Evaluation of atomic polarisabilities using the variational perturbation approach: the first transition series

Abstract

Using the variational perturbation approach, mean static dipole polarisabilities for the first transition series, resulting from the contribution to the total polarisability of the polarisation of the 4s shell, are calculated. Two different sets of calculations are performed. With the exception of zinc, the polarisabilities calculated using a 4p polarising function, determined by minimising the second-order energy functional and representing the zero-order wavefunction by the Hartree-Fock configuration 3dn(2S+1L)4s2 and each component of the perturbed function by the configurational function 3dn(2S+1L)4s(2SL)4p, are within 2% of that obtained from the theoretically more correct calculation, consisting of a 4p correlating function, determined to describe the important near-degeneracy effect 4s2 to 4p2, and a 5p polarising function, determined by optimising the second-order functional. In the latter optimisation the unperturbed wavefunction is represented by the Hartree-Fock single configuration 3dn4s2, augmented by the near-degenerate configuration 3dn4p2, and each component of the perturbed function consists of the most important polarising and configurational functions. In addition, it is shown that the configurations 3dn-14s24p and 3dn-14p3, from the 3d to 4p replacement, can be eliminated from the perturbed-states expansion, as their inclusion in the configuration interaction expansion of the perturbed states causes less than a 1% change in the polarisability.