GAUGE DEPENDENCE IN A PERTURBATION THEORY CALCULATION OF THE DIAMAGNETIC SUSCEPTIBILITY AND MAGNETIC SHIELDING CONSTANT OF A HYDROGEN ATOM
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Date
1959
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Ohio State University
Abstract
The perturbation theory based on methods of Van Vleck and Ramsey for computing the magnetic susceptibility $x_{m}$ of a molecule and the magnetic shielding constant $\sigma_{N} at \vec{r}_{N}$ have been applied to the hydrogen atom. The guage of the vector potential $\vec{A}_i (r_o, r_N)$ has been chosen so that the troublesome """"Paramagnetic"""" terms are non-zero. In the computation of terms it is found that the continuum functions are required to compute about 50% of the """"Paramagnetic"""" terms for both $x_{m}$ and $\sigma_{N}$: the continuum functions are found relatively more important in computing $\sigma_{N}$. The first interacting discrete excited state function contributes about 70% of the contribution of all discrete state functions to the """"Paramagnetic"""" terms of $X_{m}$ or $\sigma_N$. A general sum rule has been applied in conjunction with an """"average"""" energy $E_{best}$ for the excited state functions to estimate the paramagnetic terms of $\sigma_{N}$. It is found that agreement of the estimate with the true value is only obtained if $E_{best}$ is a function of $\vec{r}_N$ which increases as $\vec{r}_N$ becomes small.
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$^{*}$ National Science Foundation Predoctoral Fellow, 1953-1956, 1956-1958.
Author Institution: Department of Chemistry, Carnegie Institution of Technology
Author Institution: Department of Chemistry, Carnegie Institution of Technology