Improved RCI techniques for Atomic 4fn Excitation Energies and Polarizabilities

Abstract. We propose an ecient method by which previously computationally expensive, but moderately important, pair correlation eects can be incorporated into fn excitation energies. Application is to Gd IV. Secondly, we extend two methods of obtaining static and tensor dipole polarizabilities and apply them to the Ni II ground state. The rst uses the sum over f-values approach, and the second is variational. 1. Calculation of Excitation Energies for Lanthanides and Actinides Our long term computational interest has been to develop (when necessary) and apply the relativistic conguration interaction (RCI) method to predict properties of complicated atoms and ions { specically, for transition metals, lanthanides and actinides. Triply ionized lanthanide and actinide ions appear as impurities in condensed matter systems where they can serve as centers of lasing activity [1], play a role in MRI medicine as endohedral metallofullerenes (e.g. Gd3N-C80) [2], appear as important constituents of high temperature super-conductors, etc. There also has been interest in the free Gd IV ion as a possible means of detecting an electron electric dipole moment [3]. Experimentally, only a few of the low lying excitation energies within the fn con guration are generally known [4, 5] from measurements made in the condensed phase. Dipole transition energies fn- fn1d are generally not known experimentally, as the d levels in the solid are not very well localized [5]. It also may be noted that most prevalent charge state of the lanthanide/actinide ion in the solid is 3+ [5]. Computationally, these excitation energies are also dicult to obtain [6]. The calculations require the use of a relativistic Hamiltonian (Dirac-Breit) and a correlated wavefunction having at least a rst order form, i.e. one that includes all the dierentially important single and double subshell excitations from a set of reference functions. At present, a reasonable ab initio accuracy goal for excitations within fn would be to position all levels to 1000 cm1relative to the ground state. Our recent Gd IV [6] achieved 1257 cm1, and we improve this to 838 cm1here, accompanied by a drop in calculation tim