Electrons DVME method

In the present work we first perform molecular orbital (MO) calculations using the relativistic DV-Xa method. Then we perform Cl calculations using the DVME method to obtain the energy levels and wave functions of a many-electron system, which will be used for calculations and analysis of the optical spectra of RE ions in crystals. 

The relativistic DVME method 3.2.1. The many-electron Dirac Hamiltonian... 

In the DVME method, the many-electron Dirac Hamiltonian is diagonalized based on the Cl approach. In this approach, the Zth many-electron wave function i l is represented as a... 

In the relativistic DVME method, eqs. (27) and (28) are calculated numerically in a similar way to the one-electron calculation such as... 

In the relativistic DVME method, the interactions among the states represented by the Slater determinants, i.e., the Cl can be analyzed using explicit many-electron wave functions expressed by eq. (23). From the orthonormality of the Slater determinants, the inner product of the /th many-electron wave function with itself can be expanded as... 

The electric-dipole transition is determined by the symmetry properties of the initial-state and the final-state wave functions, i.e., their irreducible representations. In the case of electric-dipole transitions, the selection rules shown in table 7 hold true (n and a represent the polarizations where the electric field vector of the incident light is parallel and perpendicular to the crystal c axis, respectively. Forbidden transitions are denoted by the x sign). In the relativistic DVME method, the Slater determinants are symmetrized according to the Clebsch-Gordan coefficients and the symmetry-adapted Slater determinants are used as the basis functions. Therefore, the diagonalization of the many-electron Dirac Hamiltonian is performed separately for each irreducible representation. 

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