron diffraction work. The internal rotational potential calculated at the MP4(SDQ)/6-3lG*//HF/6-31G* level was shallow near the minimum but had a steep slope in the region of 4 = 0-30'. The equation V ( ~ ) = 1 / 2 V 2 ( 1 - c o s 2 4 ) + ' / 2 V 4 ( 1 - ~ ~ 4 ~ ) + C , w h i c h was used for the estimation of the internal rotational potential from the experimental measurements was fitted to reproduce the calculated potential in the low-energy region. The barrier height at 0' estimated from the fitted equation was much lower than the value from the a b initio calculation. This showed that this equation was not appropriate to estimate the barrier height from the shape of the potential in the low-energy region, if the shape of the experimental potential was close to the potential shape obtained from the calculation. (50) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (51) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1997. (52) Mulliken, R. S. J . Chem. Phys. 1955, 23, 2343.
