Extended permutation-inversion groups for simultaneous treatment of the rovibronic states of trans-acetylene, cis-acetylene, and vinylidene

Published

March 25, 2011

Author(s)

Jon T. Hougen, Anthony J. Merer

Abstract

The electronic ground-state potential surface of acetylene (H-CC-H) has a minimum at the linear conformation, but the excited electronic states may have potential minima at a variety of nonlinear equilibrium shapes. This work is concerned with the group theoretical ideas necessary to treat simultaneously the symmetry properties of rovibronic states associated with three different planar acetylene equilibrium configurations, namely trans bent acetylene, cis bent acetylene, and vinylidene (H2C=C). We make use of three different kinds of groups: (i) point groups, (ii) permutation-inversion (PI) groups, and (iii) extended PI groups. Because group theoretical symmetry operations must ultimately be applied to the variables in the molecular wavefunctions for these various shapes, and because some of the confusion arises as a result of the different coordinate systems used to describe rovibrational wavefunctions built on different electronic equilibrium structures, we make extensive use of an equation relating laboratory-fixed Cartesian coordinates to the rotational and large-amplitude vibrational coordinates used to describe the rovibronic wavefunctions of interest. Some application of these group theoretical ideas to the observed spectrum of acetylene is also presented.

Citation

Journal of Molecular Spectroscopy

Pub Type

Journals

Download Paper

Local Download

Keywords

acetylene, cis-trans isomerization, extended permutation-inversion groups, inter-conformational perturbations, S1 electronic state, vinylidene

Citation

Hougen, J. and Merer, A. (2011), Extended permutation-inversion groups for simultaneous treatment of the rovibronic states of trans-acetylene, cis-acetylene, and vinylidene, Journal of Molecular Spectroscopy, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=907571 (Accessed May 7, 2026)

Additional citation formats