ISSN:
0192-8651
Keywords:
Computational Chemistry and Molecular Modeling
;
Biochemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Computer Science
Notes:
A variety of quantum mechanical models have guided the interpretation of the far infrared (IR) spectrum of easily deformed ring systems, but an explicit guide to such modelling would ease further analysis. The coordinates introduced by Cremer and Pople provide a starting point for description of puckering, separate from other internal motions of a ring system. For a ring of N atoms there are N-3 puckering modes, composed of [N - (2)/2] pseudorotation “amplitudes” and [(N - 3)/2] “angles.” (The brackets [] mean “truncate to the integer.”) Separation of the Schroedinger equation is possible for the “free puckerer,” the “puckerer in a box,” and for puckering opposed by a separable harmonic potential; in this latter case the energy is determined and the state is labeled by a set of pseudorotation quantum numbers Mk and radial quantum numbers nk: \documentclass{article}\pagestyle{empty}\begin{document}$$E_k = \sum\limits_k {hv_k (2n_k + M_k + 1)}$$\end{document} Here vk is the harmonic frequency for the k-th mode, and h is Planck's constant. Since most ring systems are nonharmonic, and require a distinct “quartic-puckering” potential for each puckering mode, a perturbation treatment of the quartic terms is required. We provide formulas and a symbolic algebra computer program to generate expressions for integrals needed for the perturbation or linear variation modeling.
Additional Material:
5 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/jcc.540090408
