Three-dimensional discrete variable representation for accurate Van der Waals vibrational states of complexes between atoms and large molecules, including fullerenes

Abstract

We discuss the recently developed method for accurate quantum three-dimensional (3D) calculation of excited Van der Waals (VdW) vibrational levels of floppy atom–large-molecule complexes. This method is designed primarily for highly anisotropic complexes, in which the radius of the molecule exceeds the equilibrium atom–molecule separation. The 3D discrete variable representation (DVR), in Cartesian coordinates, is used for all three intermolecular degrees of freedom. The quantum dynamics of coupled anharmonic VdW vibrations are treated exactly. Our 3D DVR computational methodology is well suited for VdW states delocalized over intermolecular potentials with multiple minima. The scope of its applicability is broad, and includes endohedral complexes of atoms inside strongly non-spherical fullerene cages. The method is used to calculate VdW vibrational levels of 2,3-dimethylnaphthalene · Ar (2,3-DMN · Ar) up to ca. 60–70 cm^–1 above the ground VdW state. This enabled assignment of the experimentally observed VdW bands and refinement of the intermolecular potential-energy surface for the S₁ state of 2,3-DMN · Ar. Using the same 3D DVR code, we also performed the first quantum 3D calculation of the VdW vibrational states of the endohedral fullerene complex Ne@C₇₀. The regular nodal patterns of the VdW wavefunctions inspected so far suggest weak coupling of the endohedral vibrational modes of Ne@C₇₀.