Compounds nonrelativistic approximation

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. 

Gagliardi and Roos conducted a series of studies on actinide compounds. They follow a combined approach with DKH/AMFI Hamiltonians combined with CASSCF/CASPT2 for the energy calculation and an a posteriori added spin-orbit perturbation expanded in the space of nonrelativistic CSFs. This strategy aims to establish a balance of sufficiently accurate wave function and Hamiltonian approximations. Since the CASSCF wave function provides chemically reasonable but not highly accurate results (as witnessed, for instance, in the preceding section), it is combined with a quasi-relativistic Hamiltonian, namely the sc alar-relativistic DKH one-electron Hamiltonian. Additional effects — dynamic correlation and spin-orbit coupling — are then considered via perturbation theory. 

Relativistic effects have to be taken into account for compounds containing transition elements with higher atomic numbers the 5d transition elements (Hf, Ta, W) are of particular concern in the present review. A fiiUy relativistic treatment requires the solution of the Dirac equation instead of the Schrodinger equation. However, in many cases, it is sufficient to use a scalar relativistic scheme (48) as an approximation. In this technique, the mass-velocity term and the Darwin 5-shift are considered. The spin-orbit splitting, however, is neglected. In this approximation a different procedure must be used to calculate the radial wave functions, but the nonrelativistic formalism, which is computationally much simpler than solving Dirac s equation, is retained. 

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