Problems in Perturbation Theory Calculation of Diamagnetic Susceptibility and Nuclear Magnetic Shielding in Molecules. Illustration with the Hydrogen Atom

Abstract

The perturbation theory expressions for the diamagnetic susceptibility and nuclear magnetic shielding constants of atoms and molecules may be written as sums of ground state and excited state terms. The effects of truncations in the evaluation of the excited state terms are studied through a specially contrived application of these expressions to the hydrogen atom. When the origin of the vector potential is taken 1.4a₀ away from the proton, computations of both properties show that the excited state part is comparable with the ground state part, that the continuum excited states contribute about as much as the discrete excited states, and that the first excited discrete state accounts for about a third of the whole excited‐state contribution. The inference is made, for molecules, that truncation of conventional perturbation formulas by omission of continuum contributions will result in major errors and a dependence of computed properties on the origin taken for the vector potential. The average excited state energy required to make a correct sum rule estimate of the excited state part of the nuclear magnetic shielding constant of the hydrogen atom is calculated, and it is shown to depend strongly on the distance of the shielded position from the proton.