Test of a Multi-Reference Many-Body Perturbation Theory for the Description of Electron Correlations in four Valence Electron States of Transition Metal Atoms

A multi-reference many-body perturbation theory (MRMBPT) method is critically tested in second order by comparing with the corresponding configuration interaction (CI) calculations. Excitation energies of the four-valence-electron states of transition metal atoms and ions are used for the comparison. The agreement between the second order MRMBPT and CI calculations is very reasonable, confirming the reliability of the second order MRMBPT method. The reliability of calculations with the present second order MRMBPT method was only been inferred empirically in the past since most results have been gauged by the agreement with experiment and/or with other MRMBPT calculations based upon different sets of orbitals and configuration spaces. The present MRMBPT method appears to be an efficient ab initio multi-reference method for the calculation of electron correlation effects in atoms and molecules, and it is shown how MRMBPT can be used to estimate core-core and core-valence correlation effects which are often omitted in CI calculations because too many configurations and correlating electrons are involved.