## An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

## Abstract

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.

- Authors:

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

- 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:
- 1303029

- Report Number(s):
- BNL-112549-2016-JA

Journal ID: ISSN 0021-9606; JCPSA6; R&D Project: CO-006; KC0301020

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

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 5; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; Vibrational spectrum; iterative diagonalization; spectral transform Lanczos method

### Citation Formats

```
Yu, Hua-Gen. An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach. United States: N. p., 2002.
Web. doi:10.1063/1.1488575.
```

```
Yu, Hua-Gen. An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach. United States. doi:10.1063/1.1488575.
```

```
Yu, Hua-Gen. Tue .
"An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach". United States. doi:10.1063/1.1488575. https://www.osti.gov/servlets/purl/1303029.
```

```
@article{osti_1303029,
```

title = {An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach},

author = {Yu, Hua-Gen},

abstractNote = {We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.},

doi = {10.1063/1.1488575},

journal = {Journal of Chemical Physics},

number = 5,

volume = 117,

place = {United States},

year = {2002},

month = {1}

}

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