The geometry and forcefield of acetylene

Contracted basis Lanczos methods for computing numerically exact rovibrational levels of methane

We present a numerically exact calculation of rovibrational levels of a five-atom molecule. Two contracted basis Lanczos strategies are proposed. The first and preferred strategy is a two-stage contraction. Products of eigenfunctions of a four-dimensional (4D) stretch problem and eigenfunctions of 5D bend-rotation problems, one for each K, are used as basis functions for computing eigenfunctions and eigenvalues (for each K) of the Hamiltonian without the Coriolis coupling term, denoted H0. Finally, energy levels of the full Hamiltonian are calculated in a basis of the eigenfunctions of H0. The second strategy is a one-stage contraction in which energy levels of the full Hamiltonian are computed in the product contracted basis (without first computing eigenfunctions of H0). The two-stage contraction strategy, albeit more complicated, has the crucial advantage that it is trivial to parallelize the calculation so that the CPU and memory costs are independent of J. For the one-stage contraction strategy the CPU and memory costs of the difficult part of the calculation scale linearly with J. We use the polar coordinates associated with orthogonal Radau vectors and spherical harmonic type rovibrational basis functions. A parity-adapted rovibrational basis suitable for a five-atom molecule is proposed and employed to obtain bend-rotation eigenfunctions in the first step of both contraction methods. The effectiveness of the two methods is demonstrated by calculating a large number of converged J = 1 rovibrational levels of methane using a global potential energy surface.

Methods for calculating vibrational energy levels

This article reviews new methods for computing vibrational energy levels of small polyatomic molecules. The principal impediment to the calculation of energy levels is the size of the required basis set. If one uses a product basis the Hamiltonian matrix for a four-atom molecule is too large to store in core memory. We discuss iterative methods that enable one to use a product basis to compute energy levels (and spectra) without storing a Hamiltonian matrix. Despite the advantages of iterative methods it is not possible, using product basis functions, to calculate vibrational spectra of molecules with more than four atoms. A very recent method combining contracted basis functions and the Lanczos algorithm with which vibrational energy levels of methane have been computed is described. New ideas, based on exploiting preconditioning, for reducing the number of matrix-vector products required to converge energy levels of interest are also summarized.Key words: vibrational energy levels, kinetic energy operators, Lanczos algorithm, contracted basis functions, preconditioning.

A study of the mode-selective trans–cis isomerization in HONO using ab initio methodology

Ab initio calculations on the six-dimensional cis--trans double minimum potential energy surface of the electronic ground state of the HONO molecule were performed using a coupled cluster approach. An analytic fit to the data points was established. The interconversion barrier was calculated to be 4105 cm(-1). The nuclear motion problem was solved variationally using a full six-dimensional Hamiltonian in internal coordinates. The eigenstates up to about 3650 cm(-1) were tentatively assigned by harmonic quantum numbers. The assignment was based on the mean values of the internal coordinates of the six-dimensional eigenfunctions and on a comparison of the eigenenergies with those calculated by second-order perturbation theory from a full quartic force field in dimensionless normal coordinates. In cold matrices the trans- and the cis-OH nu(1) stretching modes and the first trans- and cis-NO 2nu(2) stretching overtones lead to isomerization. In the isolated molecule these modes (J=0) were found to be entirely localized. However, several overtones of the nu(4) ONO bending and nu(5) N-O stretching, which are close in energy to the OH stretch and combined with the torsional mode, were found to be strongly cis-trans delocalized.