Using nondirect product Wigner D basis functions and the symmetry-adapted Lanczos algorithm to compute the ro-vibrational spectrum of CH4–H2O

Abstract

By doing calculations on the methane-water Van der Waals complex, we demonstrate that highly converged energy levels and wavefunctions can be obtained using Wigner D basis functions and the Symmetry Adapted Lanczos (SAL) method. The Wigner D basis is a nondirect product basis and therefore efficient when the kinetic energy operator has accessible singularities. The SAL makes it possible to exploit symmetry to label energy levels and reduce the cost of the calculation, without explicitly using symmetry-adapted basis functions. Line strengths are computed and new bands are identified.

Exact quantum dynamics developments for floppy molecular systems and complexes

“…The size of the direct-product basis and the direct-product grid grows exponentially with the number of active vibrational degrees of freedom. The corresponding computational cost can be mitigated by efficient algorithmic and implementation techniques, most importantly by (a) evaluating nested sums, e.g., eqn (52), sequentially; 43,[45][46][47][48][49][50] (b) using an iterative (Lanczos) eigensolver, 51,52 which requires only multiplication of a trial vector with the Hamiltonian matrix without storage or even explicit construction of the full matrix. 21,52,53 Nevertheless, even in the most efficient implementation, a few vectors of the total size of the basis (and the grid) must be stored, which grows exponentially with the vibrational dimensionality.…”

“…This implementation has been reported and was tested for the example of electric dipole transitions (for O = 1) of the methane-water complex 31 in comparison with the transition moments reported by Wang and Carrington. 43 In what follows, the expressions are summarized for rovibrational infrared (O = 1) and Raman (O = 2) experiments.…”

Exact quantum dynamics developments for floppy molecular systems and complexes

“…This implementation has been reported and was tested for the example of electric dipole tran-sitions (for Ω = 1) of the methane-water complex 31 in comparison with the transition moments reported by Wang and Carrington. 43 In what follows, the expressions are summarized for rovibrational infrared (Ω = 1) and Raman (Ω = 2) experiments.…”

Noncovalently bound molecular complexes beyond diatom–diatom systems: full-dimensional, fully coupled quantum calculations of rovibrational states

“…The rigid-monomer approach continues to be used widely, as illustrated by just a small sample of recent papers dealing with the rovibrational states of H 2 O/D 2 O-CO 2 , 7 (NH 3 ) 2 , 8 H 2 O-HF, 9,10 HCS + -H 2 , 11 and CH 4 -H 2 O. 12,13 The rigid-monomer calculations are capable of delivering results in respectable agreement with a range of experimental data pertaining to the monomers in their ground vibrational states, Peter M. Felker Peter M. Felker was born in Rochester, NY in 1957. He attend Union College and then trained as a spectroscopist under the direction of Ahmed H. Zewail at Caltech from 1979 to 1985.…”

“…The rigid-monomer approach continues to be used widely, as illustrated by just a small sample of recent papers dealing with the rovibrational states of H 2 O/D 2 O–CO 2 , 7 (NH 3 ) 2 , 8 H 2 O–HF, 9,10 HCS + –H 2 , 11 and CH 4 –H 2 O. 12,13…”