### Abstract

A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia (^{14}NH_{3}) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J 0, 1, 2, 3, and 4.

Original language | English |
---|---|

Article number | 074105 |

Journal | The Journal of Chemical Physics |

Volume | 134 |

Issue number | 7 |

DOIs | |

Publication status | Published - Feb 21 2011 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**Rotating full- and reduced-dimensional quantum chemical models of molecules.** / Fábri, Csaba; Mat́yus, E.; Császár, A.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 134, no. 7, 074105. https://doi.org/10.1063/1.3533950

}

TY - JOUR

T1 - Rotating full- and reduced-dimensional quantum chemical models of molecules

AU - Fábri, Csaba

AU - Mat́yus, E.

AU - Császár, A.

PY - 2011/2/21

Y1 - 2011/2/21

N2 - A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia (14NH3) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J 0, 1, 2, 3, and 4.

AB - A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia (14NH3) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J 0, 1, 2, 3, and 4.

UR - http://www.scopus.com/inward/record.url?scp=79951885211&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951885211&partnerID=8YFLogxK

U2 - 10.1063/1.3533950

DO - 10.1063/1.3533950

M3 - Article

C2 - 21341826

AN - SCOPUS:79951885211

VL - 134

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

M1 - 074105

ER -