10804
J. Phys. Chem. 1992,96, 10804-10808
HOMO of the a1 representation. Acknowledgment. We are pleased to thank the Conseil Scientifique du Centre de Calcul Vectoriel de la Recherche for allowing us a grant of computer time on the CR4Y-2 computer of the CCVR.
References md Notes (1) (a) Herrmann, W. A.; Serrano, R.; Bock, H. Angew. Chem. 1984,96, 364; Angew. Chem., Inr. Ed. Engl. 1984,23, 383. (b) Klahn-Oliva, A. H.; Sutton, D. Organometallics 1984, 3, 1313. (2) (a) Herrmann, W. A.; Romao, C. C.; Fischer. R. W.; Kiprof, P.; de MCric de Belkfon, C. Angew. Chem. 1991,103,183; Angew. Chem., Inr. Ed. Engl. 1991, 30, 185. (b) Herrmann, W. A,; Taillefer, M.; de M€ric de Bellefon, C.; Behm, J. I w g . Chem. 199L30.3247. (c) de MCric de Bellefon, C.; Herrmann, W. A.; Kiprof, P.; Whitaker, C. R. Orgunometallics 1992.11, 1072. (3) Herrmann, W. A.; Kiprof, P.; Rypdal, K.; Tremmel, J.; Blom, R.; Alberto, R.; Behm, J.; Albach, R. W.; Bock, H.; Solouki, B.; Mink, J.; Lichtcnberger, D.; Gruhn, N. E. J. Am. Chem. Soc. 1991, 113, 6527. (4) Lotspeich, J. F.; Javan, A. J . Chem. Phys. 1959, 31, 633. (5) Szyperski,T.; Schwerdtfeger, P. Angew. Chem. 1989, 101, 1271; Angew. Chem., Inr. Ed. Engl. 1989, 28, 1228. (6) Ara, I.; Fanwick, P. E.; Walton, R.A. J . Am. Chem. SOC.1991, 113, 1429. (7) Costas, M.; Leininger, T.; Jeung, G.-H.; BCnard, M. Inorg. Chem. 1992, 31, 3317. (8) Rohmer, M.-M.; Emenwein, R.; Ulmschneider, M.; Wiat, R.; Mnard, M. lnr. J . Quantum Chem. 1991, 40, 723 and references therein. (9) Ross, R. B.; Powers, J. M.; Atashroo, T.; Ermler, W. C.; LaJohn, L. A.; Christianacn, P. A. J . Chem. Phys. 1990, 93, 6654. (10) (a) Huzinaga, S. Approximate Atomic Funcrions; Technical Report, University of Alberta, Canada, 1971. (b) Huzinaga, S.J . Chem. Phys. 1965, 42, 1293. (11) Dunning, T. H. J. Chem. Phys. 1971,55, 716. (12) At the SCF level, the averaged geometry taken for 1 (dR4 = 1.706 A, dcq = 1.425 A) was found more stable by 1.8 kJ-mol-' than the experimental one, a C, symmetry being assumed in both calculations. Then, a
12-deg rotation of the Cp ring did not modify the energy by more than 0.1 kJ-mol-'. (13) Carter, E. A.; Goddard 111, W. A. J . Chem. Phys. 1988.88, 3132. (14) (a) Schilling, J. B.; Goddard 111, W. A.; Beauchamp, J. L. 1.Phys. Chem. 1987,87,5616; J . Am. Chem. Soc. 1987,109,5565. (b) Ohanessian, G.; Brusich, M. J.; Goddard 111, W. A. J . Am. Chem. Soc. 1990,112,7179. (c) Merchan, M.; Daudey, J. P.; Gonzalez-Luque, R.; Nebot-Gil, I. Chem. Phys. 1990,141, 285. (d) Merchan, M.; Gonzalez-Luque, R.; Nebot-Gil, I. J. Chem. Phys, 1990, 93,495. (15) (a) Maitre, P.; Lefour, J. M.; Ohanessian, G.; Hibcrty, P. C. J. Phys. Chem. 1990,94,4082. (b) Hiberty, P. C.; Noizet, E.; Flament, J. P. Chem. Phys. krr. 1992, 189, 259. (16) Smith, G. W.; Carter, E. A. J . Phys. Chem. 1991, 95, 2327. (17) A previous study (Lotspeich, J. F. J . Chem. Phys. 1959, 31, 643) assumed the electronegativity of the ReOl radical to be 1.8 only, leading to strongly ionic descriptions of the rhenium-halogen bonds in OIReX (X = F, Cl). (1 8) The fragments are computed at the SCF level with the same geometry as in the molecule. All fragments, including the halogen atoms, are assumed to be in the du*O state, which means that the F and CI fragments are not spherical atoms, but polarized ones (see, for instance: Schwarz, W. H. E.; Ruedenberg, K.; Mensching, L. J . Am. Chem. SOC.1989, I l l , 6926 and references therein). (19) Huheey, J. E. Inorgunic Chemistry; Harper & Row: New York, 1978; Table F1, pp 842-850. (20) Doran, M.; Hillier, I. H.; Seddon, E. A.; Seddon, K. R.;Thomas, V. H.; Guest, M. F. Chem. Phys. Lerr. 1979, 63, 612. (21) (a) Granozzi, G.; Mougenot, P.; Demuynck, J.; BCnard, M. Inorg. Chem. 1987, 26, 