J . Phys. Chem. 1993,97,3937-3938
3937
New Structure for the Most Stable Isomer of the Benzene Dimer: A Quantum Chemical Study Pave1 Hobza,+Heinrich L. Selzle, and Edward W. Schlag' Institute of Physical and Theoretical Chemistry, Technical University of Munich, 0-8046 Garching, Germany Received: January 26, 1993; In Final Form: February 25, 1993
New and surprising ab initio calculations suggest that the potential curve between two benzene molecules is more complicated than hitherto assumed. In fact, the calculations propose two minima on the potential energy surface of the benzene dimer. The most stable one is found to be the parallel-displaced structure so that the T-shaped structure is now found to be at slightly higher energy. The intermolecular distance found for the T-shaped structure agrees nicely with that predicted from new experiments.
Introduction The loose interaction between two benzene molecules represents an archetypal system for the interaction of aromatic molecules. Early work' showed that there exists a benzene dimer which possesses a dipole moment. Hence, a sandwich structure must be excluded for this dimer. The data are consistent with the suggestion*that both molecules are located in perpendicular planes forming a T-shaped (TS) structure. The dimer was studied experimentally3q4and theoretically526 in this laboratory. From the experiment of the observed splitting of the 0-0 line: the dihedral angle between two planes was evaluated to be 70-80'; ab initiocalculationsgivea floppy TS structure with a very shallow minimum not consistent with the experimental result. On the basis of low-resolution optical absorption spectra of the 0-0 transition, Law et al.' suggested a different structure for the dimer. From their experiment which did not see the splitting in the spectrum, they concluded that the two dimer halves were indistinguishable. Hence, their low-resolution experiments precluded a TS structure. This was then supported with a theoretical calculation using an empirical potential, containing only an exponential-six atom-atom potential plus the quadrupolequadrupole electrostatic term which in the final analysis turns out to be less dominant (vide infra). This leads to a paralleldisplaced (PD) structure of the dimer in accordance with their experimental result.8 This reasoning cannot be maintained for higher-resolution experiment^.^ Experiments by Henson et al.9 as well as isotopically resolved hole-burning spectralo in this laboratory proved the existence of two nonequivalent halves suggesting a T S structure. Highresolution microwave experiments' 1 in addition give a center distance of 4.96 A for the TS structure. Now, however, very recent experiments from this laboratoryi0 lead to most surprising results-there exist more than one dimer ground-state configuration and hence more than one minimum on the potential energy surface (PES) of the benzene dimer. The experiments make use of a resonant absorption to the SIstate. For the 0-0 transition which is forbidden in the monomer only the TS structure contributes to the absorption due to its fairly large dipole moment.5 When the 6; transition is involved, all configurations will be optical visible. A high-level theoretical calculations should be used to elucidate the problem of the new isomer. Nine different structures of the benzene dimer were theoretically investigated in our previous paper.5 Among these, the TS structure was found to be the most stable and the sandwich (parallel) structure was considerably less stable. Shifting the ~
To whom correspondence should be addressed. On leave from the J. Heyrovskg Institute of Physical Chemistry and Electrochemistry,Czech Academy of Sciences, DolejSkova 3, 128 23 Prague 8, Czech Republic. +
0022-3654/93/2097-3937$04,00/0
upper molecules (Le., forming the PD structure) resulted5 in a larger stabilization energy which was, however, still lower than that found for the TS structure. It must be mentioned that the detail search on the PES was made5 with a small basis set (of DZ quality), and only the energetically most favorable structure, the TS one, was later reinvestigated with a more reliable, larger basis set (of TZP quality). The aim of the present paper is to study the TS and PD structures of the benzene dimer ab initio using the second-order Moller-Plesset theory with a large basis set.
