### Abstract

The use of one- and two-mode reduced-density matrices (RDM), (Formula presented.) and (Formula presented.), respectively, and in particular the use of their diagonal elements, (Formula presented.) and (Formula presented.), is suggested for the assignment of normal-mode-like quantum numbers to variationally computed vibrational wave functions of semirigid molecules when the computation is based on a nuclear-motion Hamiltonian expressed in curvilinear internal coordinates (Formula presented.). The use of RDMs for the semi-automatic assignment of vibrational states is tested on the H
_{2}
^{16}
O molecule, whereby about the first 250 states, in the energy range of 0–25,000 cm
^{−1}
, are assigned. The proposed semi-automatic assignment procedure takes advantage of the fact that (a) for semirigid molecules it is often possible to define internal coordinates which mimick normal coordinates defined by the harmonic counterparts of the anharmonic vibrations, (b) overlaps between already assigned and yet unassigned RDMs provide outstanding and often unambiguous suggestions for the quantum numbers, and (c) an energy-decomposition scheme helps to decide among possible assignment possibilities suggested by the computed density overlaps.

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

Journal | Molecular Physics |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- one- and two-mode reduced-density matrices
- quantum numbers
- vibrational assignment
- Wave-function analysis

### ASJC Scopus subject areas

- Biophysics
- Molecular Biology
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

**On the use of reduced-density matrices for the semi-automatic assignment of vibrational states.** / Šmydke, Jan; Császár, A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the use of reduced-density matrices for the semi-automatic assignment of vibrational states

AU - Šmydke, Jan

AU - Császár, A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The use of one- and two-mode reduced-density matrices (RDM), (Formula presented.) and (Formula presented.), respectively, and in particular the use of their diagonal elements, (Formula presented.) and (Formula presented.), is suggested for the assignment of normal-mode-like quantum numbers to variationally computed vibrational wave functions of semirigid molecules when the computation is based on a nuclear-motion Hamiltonian expressed in curvilinear internal coordinates (Formula presented.). The use of RDMs for the semi-automatic assignment of vibrational states is tested on the H 2 16 O molecule, whereby about the first 250 states, in the energy range of 0–25,000 cm −1 , are assigned. The proposed semi-automatic assignment procedure takes advantage of the fact that (a) for semirigid molecules it is often possible to define internal coordinates which mimick normal coordinates defined by the harmonic counterparts of the anharmonic vibrations, (b) overlaps between already assigned and yet unassigned RDMs provide outstanding and often unambiguous suggestions for the quantum numbers, and (c) an energy-decomposition scheme helps to decide among possible assignment possibilities suggested by the computed density overlaps.

AB - The use of one- and two-mode reduced-density matrices (RDM), (Formula presented.) and (Formula presented.), respectively, and in particular the use of their diagonal elements, (Formula presented.) and (Formula presented.), is suggested for the assignment of normal-mode-like quantum numbers to variationally computed vibrational wave functions of semirigid molecules when the computation is based on a nuclear-motion Hamiltonian expressed in curvilinear internal coordinates (Formula presented.). The use of RDMs for the semi-automatic assignment of vibrational states is tested on the H 2 16 O molecule, whereby about the first 250 states, in the energy range of 0–25,000 cm −1 , are assigned. The proposed semi-automatic assignment procedure takes advantage of the fact that (a) for semirigid molecules it is often possible to define internal coordinates which mimick normal coordinates defined by the harmonic counterparts of the anharmonic vibrations, (b) overlaps between already assigned and yet unassigned RDMs provide outstanding and often unambiguous suggestions for the quantum numbers, and (c) an energy-decomposition scheme helps to decide among possible assignment possibilities suggested by the computed density overlaps.

KW - one- and two-mode reduced-density matrices

KW - quantum numbers

KW - vibrational assignment

KW - Wave-function analysis

UR - http://www.scopus.com/inward/record.url?scp=85061912632&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061912632&partnerID=8YFLogxK

U2 - 10.1080/00268976.2018.1562124

DO - 10.1080/00268976.2018.1562124

M3 - Article

AN - SCOPUS:85061912632

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

ER -