# Numeric kinetic energy operators for molecules in polyspherical coordinates

## Abstract

Generalized curvilinear coordinates, as, e.g., polyspherical coordinates, are in general better adapted to the resolution of the nuclear Schroedinger equation than rectilinear ones like the normal mode coordinates. However, analytical expressions of the kinetic energy operators (KEOs) for molecular systems in polyspherical coordinates may be prohibitively complicated for large systems. In this paper we propose a method to generate a KEO numerically and bring it to a form practicable for dynamical calculations. To examine the new method we calculated vibrational spectra and eigenenergies for nitrous acid (HONO) and compare it with results obtained with an exact analytical KEO derived previously [F. Richter, P. Rosmus, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 120, 6072 (2004)]. In a second example we calculated {pi}{yields}{pi}* photoabsorption spectrum and eigenenergies of ethene (C{sub 2}H{sub 4}) and compared it with previous work [M. R. Brill, F. Gatti, D. Lauvergnat, and H.-D. Meyer, Chem. Phys. 338, 186 (2007)]. In this ethene study the dimensionality was reduced from 12 to 6 by freezing six internal coordinates. Results for both molecules show that the proposed method for obtaining an approximate KEO is reliable for dynamical calculations. The error in eigenenergies was found to be below 1 cm{sup -1}more »

- Authors:

- Theoretische Chemie, Ruprecht-Karls-Universitaet, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)
- CNRS, Laboratoire de Chimie Physique (UMR 8000), Universite Paris-Sud, F-91405 Orsay (France)
- CTMM, Institut Charles Gerhardt (UMR 5253), CC 1501, Universite Montpellier II, F-34095 Montpellier Cedex 05 (France)

- Publication Date:

- OSTI Identifier:
- 22098885

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 136; Journal Issue: 23; Other Information: (c) 2012 American Institute of Physics; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CURVILINEAR COORDINATES; ERRORS; ETHYLENE; KINETIC ENERGY; MOLECULAR DYNAMICS METHOD; NITROUS ACID; SCHROEDINGER EQUATION; SPECTRA; VIBRATIONAL STATES

### Citation Formats

```
Sadri, Keyvan, Meyer, Hans-Dieter, Lauvergnat, David, and Gatti, Fabien.
```*Numeric kinetic energy operators for molecules in polyspherical coordinates*. United States: N. p., 2012.
Web. doi:10.1063/1.4729536.

```
Sadri, Keyvan, Meyer, Hans-Dieter, Lauvergnat, David, & Gatti, Fabien.
```*Numeric kinetic energy operators for molecules in polyspherical coordinates*. United States. doi:10.1063/1.4729536.

```
Sadri, Keyvan, Meyer, Hans-Dieter, Lauvergnat, David, and Gatti, Fabien. Thu .
"Numeric kinetic energy operators for molecules in polyspherical coordinates". United States. doi:10.1063/1.4729536.
```

```
@article{osti_22098885,
```

title = {Numeric kinetic energy operators for molecules in polyspherical coordinates},

author = {Sadri, Keyvan and Meyer, Hans-Dieter and Lauvergnat, David and Gatti, Fabien},

abstractNote = {Generalized curvilinear coordinates, as, e.g., polyspherical coordinates, are in general better adapted to the resolution of the nuclear Schroedinger equation than rectilinear ones like the normal mode coordinates. However, analytical expressions of the kinetic energy operators (KEOs) for molecular systems in polyspherical coordinates may be prohibitively complicated for large systems. In this paper we propose a method to generate a KEO numerically and bring it to a form practicable for dynamical calculations. To examine the new method we calculated vibrational spectra and eigenenergies for nitrous acid (HONO) and compare it with results obtained with an exact analytical KEO derived previously [F. Richter, P. Rosmus, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 120, 6072 (2004)]. In a second example we calculated {pi}{yields}{pi}* photoabsorption spectrum and eigenenergies of ethene (C{sub 2}H{sub 4}) and compared it with previous work [M. R. Brill, F. Gatti, D. Lauvergnat, and H.-D. Meyer, Chem. Phys. 338, 186 (2007)]. In this ethene study the dimensionality was reduced from 12 to 6 by freezing six internal coordinates. Results for both molecules show that the proposed method for obtaining an approximate KEO is reliable for dynamical calculations. The error in eigenenergies was found to be below 1 cm{sup -1} for most states calculated.},

doi = {10.1063/1.4729536},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 23,

volume = 136,

place = {United States},

year = {2012},

month = {6}

}