Vibration–rotation-tunneling states of the benzene dimer: an ab initio study

Abstract

An improved intermolecular potential surface for the benzene dimer is constructed from interaction energies computed by symmetry-adapted perturbation theory, SAPT(DFT), with the inclusion of third-order contributions. Twelve characteristic points on the surface have been investigated also using the coupled-cluster method with single, double, and perturbative triple excitations, CCSD(T), and triple-zeta quality basis sets with midbond functions. The SAPT and CCSD(T) results are in close agreement and provide the best representation of these points to date. The potential was used in calculations of vibration-rotation-tunneling (VRT) levels of the dimer by a method appropriate for large amplitude intermolecular motions and tunneling between multiple equivalent minima in the potential. The resulting VRT levels were analyzed with the use of the permutation-inversion full cluster tunneling (FCT) group G 576 and a chain of subgroups that starts from the molecular symmetry group C s (M) of the rigid dimer at its equilibrium C s geometry and leads to G 576 if all possible intermolecular tunneling mechanisms are feasible. Further information was extracted from the calculated wave functions. It was found, in agreement with the experimental data, that for all of the 54 G 576 symmetry species (with different nuclear spin statistical weights) the lower VRT states have a tilted T-shape (TT) structure; states with the parallel-displaced structure are higher in energy than the ground state of A + 1 symmetry by at least 30 cm À1 . The dissociation energy D 0 equals 870 cm À1 , while the depth D e of the TT minimum in the potential is 975 cm À1 . Hindered rotation of the cap in the TT structure and tilt tunneling lead to level splittings on the order of 1 cm À1 . Also intermolecular vibrations with excitation energies starting at a few cm À1 were identified. A further small, but probably significant, level splitting was assigned to cap turnover, although in scans of the potential surface we could not find a plausible 'reaction path' for this process. Rotational constants were extracted from energy levels calculated for total angular momentum J = 0 and 1, and from expectation values of the inertia tensor. Although the end-over-end rotational constant B + C agrees well with the measured microwave spectra, there is disagreement with the measurements concerning the (a)symmetric rotor character of the benzene dimer. It is concluded from calculations for the 54 nuclear spin species that the microwave spectrum should show overlapping contributions from many different species. Another interesting conclusion regards the role of the quantum number K, for a prolate near-symmetric rotor the projection of the total angular momentum on the prolate axis. For the benzene dimer, K has a substantial effect on the energy levels associated with the intermolecular motions of the complex.

Comment on “Communication: Benzene dimer—The free energy landscape” [J. Chem. Phys. 139, 201102 (2013)]

“…7 amounts to 0.005 a.u., which is 3.14 kcal/mol. This is much larger than the energy difference of about 0.2 kcal/mol between the TT and PD structures and the height of the energy barrier that separates these structures, 1 and even larger than the total binding energy of 2.7 kcal/mol. In the metadynamics literature, [9][10][11] it is recommended to use relatively high Gaussian bias potentials in the first stage of the simulation, but subsequently to lower the Gaussian heights in order to reach convergence.…”

The elusive S2 state, the S1/S2 splitting, and the excimer states of the benzene dimer

“…2 More recently, Szalewicz, van der Avoird, and their co-workers made great advances in the calculation of the intermolecular potential energy surface. 3,4 Upon incorporating a detailed permutation/inversion group-theoretical treatment of the non-rigid benzene dimer, they were able to predict the low-lying internal-rotation/tunneling states of (Bz) 2 . 4 Schnell et al recently re-measured and assigned the fine structure of the (Bz) 2 microwave spectrum in terms of vibration-rotationtunneling (VRT) processes.…”

“…3,4 Upon incorporating a detailed permutation/inversion group-theoretical treatment of the non-rigid benzene dimer, they were able to predict the low-lying internal-rotation/tunneling states of (Bz) 2 . 4 Schnell et al recently re-measured and assigned the fine structure of the (Bz) 2 microwave spectrum in terms of vibration-rotationtunneling (VRT) processes. [5][6][7] The vibronic spectrum of supersonically cooled (Bz) 2 has been investigated since the 1980s using mass-selective resonant two-photon ionization (R2PI) spectroscopy.…”

“…Smalley and coworkers already suggested "asymmetry in the crystal field" as a cause, i.e., that symmetry lowering of one or both of the Bz monomers renders the S 0 → S 1 transition slightly allowed. 8 While the fluorescence quantum yield of (Bz) 2 is low, its ionization efficiency is high when compared to those of the (Bz) 3 and (Bz) 4 clusters produced in the same supersonic-jet expansion. 8,9,18 This was interpreted in terms of vertical excitation of (Bz) 2 into a T-shaped S 1 state local minimum, followed by rapid rearrangement to a stacked-parallel structure corresponding to the lowest excimer state of 1 B 1g symmetry.…”

“…3 They later complemented this work by performing CCSD(T): coupled-cluster with singles, doubles and perturbative triples excitations calculations at three minima and nine index-1 stationary points. 4 Below, we employ their nomenclature 3 for the stationary points M2, S3, S3a, M1, and S8, which are shown in Figure 1. Xantheas and co-workers have recently performed a complete basis set (CBS) study of the M1 parallel-displaced dimer with the CCSD(T) method and obtained a CCSD(T)/CBS binding energy D e = −2.65 ± 0.02 kcal/mol.…”