ON THE ROTATIONAL PARTITION FUNCTION FOR TETRAHEDRAL MOLECULES
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Date
1970
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Publisher
Ohio State University
Abstract
A calculation of the quantum-mechanical rotational partition function for tetrahedral $XY_{4}$ molecules is presented. Emphasis is placed on the inclusion of nuclear-spin statistical weight factors in a rigorous way, and on the evaluation of infinite sums in closed form with rigorous error bounds. The theory of theta functions and the Jacobi transformation are used extensively. The partition function is $Q_{1} = (1/12) (2I_{Y}+1)^{4}\pi^{\frac{1}{2}}\alpha^{-\frac{3}{2}} \exp(\alpha4)$, where $I_{Y}$ is the spin of the Y nucleus, and $\alpha\equiv$ Bhc/kT. This result is accurate to 1% or better for all values of B and T such that $\alpha<\frac15$.
Description
This work done while the author was an N.R.C.-N.A.S.A. Resident Research Associate (1967-69) at JPL.
Author Institution: Jet Propubation Laboratory,, California Institute of Technology
Author Institution: Jet Propubation Laboratory,, California Institute of Technology