Excitation energies and oscillator strengths of Ca I using multireference many-body perturbation theory

Abstract

Atomic transition lines of neutral calcium were first found in solar spectrum as early as the middle of the 19th century, when the 4227-A line was identified along with the famous singly ionized H and K lines @1#. Neutral calcium lines have also been observed in all types of stellar and interstellar spectra, such as late-type dwarf stars. The crude abundance of Ca I (l56717.7 A ) has been observed in Am binaries@2#. To confirm those identifications and to find new lines, one has to depend on atomic experimental data or computational data based on theoretical models of the calcium atom. The abundances of neutral calcium in these astronomical bodies depend on the oscillator strengths of those lines, which come from the excitation energies of various levels and transition moments among those levels. The difficulty in accurately estimating transition energies and oscillator strengths of neutral calcium atom arises mainly due to the following reasons: ~a! The precise computation of transition energies and oscillator strengths requires a balanced description of the ground and excited states. ~b! The use of an inadequate basis leads to difficulties in describing the excited states and an unbalanced treatment of dynamical correlation and polarization effects. The problems due to basis set inadequacy can be removed partially by enlarging the basis for small and moderate-sized atomic and molecular systems. Here, the size extensivity @3# of the theory plays an important role in handling the proper treatment of electron correlation, and in that way it properly treats the differential correlation energies of the interacting ~initial and final states! zeroth-order states. It ensures that the state energies scale linearly with the number of electrons in a rigorous way. The accuracy of the computed excitation energy depends mostly upon the quality of the unoccupied valence orbitals in which excitation occurs. The traditional choice of some unoccupied valence orbitals from a ground-state selfconsistent-field ~SCF! computation introduces V N orbitals that are best suited for describing negative ions, and not lowlying excited states. Thus the valence orbitals, those that are not occupied in the ground-state SCF, should be taken as more representative orbitals suitable for excited states. One possible choice emerges from the restricted single excitation configuration interaction procedure@4#, where excitations are only permitted from the highest occupied orbitals. A simpler and often equivalent approaches involves using improved virtual orbitals ~IVO’s !@ 5 #in the H v valence space or reference space. Here the IVO’s are generated by single orbital SCF optimization in which the Fock operator is defined by promoting an electron from the highest occupied orbital to the orbital being optimized, while all the previously determined orbitals are kept frozen. Alternatively this can be accomplished by a unitary transformation @6#. The IVO orbital energies obtained in this way are lower than those evaluated from the traditional SCF procedure due to the absence of an extra Coulomb operator in the former procedure. For example, in a neutral calcium atom H v calculation, the twoorbital (4 s,4p) minimal reference space is produced by the sequence