2588. (b) Quelch, G. E., Hillier, I. H. Chem. Phys. Lcrr. 1988, 144, 153. (c) Clark, D. L.; Green, J. C.; Redfem, C. N.; Quelch, G. E.; Hillier, I. H.; Guest, M. F. Chem. Phys. Lcrr. 1989, 154, 326. (22) No sign of spin-orbit splitting is visible on the He I photoelectron spectrum in the region 11.8-13.2 eV, containing the four peaks with lowest energy. The fifth band only shows twin peaks (13.8 and 14.0 eV) that can be assigned to spin-orbit coupled ionization events. The influence of spimrbit interaction on the three bands still observed at higher energies has not becn clearly established.' (23) The a2 orbital is the only occupied valence MO belonging to that represcntation. The highest e level, almost completely localized on the oxygen lone pairs, also remains largely unaffected by interactionsinvolving the orbitals of the L ligand.
Nonbonding Interaction Potential of Ethylene Dimer Obtained from ab Initio Molecular Orbital Caicuiatlons: Prediction of a Dtd Structure Seiji T s d * and Kazutoshi Tanabe National Chemical Laboratory for Industry, Tsukuba. Ibaraki 305, Japan (Received: August 17, 1992)
Nonbonding interaction potentials of 12 orientations of ethylene dimer were calculated at the MP2/6-31 1G(2d,2p) level with basis set superposition error correction. The potential of a DM orientation has a deepest minimum of -1.07 kcal/mol. This orientation agrees with the structure predicted from the analysis of infrared spectra by Ritter and Gruen. The calculated Coulombic interaction between ethylene molecules based on the HF/6-31G level Mulliken charge of the monomer shows that the Coulombic interaction stabilizes this orientation. Evaluation of the basis set effect on the calculated interaction energy using several basis sets up to the 6-311G(2d,3p) basis set shows that the dispersion energy component, which was calculated as the electron correlation energy, significantly depends on the basis set used. Smaller basis sets underestimate the dispersion energy, whereas the repulsive and Coulombic energy component calculated at the HF level is little affected by the basis set used.
Introduction Recently, structures and properties of weakly bound complexes have attrached much interest, since the information is important to understand the nature of the nonbonding interaction. Nonbonding interactions frequently play a crucial role in determining the conformation and crystal structure of organic m~lecules.~-~ Nonbonding interactionsof wsystems have been studied by several group^,^^* since these interactions amtrol several phenomena such as crystal packing of unsaturated hydrocarbon molecules,29-M.Se61 conformational preference of nucleic a ~ i d s , 6and ~ * ~host-guest ~ interactions of aromatic molecules.64*6'Accurate understanding 0022-3654/92/2096-l0804SO3.00/0
of the nonbonding interactions of mystems is necessary to study these phenomena. Recently, computer simulations such as molecular mechani c ~and~molecular * ~ d~ynamcis~@-"' ~ have been frequently applied to predict molecular structures and related properties of organic compounds. Detailed information on the nonbonding interaction of unsaturated hydrocarbon molecules is also requested to carry out these simulations. Ethylene dimer is the simplest system that has a nonbonding interaction between r-systems. Hence several experimental and theoretical studies of ethylene dimer have been r e ~ a r t e d . ~ * ~ ~ 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10805
Interaction Potential of Ethylene Dimer
TABLE I: Cdculatcd Iatermdeclrlrr Interaction Eaergiea and BSSE (Basis Set Suwrposition Error) of Ethvlew DimeP interaction interaction energy + basis set energy BSSE BSSE correction Orientation B 6-31G* -1.215 1.011 -0,204 6-311G* -1.025 0.608 -0,417 ~~
C
A
E
-w I
Figure 1.
