# Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

## Abstract

A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

- Authors:

- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest (Hungary)

- Publication Date:

- OSTI Identifier:
- 22410269

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COORDINATES; HAMILTONIANS; KINETIC ENERGY; MOLECULES

### Citation Formats

```
Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu.
```*Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator*. United States: N. p., 2015.
Web. doi:10.1063/1.4919606.

```
Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu.
```*Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator*. United States. doi:10.1063/1.4919606.

```
Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu. Thu .
"Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator". United States. doi:10.1063/1.4919606.
```

```
@article{osti_22410269,
```

title = {Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator},

author = {Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu},

abstractNote = {A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.},

doi = {10.1063/1.4919606},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 17,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}

DOI: 10.1063/1.4919606

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