Calculation of vibrational (J=0) excitation energies and band intensities of formaldehyde using the recursive residue generation method

Abstract

We use the recursive residue generation method (RRGM) with an exact kinetic energy operator to calculate vibrational excitation energies and band intensities for formaldehyde. The basis is a product of one-dimensional potential optimized discrete variable representation (PO-DVR) functions for each coordinate. We exploit the symmetry by using symmetry adapted basis functions obtained by taking linear combinations of PO-DVR functions. Our largest basis set consists of 798 600 functions (per symmetry block). The Lanczos tridiagonal representation of the Hamiltonian is generated iteratively (without constructing matrix elements explicitly) by sequential transformations. We determine a six-dimensional dipole moment function from the ab initio dipole moment values computed at the QCISD level with a 6-311++G(d,p) basis set. We converged all A1, B2 and B1 vibrational states up to the combination band with two quanta in the C–O stretch and one quantum in a C–H stretch at about 6 350 cm−1 above zero point energy. We present a simulated (J=0) infrared spectrum of CH2O for transitions from the ground state.