The direct and indirect effects in the relativistic modification of atomic valence orbitals

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Abstract
The relative importance of the direct and indirect relativistic effects on the behaviour of atomic valence electrons in the Dirac-Fock scheme is investigated for the ground configurations of gold, thallium and lutetium which give information on s, p, p, d and d orbitals. The direct effect, which is always found to contract the relativistic orbital, is completely responsible for the relativistic contraction of the 6s orbital in gold, and the effect is found to become progressively smaller in the order s>p>d approximately d; for none of the systems studied is the direct relativistic effect negligible. The indirect effect is always found to expand the orbital and increases according to the order s<p<p<d approximately d. The consequences of the results for calculations on molecules containing heavy atoms are discussed.