# Multi-layer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules

## Abstract

We report a rigorous full dimensional quantum dynamics algorithm, the multi-layer Lanczos method, for computing vibrational energies and dipole transition intensities of polyatomic molecules without any dynamics approximation. The multi-layer Lanczos method is developed by using a few advanced techniques including the guided spectral transform Lanczos method, multi-layer Lanczos iteration approach, recursive residue generation method, and dipole-wavefunction contraction. The quantum molecular Hamiltonian at the total angular momentum J = 0 is represented in a set of orthogonal polyspherical coordinates so that the large amplitude motions of vibrations are naturally described. In particular, the algorithm is general and problem-independent. An application is illustrated by calculating the infrared vibrational dipole transition spectrum of CH{sub 4} based on the ab initio T8 potential energy surface of Schwenke and Partridge [Spectrochimica Acta, Part A 57, 887 (2001)] and the low-order truncated ab initio dipole moment surfaces of Yurchenko et al. [J. Mol. Spectrosc. 291, 69 (2013)]. A comparison with experiments is made. The algorithm is also applicable for Raman polarizability active spectra.

- Authors:

- Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973-5000 (United States)

- Publication Date:

- OSTI Identifier:
- 22416034

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALGORITHMS; ANGULAR MOMENTUM; COMPARATIVE EVALUATIONS; DIPOLE MOMENTS; DIPOLES; HAMILTONIANS; INFRARED SPECTRA; LAYERS; METHANE; MOLECULES; POLARIZABILITY; POTENTIAL ENERGY; RESIDUES; SURFACES; WAVE FUNCTIONS

### Citation Formats

```
Yu, Hua-Gen, E-mail: hgy@bnl.gov.
```*Multi-layer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules*. United States: N. p., 2015.
Web. doi:10.1063/1.4906492.

```
Yu, Hua-Gen, E-mail: hgy@bnl.gov.
```*Multi-layer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules*. United States. doi:10.1063/1.4906492.

```
Yu, Hua-Gen, E-mail: hgy@bnl.gov. Wed .
"Multi-layer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules". United States.
doi:10.1063/1.4906492.
```

```
@article{osti_22416034,
```

title = {Multi-layer Lanczos iteration approach to calculations of vibrational energies and dipole transition intensities for polyatomic molecules},

author = {Yu, Hua-Gen, E-mail: hgy@bnl.gov},

abstractNote = {We report a rigorous full dimensional quantum dynamics algorithm, the multi-layer Lanczos method, for computing vibrational energies and dipole transition intensities of polyatomic molecules without any dynamics approximation. The multi-layer Lanczos method is developed by using a few advanced techniques including the guided spectral transform Lanczos method, multi-layer Lanczos iteration approach, recursive residue generation method, and dipole-wavefunction contraction. The quantum molecular Hamiltonian at the total angular momentum J = 0 is represented in a set of orthogonal polyspherical coordinates so that the large amplitude motions of vibrations are naturally described. In particular, the algorithm is general and problem-independent. An application is illustrated by calculating the infrared vibrational dipole transition spectrum of CH{sub 4} based on the ab initio T8 potential energy surface of Schwenke and Partridge [Spectrochimica Acta, Part A 57, 887 (2001)] and the low-order truncated ab initio dipole moment surfaces of Yurchenko et al. [J. Mol. Spectrosc. 291, 69 (2013)]. A comparison with experiments is made. The algorithm is also applicable for Raman polarizability active spectra.},

doi = {10.1063/1.4906492},

journal = {Journal of Chemical Physics},

number = 4,

volume = 142,

place = {United States},

year = {Wed Jan 28 00:00:00 EST 2015},

month = {Wed Jan 28 00:00:00 EST 2015}

}