Calculations The interaction energy ( M )of the dimer was determined as the sum of SCF interaction energy and correlation (COR) interaction energy
+
= &CF &OR (1) evaluated using second-order Mdler-Plesset theory (MP2). The interaction energy was determined with the final basis set, and therefore, the basis set superposition error is to be eliminated. The counterpoise method of Boys and Bernardi12 was applied; all theorbitalsof the"ghost" system were considered. The 6-3 l+G* basis set was used through all the calculations; the exponents of the diffuse sp shell and diffuse d shell were equal to 0.056 and 0.25, respectively. (For details see ref 5 . ) This basis set was shownS to give accurate values of benzene polarizability and quadrupole moment. Contrary to our previous study, we have used the GAUSSIAN 9213 set of programs, utilizing the direct SCF as well as MP2 options. M C O R was
Results and Discussion Characteristics of the optimized TS and PD structures (cf. Figure 1) are summarized in Table I. From these data it is clearly evident that the PD structure is considerably more stable. Let us first analyze from where the stabilization of both structures originates. The stabilization of the dimer can originate only from the interaction of permanent electric quadrupoles and from electron correlation. The electrostatic quadrupolequadrupole interaction is included in the A E C F ,the electron correlation term in MCoR. The M C F term is for both structures repulsive (cf. Table I). This is due to the exchange-repulsion term which is also included in PEScF. The quadrupolsquadrupole interaction (EQQ) is attractive for both structures, but more for the TS structure. (EQQ = -3Q2/r5 for TS structure and -0.88 Q2/r5 for PD structure, where Q is the quadrupole moment and r is the distance between centers of mass.) For the optimal distances the EQQterm for TS and PD structures is equal to -134 and -494 cm-1, respectively. (Values of Q were taken from ref 5.) The larger value of EQQ for the PD structure is clearly due to the considerably smaller distance r. Let us only recall that this term is repulsive for the sandwich (parallel) structure, and it becomes 0 1993 American Chemical Society
Letters
3938 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
total energy increased in all cases, and this gives evidence that the PD structure corresponds to an energy minimum. The intermolecular distance found for the TS structure (5.0 A) agrees nicely with those originating from experiment” (4.96
I
A).
I
T- Shape
Parallel
- Displaced
Figure 1. Structures of T-shaped and parallel-displaced conformers of the benzene dimer.
TABLE I: Geometry Data, Interaction Energies (in cm-I), and Dipole Moments for the Optimized T-Shaped (TS)and Parallel-Displaced(PD) Structures structure“ R (A)b a (deg) A I F F G O R AE p (D) TS 5.00 90 352 -1276 -924 0.537 65 1486 -2716 -1230 0.004 PD 3.85 a
Cf. Figure 1. Distance between centers of mass.
TABLE 11: Interaction Energies (in cm-I) for Different Distances of T-Shaped (TS)and Parallel-Displaced (PD) structures structure“ R (A) L P C F &OR AE
a
TS
5.0
PD
3.85 3.85 5.0
352 17121 1486 21 1
-1276 -6338 -2716 -654
-924 10783 -1230 -443
Cf. Figure 1.
attractive either by rotation of one molecule (passing to the TS structure) or by displacement of one molecule (passing to PD structure). The A S O R term is again more attractive for the PD structure. This is again understandable; the dominant contribution to A B o R comes from dispersion energy which is proportional to r-6. The distance r is considerably smaller for the PD structure. The direct comparison of both structures is therefore not straightforward due to different intermolecular distances. To make it easier, we calculated the interactionenergies for TS and PD structures also for distances found for the other isomer; the respective values are presented in Table 11. It clearly follows from the table that at the same intermolecular distances the AECoRis more attractive for the TS structure while the A E C F is more repulsive for this structure. Hence, despite the fact that for any distance neither EQQnor & F O R is more attractive for the PD structure than for the TS one, it is the former structure which is more stable. This is evidently a “cooperative”effect of all the interaction energy contributions which is responsible for the stability of this structure. The question arises whether the PD structure corresponds to an energy minimum. We were not able to calculate the second derivatives of the energy with respect to