Interaction of Variational Localized Correlation Functions for Atomic Properties

• Variational methods are used for targeting speci c correlation e ects by tailoring the con- guration space. Independent sets of correlation orbitals, embedded in the localized correlation functions (LCFs), are produced from the multicon guration Hartree-Fock (MCHF) or Dirac- Hartree-Fock (MCDHF) calculations [1,2]. These non-orthogonal functions are then coupled to each other by solving the associated generalized eigenproblem. The Hamiltonian and overlap matrix elements are evaluated using the biorthonormal orbital transformations and e cient counter-transformations of the con guration interaction eigenvectors [3]. This method was successfully applied for describing the total energy of the ground state of beryllium [4]. Moreover it has been shown that the energy convergence is faster than with the usual SD-MCHF method for which a single set of orthonormal one-electron orbitals spanning the complete con guration space is optimized. In the present work, we investigate the interaction of localized correlation functions (LCFI), not only for the 1s22s2 1S state of beryllium but also for the rst two excited states: 1s22s2p 3Po and 1s22s2p 1Po. For these three states, we evaluate the total energy but also the expectation values of the speci c mass shift (SMS) operator, the hyper ne structure (HFS) parameters and the transition probabilities. The comparison between the SMS and HFS results obtained using the LCFI method and the traditional MCHF one stresses the importance of the mixing coe cients contraction within each LCF function. We demonstrate that this unwanted contraction e ect can be bypassed by enlarging the associated generalized eigenproblem. The beryllium atom is a system for which it is still possible to saturate a single orthonormal orbital set through the complete active space MCHF expansions. As such, it constitutes the perfect benchmark for the LCFI method. For larger systems, it becomes hopeless to saturate a single common set of orthonormal orbitals, the LCFI method should be a good alternative for reaching a full-correlated wave function. The present study is a rst step in the current development of the extension of both ATSP2K and GRASP2K packages [1,2] that will adopt the biorthonormal treatment for energies, isotope shifts, hyper ne structures and transition probabilities.

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