Six-dimensional intermolecular potential energy surface and vibrational states of the benzene–methane vdW complex

Abstract

We have developed a six-dimensional (6D) model to describe the intermolecular potential energy surface (IPS) pertinent to binary van der Waals (vdW) complexes composed of a benzene (Bz) and a small molecule X. In the present formalization, termed Coupled-Stretch-Bend-Internal-rotation (CSBI) model, the longitudinal displacement of X from the Bz plane (as vdW stretch), the 2D displacements of X parallel to the Bz ring (vdW bend), and the 3D internal rotation of X inside the complex are taken as internal coordinates, and the IPS is composed of symmetry-adapted terms, which are expanded as explicit functions of the coordinates. Here Bz–methane has been chosen to apply the model because of its importance to gain detailed understanding on the C–H/π interaction. Quantum chemical calculation at the CCSD(T)/aug-cc-pVTZ level of theory has been conducted to obtain single-point energies of 525 grids for various complex conformation, and the calculated results have been processed with the least-squares regression to determine potential parameters in the CSBI model. The IPS thus constructed has shown that in the most stable conformation the methane resides on the aromatic ring (with the intermolecular distance of 3.712 Å), pointing one of its C–H bond to the center of the Bz ring. The barrier for the internal rotation along the minimum energy path is moderately low (of 57 cm⁻¹). The IPS exhibits substantial coupling between the three coordinate spaces, and effects of such mode coupling can be visualized as the difference in the potential profiles with and without the coupling terms. Eigenstates for the intermolecular motion have been determined by diagonalizing the full Hamiltonian matrices with the CSBI potential. Character of each eigenstate is assessed by examining its composition projected onto the basis functions as well as vibrationally averaged geometrical parameters.