all the coordinates-a calculation of this type would will give unambiguously the character of the stationary point. Such a calculation (at the MP2/6-31+G* level) is still beyond the capabilities of existing computers. We have proved the character of the stationary point in the following way. There exist six intermolecular degrees of freedom determining completely the stationary point. If the change of each of them leads to an energy increase, the stationary point in question corresponds to a minimum. We have chosen the three translations ( x , y, and z) and three rotations (around x , y , and z) of one subsystem. For the calculations the intermolecular distance was changed by f0.1 A, and all the angular coordinates were changed by &lo0. We found that the
The PD structure has a very small dipole moment (cf. Table I), much smaller than that of the TS structure, and this explains theabsenceofthisconformer in thespectrumofthe0-0transition to SI.The rotation of a benzene molecule around the intramolecular C6axis is not free, but the energy increase when passing to the C Zstructure ~ is almost negligible (about 2 cm-I). Structure C2h possesses no dipole moment. On the basis of recent experiments and present calculations, it is possible to conclude that there exist (at least) two stable minima on the PES of the benzene dimer. The most stable one possesses the PD structure and the less stable minimum the TS structure. The transition structure separated both minima was not yet found, but we estimate it is localized at least 500 cm-I above the TS minimum. Most experiments so far have found the TS structure to be prominent and not the PD structure. The theoretical calculation however slightly prefers the PD structure over the TS as the more stable one (306 cm-I). This discrepancy could be explained by the increased entropy of the TS structure. The internal rotation in theTSstructureisfree(oralmostfree),andfurther, the wagging motion around the lowest hydrogen pointing to the center of the ring of the second benzene is practically nonhindered. The PD structure does not possess such soft modes. Consequently, the entropy term for the TS structure should be considerably higher and therefore prefer the TS structure at higher temperatures. The cooling in the supersonicjet is dependent on the expansion conditions, and it is known that high-temperature conformations can be trapped in local minima during the expansion and therefore lead to a cluster distribution which more closely resembles the higher temperature structure.14 In fact, experiments in this 1aboratorylOhave produced a sharp band for the dimer which is unique in the fact that it is strongly dependent on the expansion conditions. Under extreme conditions of the driving pressure and low seed ratio, this band can be of the same magnitude as the TS band. Since this band is also missing for the 0-0transition, it might be a candidate for the PD structure-but this requires further experiments. In conclusion, we show here that theoretical calculations call for yet another structure for the benzene dimer, which is even slightly more stable than the known TS structure. Previous hole burning experiments revealed four sets of lines for the dimer.
References and Notes (1) Janda, K. C.; Hemminger, J. C.; Winn, J. S.;Novick, S.E.; Harris, S.J.; Klemperer, W. J . Chem. Phys. 1975,63, 1419. (2) Steed, J. M.; Dixon, T. A.; Klemperer, W. J . Chem. Phys. 1979,70, 4940. (3) Fung, K. H.; Selzle, H. L.; Schlag, E. W. J . Phys. Chem. 1983,87, 5113. (4) B6rnsen, K. 0.; Selzle, H. L.; Schlag, E. W. J . Chem. Phys. 1986, 85, 1726. ( 5 ) Hobza, P.; Selzle, H. L.; Schlag, E. W. J. Chem. Phys. 1990, 93, 5893. (6) Hobza, P.; Selzle, H. L.; Schlag, E. W. Collect. Czech. Chem. Commun. 1992, 57, 1186. (7) Law, K. S.;Schauer, M.; Bernstein, E. R. J . Chem. Phys. 1984,81, 4871. (8) Schauer, M.; Bernstein, E. R. J . Chem. Phys. 1985, 82, 3722. (9) Henson, B. F.; Hartland, G. V.; Venturo, V. A.; Felker, P. M. J . Chem. Phys. 1992, 97, 2189. (10) Schemer, W.; Kratzschmar, 0.;Selzle, H. L.; Schlag, E. W. Z. Naturforsch. 1992, 47A, 1248. (1 1) Arunan, E.; Gutowsky, H. S. Private communication. (12) Boys, S.F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (13) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomberts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
J.S.;Gonzales,C.;Martin,R.L.;Fox,D. J.;Defrees,D. J.;Baker, J.;Stewart, J. J. P.; Pople, J. A. Gaussian 92; Gaussian, Inc.: Pittsburgh, PA, 1992. (14) Selzle, H. L.; Schlag, E. W. Chem. Phys. 1979, 43, 1 1 1.
