Correlated effective valence shell Hamiltonian for the first-row transition metal atoms

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Abstract
Ab initio calculations of the effective valence shell Hamiltonians are presented for the 3dn4sm first‐row transition metal atoms using quasidegenerate many‐body perturbation theory in order to further study the role of electron correlation and relativistic effects in these systems. Prime emphasis is placed here on the individual matrix elements of the effective valence shell Hamiltonian, the true parameters, and in comparing calculated and empirically determined values. The true parameters from second order calculations are supplemented with selected new third order calculations to test the convergence of the quasidegenerate many‐body methods with respect to excitation energies and individual true parameters. Valence orbital basis sets can be introduced which lead to good convergence for energies and parameters, but different sets may be necessary for these two purposes. The calculated one‐ and two‐electron true parameters for Ti, V, and Cr compare well with empirical ones, while individual three‐electron empirical true parameters are unavailable. Criteria are discussed governing convergence of quasidegenerate many‐body perturbation theory for the transition metal atoms.