Expressions of Energy and Potential due to Orbital Polarization

Abstract

The simple and tractable representation for the LS-multiplet energy in l₁l₂-configuration in an atom is derived in the form of the polynomials being a function of l₁·l₂ which obey the recurrence formulae, and is suitable for the vector model. Moreover, it is extended to lⁿ configurations. On a basis of the model, the definition of the orbital polarization energy is given. The more precise expressions of the energies compared to those so far proposed by Eriksson et al. are derived for the maximal spin multiplets in pⁿ, dⁿ, and fⁿ. They are composed of two terms depending on −3L²⁄2 and n(n−2l−1). They are the exact for pⁿ and dⁿ, but it for fⁿ is correct only for a ground multiplet. Other expressions are also derived as a function of L² for fⁿ, though more complicated. For the actual atomic and band structure calculations based on local-spin-density-approximation (LSDA), the modified expression for the energy is proposed. The potential is derived from its expression in terms of the density functional theory, and can be applied to their structure calculations.