work.
P
0
D
H
6-31 lG** 6-31 1G(2d,p) 6-311G(2d,2p)
-1.107 -1.321 -1.455
6-31G* 6-31 1G* 6-31 1G** 6-31 1G(2d,p) 6-31 1G(2d,2p) 6-31 1G(3d,2p) 6-31 lg(2d,3p) 6-31 lG(2df,2p)
-1.321 -1.394 -1.526 -1.668
0.591 0.590 0.631
-0.516 -0.731 -0.824
Orientation K
1
K
L
Twelve orientations of ethylene dimer considered in the present
-1.823 -1.991 -1.984
1.106
0.973 0.922 0.769 0.756 0.846 0.833 0.669
-0.215 -0.42 1 -0.604 -0.899 -1.067
-1.145 -1.151
Infrared and Raman spectra and the dipole moment of ethylene -1.791 -1.122 *~ dimer have been measured to analyze the ~ t r u c t u r e . * ~ ~Several Energies are in kcal/mol. Electron correlation energy is corrected levels of molecular orbital calculations have been applied to this by the second-order Maller-Plesset perturbation method (MP2). ~ y s t e m . ~However, ~”~ the structure of ethylene dimer is still a BSSE is corrected by the counterpoise method. The intermolecular controversial issue. distances are 3.8 A for both dimers. While early calculations of the ethylene dimer are semiempirical , ~ ~ ~ ~ ~ ~the ~ ~Morller-Plesset ~~~ or Hartrce-Fock (HF) level ab initio c a l c u l a t i ~ n s these perturbation m e t h 0 d . 8 ~BSSE ~ ~ was corrected levels of calculations cannot accurately evaluate the dispersion by the counterpoise method.82 The intermolecular distance is the energy, which is an important interaction energy term of hydistance between the centers of gravity of two ethylene molecules. drocarbon molecules. An electron correlation correction is necHarmonic vibrational frequencies were calculated by using the essary to evaluate the dispersion energy. normal mode analysis routine in the program. Recently, Alberts et al. reported ab initio molecular orbital Results and Discussion calculationsof the nonbonding interaction of ethylene dimer using Electron ComelationEnergy. To evaluate the effect of electron a polarized basis set with a Morller-Plesset second-order electron correlation, the electron correlation energies of the two orientations correlation correction (MP2).58 They optimized geometries of B and K (Figure 1) of ethylene dimers were calculated by the five stationary points of the potential energy surface of the ethylene second, third, and fourth-order Morller-Plesset method by using dimer. They predicted the orientation F (Figure 1) as an energy the 6-311G** basis set. The intermolecular distances of these minimum structure for ethylene dimer. dimers were 3.8 A. The calculated electron correlation energies The basis set effect is an important issue in evaluating the of the orientation B at the MP2, MP3, and MP4(SDTQ) levels interaction potential calculated by the ab initio method. Recently, are -1.367, -1.236, and -1.281 kcal/mol, respectively. Those of we have reported the effects of basis set and basis set superposition the orientation K are -1.163, -1.057, and -1.123 kcal/mol, reerror (BSSE) correction on the calculation of the nonbonding spectively. The calculated correlation energies at the MP2 level interaction of methane dimer.78 The calculated dispersion energy are only a few percent different from those obtained at the greatly depends on the used basis set. A large basis set that has MP4(SDTQ) level. The dispersion energies calculated at the MP3 two or more sets of polarized functions of different exponents on level are slightly smaller than those at the MP4(SPTQ) level. The each atom is newwry to evaluate the dispersion energy correctly. same tendency has been observed for the calculations of methane Smaller basis sets underestimate the dispersion energy considdimer.78 The electron correlation energies of methane dimer erably. We have found that the BSSE correction has a significant calculated at the MP2 level deviate only less than 10% from those effect on the calculated interaction potential.78 obtained at the MP4(SDTQ).78 Due to the good performance The accuracy of the BSSE correction by