Energies of N equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. II. Application to 3dNconfigurations

Abstract

For pt.I see ibid., vol.17, p.23-75 (1984). As an illustration of the theory developed in the first paper in this series, a set of five orthogonal parameters is used to describe all electrostatic two-particle excitations in the 3dN configurations completely to second order. These parameters represent the term energies of d2 and, consequently, the 3dN configurations are perceived as a collection of 1/2N(N-1)d2 pairs, the total energy of the configuration being the sum of the corresponding pair energies. As regards their effects, the parameters are partitioned into a structural and an additive part; the structural part is found to behave as a linear function of N, whereas the additive part is proportional to the average energy of the configuration. In order to take into account all electrostatic one-particle effects as well, two orthogonalised three-body parameters T1 and T2 are used, the first corresponding to the well known Trees parameter and the second covering the remaining class of one-electron excitations. With a least-squares fitting procedure, both the d2 energies and the three-electron parameters are determined for the dN ground configuration in the III, IV, V and VI spectra of the iron group elements. Surprisingly, the effects of T2 turn out to be important, especially for the lower ionisation stages. Amongst other things, old problems concerning the far-off position with respect to calculations of the 12D term in the 3d6, and parameter irregularities in the 3d7 configurations, seem to be solved with the introduction of T2. As a result, the mean error of the fit in some of these cases is reduced by factors of three to four. Using the above set of parameters, a prediction of the 3d4 ground configuration of Mn IV is made.