Dipole Shielding Tensor
1.E. S. Chang, J. Chem. Phys. 49, 2904 (1968).
2.R. Sternheimer, Phys. Rev. 96, 951 (1954).
3.The generalization to a finite‐mass nucleus is a straightforward and yields results like those of Ref. 2, Footnote 25.
4.As is well known, for a static field and Ψ an energy eigenfunction, Ψ is not normalizable and hence (1) will not hold in general. However, the perturbation expansion of Ψ in powers of the field does exist, as an asymptotic normalizable series, and it is in this sense that one should understand Eq. (1).
5.Static case, Ψ an energy eigenfunction: S. T. Epstein and J. O. Hirschfelder, Phys. Rev. 123, 1405 (1961).
5.General timedependent case: S. T. Epstein, J. Chem. Phys. 45, 584 (1966), especially Footnote 6. For our present application
6.This same result has been found, in a rather different way, by A. Dalgarno and R. P. Hurst (private communication from R. P. Hurst).
7.If one is doing a variation‐perturbation calculation starting with a function which is exact in the absence of the field, then to satisfy (1) through first order requires only that be an allowed variation of the first‐order wavefunction. See J. O. Hirschfelder, W. B. Brown, and S. T. Epstein, in Recent Advances in Quantum Chemistry, P.‐O. Löwdin, Ed. (Academic Press Inc., New York, 1964), Vol. 1, Sec. (j), p. 305. Note that the equation contains a misprint and should read
8.We have also investigated more general open‐shell situations and hope to publish the results at a later time. [R. E. Johnson (unpublished).]
9.In a similar way, we can easily understand the result found by M. Cohen and A. Dalgarno, Proc. Roy. Soc. (London) A275, 492 (1963), that for the ground state of lithium, there are no first‐order corrections to the expectation values of one‐electron spin‐independent operators given by the restricted Hartree‐Fock approximation, but that there are corrections for spin‐dependent operators.
10.M. Cohen [Proc. Roy. Soc. (London) A293, 365 (1966);
10.M. Cohen, Proc. Phys. Soc. 92, 23 (1967)]
10.has reported calculations for alkalilike ions which seem to contradict this result. However, in fact his Hartree‐Fock method is not coupled Hartree‐Fock, but is version of uncoupled H.‐F. [G. W. F. Drake (private communication);
10.see also G. W. F. Drake and M. Cohen, J. Chem. Phys. 48, 1168 (1968), Footnote 11].
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