Interfacing relativistic and nonrelativistic methods. III. Atomic 4-spinorexpansions and integral approximations

Two approximations to the normalized elimination of the small component are presented which enable the work of a relativistic calculation to be substa ntially reduced. The first involves fixing the ratio of the large and small components in atomic calculations, which corresponds to a basis set expans ion in terms of positive energy atomic 4-spinors. The second involves the d efinition of a local, i.e., center-dependent, fine structure constant, whic h has the effect of making atoms with alpha=0 nonrelativistic. A series of test calculations on a variety of molecules and properties indicates that t he errors incurred in the first approximation are negligible. In the second approximation, the errors are dependent on the property, the chemical envi ronment and the atomic number. For the second period elements the errors in the approximation are for chemical purposes negligible. In the third perio d this is true for many properties, but for some, such as ligand-metal bind ing energies, there are discrepancies which may be a cause for concern in m ore accurate calculations. Beyond the third period it is usually necessary to treat atoms relativistically. (C) 1999 American Institute of Physics. [S 0021-9606(99)30146-X].