Ansatz for the evaluation of the relativistic contributions to core ionization energies in complex molecules involving heavy atoms

On the basis of numerical, ab initio Delta DF and Delta HF computations of 1s-core, 2s-core, and 2p-core ionization energies of atoms, from Li through Xe, an allometric empirical formula that was proposed for evaluating relativistic corrections (including QED effects) to nonrelativistic values is assessed for homogeneous sets of elements in the periodic table. The two coefficients involved in this formula are precisely determined for 1s-core ionization in the sets of atoms Be-Ne, Mg-Ar, Zn-Kr, and Cd-Xe; 2s-core ionization in the sets of atoms Mg-Ar, Zn-Kr, and Cd-Xe; and 2p-core ionization in the set Mg-Ar. It is shown that the medium relative error on the results obtained using this formula, with respect to those directly computed, decreases from a few percent to a few hundredths of 1% when the depth of the ionized level increases. This formula could be used to include relativistic (and QED) corrections to results yielded by simpler, nonrelativistic calculations on complex molecules involving heavy atoms. (c) 2005 Wiley Periodicals, Inc.