The size and energy of d orbitals in excited states of the sulphur atom

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Abstract
Wave-mechanical calculations are reported for the sulphur atom in varying degrees of ionization. The Dirac vector model is used to set up the self-consistent-field equations appropriate to (1) spectroscopic states involving one or more electrons in d orbitals; (2) valence-states with one or more d electrons; (3) valence-states in which octahedral, square-planar, and distorted tetrahedral hybrids are used. The equations are solved to determine the total atomic energy and the size and shape of the orbitals. Previous less accurate work with use of simple analytical approximations to the orbitals is confirmed and improved. The sizes of the 3s and 3p orbitals change very little, even when the total number of valence electrons changes; but the size of the 3d orbital is very sensitive both to the number of d electrons and the formal charge on the atom. The importance of this is stressed for an understanding of the higher valences of sulphur, and of sulphur, and of other atoms where d electrons may reasonably occur.

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