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

Jan Šmydke, A. Császár

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
JournalMolecular Physics
DOIs
Publication statusPublished - Jan 1 2019

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Vibration
vibrational states
Molecules
Hamiltonians
quantum numbers
Wave functions
molecules
Decomposition
suggestion
wave functions
harmonics
decomposition
vibration
energy

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.

In: Molecular Physics, 01.01.2019.

Research output: Contribution to journalArticle

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