The theoretical (quantum) description of large amplitude vibrations of systems containing four or more atoms using orthogonal internal coordinates requires three or more angular coordinates. The basis commonly used to represent these coordinates is the coupled angular momentum basis. We show that a direct product angular discrete variable representation (DVR) can be used advantageously, particularly for systems with high permutation-inversion symmetry and nonlinear equilibrium geometry. The DVR permits full symmetry projection and solution by the sequential diagonalization and truncation method. Application to the dimer of rigid CO2 demonstrates the accuracy and efficiency of the approach.

Fully coupled four-dimensional quantum-mechanical calculations are presented for intermolecular vibrational states of rigid carbon dioxide dimer for J=0. The Hamiltonian operator is given in collision coordinates. The Hamiltonian matrix elements are evaluated using symmetrized products of spherical harmonics for angles and a potential optimized discrete variable representation (PO-DVR) for the intermolecular distance. The lowest ten or so states of each symmetry are reported for the potential energy surface (PES) given by Bukowski et al. [J. Chem. Phys. 110, 3785 (1999)]. Due to symmetries, there is no interconversion tunneling splitting for the ground state. Our calculations show that there is no tunneling shift of the ground state within our computation precision (0.01 cm−1). Analysis of the wave functions shows that only the ground states of each symmetry are nearly harmonic. The van der Waals frequencies and symmetry adapted force constants are found and compared to available experimental values. Strong coupling between the stretching coordinates and the bending coordinates are found for vibrationally excited states. The interconversion tunneling shifts are discussed for the vibrationally excited states.

We present results of six-dimensional bound-state calculations of the vibrations of rigid water dimer based on two older and two very recent potential energy surfaces. The calculations are done by a new sequential diagonalization–truncation approach using the symmetrized angular basis presented most recently by Althorpe and Clary [J. Chem. Phys. 101, 3603 (1994)] and a potential optimized discrete variable representation (DVR) in the monomer–monomer distance coordinate. The lowest ten or so states of each symmetry are apparently converged to 0.5 cm−1 using a coupled angular basis of Wigner rotation functions with Jmax=11 and mmax=5 on each monomer. The results differ significantly from the results presented by Leforestier et al. [J. Chem. Phys. 106, 8527 (1997)] and demonstrate that the ASP-S potential yields more accurate tunneling splittings than the more recent ASP-Wx potentials [C. Millot et al., J. Phys. Chem. A 102, 754 (1998)].