Coordinates, Hamiltonian and symmetry operations for the small-amplitude vibrational problem in internal-rotor molecules like CH{sub 3}CHO
- National Institute of Standards and Technology, Gaithersburg, MD (United States)
Motivated by the long-term goal of trying to understand the mechanisms by which internal rotation of methyl tops strongly enhances intramolecular vibrational energy redistribution, the authors have constructed a vibration-torsion-rotation Hamiltonian for molecules containing one C{sub 3v} rotor, which has many analogies with that for quasi-linear molecules. In this formalism, internal rotation motion is taken to be slow compared to all other vibrational motions, so that (i) the small-amplitude vibrational problem is solved for each value of the torsional angle, and (ii) the angular momentum operator associated with internal rotation motion is grouped with the three components of the total angular momentum operator rather than with the vibrational linear momentum operators. One surprising group-theoretical result has emerged. Even though the molecular symmetry group for basis set functions in the principal axis system (or rho axis system) is isomorphic with C{sub 3v}, small-amplitude vibrational eigenvectors resulting from diagonalization of the GF matrix do not necessarily belong to irreducible representations of C{sub 3v}, but may in fact change sign when the methyl top is rotated by 2{pi}4. As a result, a double group of C{sub 3v} must be used to classify these eigenvectors. This sign change in vibrational wavefunctions under one torsional revolution, which is reminiscent of the sign change in electronic wavefunctions under one vibrational {open_quotes}revolution{close_quotes} when a Jahn-Teller effect is present seems to be related to the fact that the CH{sub 3}CHO molecule passes through two chemically different C{sub s} configurations during the internal rotation motion.
- OSTI ID:
- 437294
- Report Number(s):
- CONF-9606118--
- Country of Publication:
- United States
- Language:
- English
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