Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split Hamiltonian pseudospectral approach

Abstract

An efficient pseudospectral method for performing fully-coupled six-dimensional bound state dynamics calculations is presented. A Lanczos-based iterative diagonalization scheme produces the energy levels in increasing energies. This scheme, which requires repetitively acting the Hamiltonian operator on a vector, circumvents the problem of constructing the full matrix. This permits the use of ultralarge molecular basis sets in order to fully converge the calculations. The Lanczos scheme was conducted in a symmetry adapted six-dimensional spectral representation. The Hamiltonian operator has been split into only four different terms, each being Hermitian and symmetry-adapted. The potential term is evaluated by a pseudospectral scheme of Gaussian accuracy, which guarantees the variational principle. Spectroscopic levels are computed with this method for one ammonia potential, and compared to experimental results. The results presented below are a direct application of our vector formulation. The latter has shown to be particularly well adapted to the split pseudospectral approach for it yields a compact and symmetry-adapted Hamiltonian.

The VMFCI method: A flexible tool for solving the molecular vibration problem

“…1-3, and in refs. [4][5][6] for the use of the discrete variable representation (DVR) and pseudospectral approaches. New progress not covered by these references include the implementation in Gaussian of an efficient perturbation scheme by Barone,7,8 the implementation in Gamess of the VSCF and correlation-corrected VSCF methods by Chaban, Jung, Gerber, and Matsunaga, 9, 10 the double-layer Lanczos algorithm of Yu and coworkers, 11 the energy selected basis of Lee and Light,12 the parallel algorithm of the Pau group, 13 and the basis selection scheme of Dawes and Carrington 14 to quote a few.…”

Variational quantum approaches for computing vibrational energies of polyatomic molecules

“…The KEO in these coordinates is given in many papers. [100,102,115,116]. One convenient form [117] is,…”

Complex symmetrized calculations on ammonia vibrational levels

“…For this reason, extensive spectroscopic measurements have been performed on 14 NH 3 as well as on its isotopomers [1][2][3][4][5][6], in a wide spectral range. Many theoretical studies have also been carried out to rationalize the extremely complicated NH 3 PES and ro-vibrational spectrum [2,3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Ammonia is a symmetric top molecule, belonging to the point group D 3h [1,7,27].…”