Relativistic DVME method

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

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. 

Figure 22.1 Status of the DVME method and the motivation to develop the relativistic DVME method.

Thanks to the rapid development of high-performance computers, the relativistic DVME method can now be applied to the analysis of multiplet spectra of RE ions. We have recently performed a systematic calculations of multiplet energy levels arising from 4f and 4f 15d configurations as well as the 4f —4f 15d transition spectra. 

In this paper, we first describe the theoretical background of the relativistic DVME method and then in order to demonstrate its wide applicability, its applications to optical and magnetic materials will be shown. 

In the relativistic DVME method, first, the relativistic DV-Xa calculation [22] is performed to obtain the fully relativistic four-component MOs used for the Cl calculations. 

In order to analyze the 4f2—4f5d transitions, multiplet structures for the 4f2 and 4f5d configurations were calculated by the relativistic DVME method. The MOs mainly consisting of Pr 4f or Pr 5d states were used in the Slater determinants. 

In this paper, a detailed description of the fully relativistic DVME method was given and some recent applications of this method were exhibited. 

Currently, development of new programs for calculation of variety of physical properties such as magnetic dipole transitions, electric quadrapole transitions, etc. are in progress. The algorithm of the program is still constantly improved in order to perform faster and larger calculations. These new programs are expected to further enhance the applicability of the relativistic DVME method to a wide variety of research fields. 

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