the counterpoise of the MP2 level correction, we decided to correct the electron method was a controversial issue. However, recently reported correlation energies at the MP2 level in all the following calcudetailed evaluations of the counterpoise method show that the lations. so-called overcorrection of the BSSE by the counterpoise method Electron correlation energy correction was important to estimate is not large, if a reasonably large basis set is used, and interaction the potential depth of ethylene dimer. The calculated potentials energies corrected by the counterpoise method are more reliable at the HF level are very shallow. For example the potential depth than noncorrected ones.’e81 of the orientation K calculated at the MP2/6-311G(2d,2p) level The basii set used by Alberts et al. has only a set of d functions is -1.07 kcal/mol, whereas the depth calculated at the HF/6on carbon atoms.58 The calculated dispersion energy from their 3 11G(2d,2p) level is shallower than -0.1 kcal/mol. basis set would be underestimated. Furthermore they did not Basii Set SuperpositionError. To evaluate the effect of BSSE correct the BSSE,82which would have a significant effect on the correction on the intermolecular interaction energies, the BSSEs calculated interaction energy of the dimer.79 In this paper we of the dimers B and K were calculated by using several basis sets calculate nonbonding interaction potentials of 12 orientations of as shown in Table I. The BSSE’s are considerably large, if crude ethylene dimers using the 6-3 11G(2d,2p) basis set with electron 6-31G* basis sets are used. The BSSE’s of the MP2 level calcorrelation and BSSE correction. Basis set and electron correlation culations are larger than the corresponding ones of the H F level. effects on the calculated interaction energy are also discussed. The use of the improved basis sets decreases the BSSEs. However, Computational Technique the BSSE’s calculated at the MP2/6-311G(2d,2P) level are still The GAUSSIAN 86 program8j was used for the molecular large and cannot be ignored. orbital calculations. The basis sets implemented in this program Effect of Geometry Relaxation. To evaluate the effect of gewere The geometry of single ethylene molecule was ometry relaxation the geometries of monomer and dimer ethylene optimized at the MP2/6-311G(2d,2p) level. The optimized ge(orientation K in Figure 1) were optimized at HF/6-31 lG* level. ometry, in which C-C and C-H bond distances and C-C-H The dimer formation little changes the geometrical parameters. The changes of bond distances and valence angles are less than valence angle are 1.330824 A, 1.078 157 A, and 121.343O, respectively, was used for the calculations of the interaction energies 0.001 A and 0 . l o ,respectively. Alberts et al. reported the geof the dimers. The electron correlation energy was corrected by ometry optimization of ethylene dimers at the MP2 level. They (I
Tsuzuki and Tanabe
10806 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 TABLE 11: Calculated Intermolecular Interaction Energies of Ethylene Dimer Using Several Basis Sets* basis set E,,,.? EWFC Eon,! Orientation B 6-31G* 6-31 1G* 6-311G** 6-31 1G(2d,p) 6-31 1G(2d,2p)
-0.204 -0.417 -0.516 -0.73 1 -0.842
0.846 0.8 13 0.851 0.884 0.917
-1.050 -1.230 -1.368 -1.616 -1.741
0.569 0.570 0.559 0.540 0.548 0.568 0.568 0.542
-0.784 -0.992 -1.163 -1.439 -1.615 -1.714 -1.720 -1.664
Orientation K 6-31G* 6-31 l G * 6-311G** 6-31 1G(2d,p) 6-31 1G(2d92p) 6-31 1G(3d,2p) 6-31 1G(2d,3p) 6-31 1G(2df,2p)
-0.215 -0.421 -0.604 -0.899 -1.067 -1.145 -1.151 -1.122
a Energies are in kcal/mol. BSSE is corrected by the counterpoise method. The intermolecular distances are 3.8 A for both dimers. Calculated interaction energies corrected by the Maller-Plesset second-order perturbation method (MP2). 'Calculated interaction energies by the H F method. dCalculated electron correlation energies by
the MP2 method.
