A SEMI-RIGID MODEL FOR THE RING-PUCKERING VIBRATION IN SOME PSEUDO-FOUR-MEMBERED RING MOLECULES
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Date
1972
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Ohio State University
Abstract
The far-infrared data previously reported for a number of pseudo-four-membered-ring molecules are reanalyzed using a Hamiltonian of the form \begin{eqnarray*} H=\frac{1}{2}\ [g_{44}^{(0)} P^{2}+g_{44}^{(2)} Px^{2}P + g_{44}^{(4)} Px^{4}P +g_{4}4^{(6)} Px^{6}P ]+ ax^{4} + bx^{2} ~ {where} ~ P = -\frac{\hbar}{i}\quad \frac{d}{dx} \end{eqnarray*} x = ring-puckering coordinate a,b = potential constants determined by fitting the data $g_{44}^{(i)}$ = coefficients in the expansion of the G-matrix element corresponding to the ring-puckering vibration The coefficients $g_{44}^{(i)}$ are calculated for a semi-rigid model for the ring-puckering vibration and then the parameters a and b are varied in an iterative least squares fitting of the data. The variance of the calculated far-infrared transition frequencies is substantially reduced by the inclu-of these higher order kinetic energy terms in the Hamiltonian. The molecule considered include 2,5-dihydrofuran, cyclopentene, 2,5-dihydrothiophene, 1-pyrazoline, silacyclopent-3-ene and silacylopent-3-ene-1, $1-\underbar d_{2}$. This work was supported, in part, by the National Science Foundation, Grant GP-13473. Present address: Department of Physics, Mississippi State University, State College, Mississippi 39762 Department of Physics, Mississippi State University State College, Mississippi 39762
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Author Institution: Spectroscopy Laboratory Massachusetts, Institute of Technology