Determining quantum molecular potentials from spectroscopic energy levels using parametric equations of motion

David A. Mazziotti, Herschel A. Rabitz

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

A system of differential equations is presented for evolving the quantum potential as a function of its energy levels. These inverse parametric equations of motion (i-PEM) offer a novel approach to determining quantum molecular potentials from spectroscopic energy levels. The technique uses singular-value decomposition to ensure that the chosen trajectory through energy space is representable by a smooth potential trajectory. The i-PEM are facilitated by discretizing the vibrational Schrödinger equation with a spectral element method which combines the features of Hamiltonian sparsity and exponential convergence of the wave function. Often, spectroscopic data significantly affect only a specific region of the potential, and the spectral elements offer a natural framework for identifying the appropriate portion of the potential. The i-PEM with spectral elements are applied in a simulation for determining the potential of hydrogen fluoride.

Original languageEnglish (US)
Pages (from-to)9770-9776
Number of pages7
JournalJournal of Physical Chemistry A
Volume104
Issue number43
DOIs
StatePublished - Nov 2 2000

All Science Journal Classification (ASJC) codes

  • Physical and Theoretical Chemistry

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