also found that dimer formation little changed the geometrical
parameter^.^^ Effect of Basis Sets. The intermolecular interaction energies of the dimers B and K were calculated by using several basis sets up to 6-31 1G(2df,2p) to evaluate the basis set effect. The calculated interaction energies are summarized in Table 11. Larger basis sets considerably increase the potential depths. The interaction energies of the orientations B and K calculated at the MP2/6-311G(2d,2p) level are 4.1 and 5.0 times larger than those calculated at the MP2/6-3 lG* level, respectively. In order to evaluate the details of the basis set effect, the interaction energy was separated into two components, the repulsive and Coulumbic energy component and the dispersion energy component. The calculated interaction energy at the HF corresponds to the repulsive and Coulumbic energy component. The basis set effect on this energy component is small. The calculated electron correlation energy corresponds to the dispersion energy component. In contrast to the HF level energy component, the calculated dispersion energies greatly change by the choice of the basis set. The calculated dispersion energies from the 6-31 1G(2d,2p) basis set are considerably larger than those calculated with cruder basis sets. The calculated dispersion energies of the orientation B at the intermolecular distance of 3.8 A using 6-31G*, 6-311G*, 6-311G**, and 6-311G(2d,p) basis sets are 60, 71, 79, and 93% of the dispersion energy obtained with the 631 1G(2d,2p) basis set. The calculated dispersion energies of the orientation K at the intermolecular distance of 3.8 A using these basis sets are 49,61,72, and 89% of the dispersion energy obtained with the 6-31 1G(2d,2p) basis set. The dispersion energy of the orientation K was also calculated with further improved 6311G(3d,2p),6-31 1G(2d,3p), and 6-31lG(2df,2p) basis sets. The further improvement of the basis set increases the calculated dispersion energy only a few percent. From these observations we decided to carry out the following calculations of the 12 orientations of ethylene dimers using the 6-31 1G(2d,2p) basis set. A similar basis set effect on the calculated dispersion energy has been observed for the calculations of methane dimer.'* The calculated dispersion energy of methane dimer is significantly increased by the use of a large basis set up to the 6-31 lG(2d,2p). But the effect of further improvement of the basis set on the calculated dispersion energy of methane dimer is small. These calculations show that the use of a flexible basis set, which has two or more sets of polarized functions of different exponents on each atom, is indispensable to evaluate the dispersion energy correctly. Polarizability. The origin of the dispersion energy is the interaction between induced dipoles of molecules. Thus the evaluation of the polarizability calculated by the ab initio method
TABLE III: Calculated Polarizability of Ethylene Monomer (au) HF MP2 basis set HF/6-31G* HF)6-311G* HF/6-311G'* HF/6-31 1G(2d,p) HF/6-311G(2d,2p) HF/6-311G(3d,2p) HF/6-311G(2d,3p) HF/6-31 lG(2df,3p) HF/6-311G(3d,3p)
axx
ayy
19.70 19.97 20.23 21.31 21.56 23.07 22.76 21.58 23.19
32.18 33.73 34.17 33.83 34.20 34.65 34.87 34.31 35.00
exp"
26.04 36.44 22.94
a
a,, 8.33 11.72 12.42 14.18 14.77 18.76 16.35 14.81 19.24
axx
ayy
azz
19.84 20.36 20.65 21.65 22.03 23.48 23.29 22.01 23.70
28.60 30.47 30.81 30.98 31.43 32.13 32.24 31.50 32.55
8.17 11.34 11.98 13.80 14.43 18.44 16.18 14.48 18.98
Reference 93.
