Comment on “Basis Set Expansion Dirac—Fock SCF Calculations and Mbpt Refinement ” by Y. Ishikawa

Abstract

Fock (1930) derived, for systems with Coulomb (±r^-1) potentials, the equations

$$c < \alpha .p > + < V > = 0$$

(1)

$$E = mc^2 + \beta $$

(1)

Later derivations and discussions are listed in Table 2.5 of Pyykkö (1986) who, however, missed the papers by Bethe (1948), and Epstein and Epstein (1962), and failed to quote in the table Breit and Brown (1948) and Brown (1950) giving

$$(Z\alpha /2) < r^{ - 2} > \, = k\int {fg\,dr} $$

(1)

and Epstein (1976), giving several relations involving α,β and rⁿ. All these papers are related to hydrogen—like atoms.