M. Barysz et Aj. Sadlej, EXPECTATION VALUES OF OPERATORS IN APPROXIMATE 2-COMPONENT RELATIVISTIC THEORIES, Theoretical chemistry accounts, 97(1-4), 1997, pp. 260-270
Two methods for the evaluation of expectation values with approximate
two-component relativistic functions are analysed. The first of them i
s based oil the change of picture for the operator whose expectation v
alue is to be calculated and associated with approximations leading to
the given two-component relativistic wave fnnction. This method, thou
gh hardly used in numerical calculations, gives the expectation values
that directly reflect the accuracy of the wave function used for thei
r calculation. The second method, most commonly used in calculations,
neglects the picture change and is shown always to introduce an error
of the order of alpha(2), where alpha is the fine structure constant.
This error is present independently of the accuracy of the approximate
two-component wave function. The perturbation formalism developed ill
this paper is illustrated by calculations of relativistic corrections
to the expectation values of r(-1) for arbitrary states of hydrogenic
ions.