would be interesting. The polarizability of ethylene was calculated at the H F and MP2 levels using several basis sets. The results are summarized in Table 111. Calculated polarizabilities using small basis sets are considerably smaller than the experimental ~alues.9~ However, the calculated polarizability increases as the used basis set becomes large. The agreement with the experimental polarizability is fairly improved, if the 6-311G(3d,3p) basis set is used. Intermolecular Interaction Potential of 12 Orientations. The structure of ethylene dimer is still a controversial issue, as mentioned in the Introduction. Rytter and Grued2and Cowieson et al.33have reported the analysis of IR spectra of ethylene dimer in an Ar matrix. Their conclusion is that ethylene dimer has DU symmetry and the orientation K is most probable. This orientation does not have a dipole moment, which agrees with the experimental measurement .46 Several molecular orbital calculations of ethylene dimer have been r e p ~ r t e d . ~Suzuki ~ - ~ ~and Iguchi calculated nine orientations of ethylene dimers using the 431G basis set. They reported that the orientation E had the deepest minimum.53 More recently Alberts et al. reported calculations of five orientations of ethylene dimers, which correspond to the orientations A, D, E, F, and G in Figure 1.58 They concluded that orientation F was the most stable structure. Unfortunately these two groups did not consider orientation K. We calculated nonbonding interaction potentials of the 12 orientations of ethylene dimers shown in Figure 1 at the MP2/ 6-31 lG(2d,2p) level with BSSE correction. The calculated potentials are shown in Figure 2. The depth of the interaction potential of the orientation F, which Alberts et al. concluded as the most stable conformer, is -0.72 kcal/mol (intermolecular distance is 4.4 A). However, three other orientations (B, J, K) have deeper minima. The orientation K (3.8 A) has the deepest minimum of -1.07 kcal/mol. This orientation agrees with the dimer structure postulated by Rytter and Gruen from the analysis of IR spectra32and also with the experimental measurement of the dipole moment.46 The depths of the potentials of the orientations B and J are close to that of orientation F. The depths of the potentials of other orientations are shallower than -0.5 kcal/mol. The potentials of orientations A and L do not have minima. A Coulombic interaction between ethylene molecules would exist, since C-H bonds of an unsaturated hydrocarbon molecule are thought to have bond dipole^.^^^*^^^' In order to examine whether the Coulombic interaction is the cause of the stability of orientation K, the Coulombic interaction energies between ethylene molecules were estimated on the basis the Mulliken charge94of the monomer. The point charge of -0.36 e was put on carbon and +0.18 e was put on hydrogen atoms. These Mulliken charges of monomer ethylene were calculated at the HF/6-3 lG* level. The Coulombic interaction energies among these charges were calculated. The Coulombic interactions of orientations A and L are strongly repulsive. The calculated interaction energies of orientations A and L at a intermolecular distance of 3.8 A are both 0.66 kcal/mol. The calculated Coulombic interaction energies of the dimers of
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10807
Interaction Potential of Ethylene Dimer
TABLE I V Calculated Vibrational Frequencies and IR Intensities of Ethylene Monomer and DimeP monomer dimer K
I\
3.0
mode C H I asym str
sym
freq
Bzu
3388
int 47.00
C H 2 asym str CH, sym str
BI, A,
3360 3308
0.0 0.0
C H I sym str C=C str
A,
1832
29.60 0.0
C H 2 sciss C H I sciss
B,, A,
1596 1480
9.95 0.0
CH2 rock C H 2 twist
BI, A,
1348 1147
0.0 0.0
CH, wag
B2,
1086
0.0
C H 2 wag C H 2 rock
BI,
1079 895
118.45 0.31
B,,, 3285
B2,
sym
freq
3389 3388 3361 3309 3308 3286 1832 1829 1598 1483 1477 1350 1152 1145 1090 1187 1081 898 895
int 0.0 99.01 0.06 0.0 0.16 26.24
0.0 0.15 10.84
0.0 0.89 0.03 0.0 0.0 0.0
0.0 104.95 0.0 1.67
Harmonic vibrational frequencies were calculated at the HF/6311G* level. Frequencies are in cm-I. IR intensities are in km/mol. -1.5
3
4
5
6
Distance (A) Figure 2. Calculated nonbonding interaction potentials of ethylene dimer.
