# 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 CH₄ based on the *ab initio* T8 potential energy surface of Schwenke and Partridge and the low-order truncated *ab initio* dipole moment surfaces of Yurchenko and co-workers. A comparison with experiments is made. The algorithm is also applicable for Raman polarizability active spectra.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Chemistry

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1182509

- Alternate Identifier(s):
- OSTI ID: 1228133

- Report Number(s):
- BNL-107475-2015-JA

Journal ID: ISSN 0021-9606; JCPSA6; R&D Project: CO006; KC0301020; TRN: US1500507

- Grant/Contract Number:
- SC00112704; AC02-98CH10886

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 4; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Eigenvalues; Wave functions; Lanczos method; Molecular spectra; dipole transition intensities; polyatomic molecules

### Citation Formats

```
Yu, Hua-Gen.
```*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.
```*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. 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. https://www.osti.gov/servlets/purl/1182509.
```

```
@article{osti_1182509,
```

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

author = {Yu, Hua-Gen},

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 CH₄ based on the ab initio T8 potential energy surface of Schwenke and Partridge and the low-order truncated ab initio dipole moment surfaces of Yurchenko and co-workers. 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}

}

*Citation information provided by*

Web of Science

Web of Science