minimum energy intermolecular distances are -0.04 (B, intermolecular distance of 4.0 A), 0.20 (C, 4.6 A), -0.18 (D, 4.6 A), -0.17 (E, 4.6 A), 4 . 2 2 (F, 4.4 A), 0.19 (G, 4.8 A), 0.14 (H, 5.4 A), -0.03 (I, 5.2 A), -0.05 (J, 3.8 A), and -0.45 (K, 3.8 A) kcal/mol. The depths of the potentials roughly correspond to the magnitude of the attractive Coulombic interactions. Orientation K has the largest attractive Coulombic interaction. Orientations A and L, whose potentials calculated by the molecular orbital method are repulsive, have strongly repulsive Coulombic interactions. Orientations C, G, and H, whose intermolecular interaction potentials calculated by the molecular oribtal method are shallow, have repulsive Coulombic interactions. These observations support the view that the Coulombic interaction originated in the bond dipole is one of the important energy components of intermolecular interaction energy of ethylene dimer and orientation K is stabilized by this Coulombic interaction. Of course the order of the calculated Coulombic interaction energy does not completely agree with the order of the potential depth calculated by the molecular orbital method. Hence the intermolecular interaction is not rationalized only by the Coulombic interaction. Harmonic Vibrational Frequencies. Vibrational frequencies for monomer ethylene and for the dimer of orientation K were calculated at the HF/6-311G* level. The calculated frequencies and IR intensities are listed in Table IV. The comparison shows that many fundamentals exhibit slight red shifts. On the other hand the experimental measurement of IR spectra in an Ar matrix by Cowieson et al. shows that the dimer's fundamentalsexhibit blue shifts. They explained the experimentally observed blue shifts by the cage effect of the Ar matrix.33 The calculations show that the shifts of the frequencies and the changes of the intensities are small. Some fundamentals do not split due to the symmetry-equivalentethylene molecules in ori.~~ et al. entation K as discussed by Ritter and G r ~ e n Cowieson argued that some of these fundamentalsfor ethylene dimer in an Ar matrix had small ~plitting.~~ Ethylene molecules of the dimer in an Ar matrix can lose the symmetry equivalence due to the cage effect of the matrix. Conclusion
The evaluation of basis set effects on the calculated nonbonding
interaction potentials of ethylene dimer shows that the repulsive and Coulumbic energy component, which was calculated at the HF level, is little affected by the used basis set. However, the dispersion energy component, calculated as the electron correlation energy, is significantly affected. A flexible basis set, which has two or more sets of polarized functions on each atom, is necessary to evaluate the dispersion energy correctly. A small basis set like the 6-3 lG* basis set considerably underestimates the dispersion energy. Calculations of 12 orientations of ethylene dimers at the MP2/6-311G(2d,2p) level show that a DU orientation, which has not been considered in previously reported calculations, has the deepest minimum. This orientation agrees with the structure postulated from the analysis of IR spectra of the ethylene dimer by Rytter and Gruen and also with the experimental measurement of the dipole moment. The evaluation of the Coulombic interactions based on the Mulliken charges of monomer ethylene supports the view that the Coulombic interaction originated in bond dipole stabilizes this orientation. Registry No. Ethene dimer, 16482-32-9.
References and Notes (1) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982. (2) Wright, J. D. Molecular Crystals; Cambridge University Press: Cambridge, 1987. (3) Dale, J. Stereochemistry and Conformational Analysis; Verlag Chemie: New York, 1978. (4) Hunter, C. A.; Sanders, J. K. M. J . Am. Chem. SOC.1990,112,5525. (5) Janda, K. C.; Hemminger, J. C.; Winn, J. S.; Novick, S.E.; Harris, S.J.; Klemperer, W. J. Chem. Phys. 1975, 63, 1419. (6) Steed, J. M.; Dixon, T. A,; Klemperer, W. J . Chem. Phys. 1979, 70, 4940. (7) Hopkins, J. B.; Powers, D. E.; Smalley, R. E. J . Phys. Chem. 1981,85, 3739. (8) Langridge-Smith, P. R. R.; Brumbaugh, D. V.; Haynam, C. A,; Levy, D. H. J . Phys. Chem. 1981,85, 3742. (9) Fung, K. H.; Selzle, H. L.; Schlag, E. W. J . Phys. Chem. 1983, 87, c11,
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