MCSCF method relativistic

Calculations of atomic quadrupole moments are still of interest, particularly for heavier atoms where relativistic accuracy is required. Sundholm102 has reported a finite-element MCSCF method to calculate the quadrupole of Ar+ and finds a final value of —0.5271 au in comparison with a recent experimental determination of —0.5208 au. The Hartree-Fock value is —0.57213 au and the valence shell correlation correction, amounting to 0.04844 au, accounts for most of the additional contribution, a result which may be of some significance for molecular calculations involving atoms in the intermediate range of atomic numbers. 

The conclusion we can draw from the discussion is that many of the systems that would be handled by open-shell RHF calculations in the nonrelativistic case do not really lend themselves to this treatment relativistically. An illustration of this point for the group 14 elements is given in section 12.1. Instead, we must resort to MCSCF methods, which we describe in section 12.9. 

The special importance of multiconfiguration SCF (MCSCF) methods in relativistic calculations was discussed in the introduction to this chapter. But quite apart from this, we know that MCSCF methods are very useful in nonrelativistic quantum chemistry, where various brands of the method, such as complete active space (CAS) SCF,... 

Relativistic methods can be extended to include electron correlation by methods analogous to those for the non-relativistic cases, e.g. Cl, MCSCF, MP and CC. Such methods are currently at the development stage. ... 

First, the operator of spin-orbit coupling is inserted at the first step in which determination of the optimal singleconfiguration wave fimction is carried out. This method, called spin-orbit SCF provides in general complex relativistic molecular spin-orbitals that are neither pure a nor pure P functions of the spin variable. In principle, the spin-orbit SCF can be followed with variational (MCSCF, MRCI) and nonva-riational (MP2, CC) steps. All these approaches are commonly dubbed yj -coupling methods (in contrast to the approaches dealing with nonrelativistic molecular orbitals, called LS-cou-pling methods) and are, due to their complexity, rarely applied to molecules composed of more than two atoms. 

Atomic calculations for the heaviest elements were also performed using other approaches while studying molecular properties (see Sect. 5). Thus, e.g., electronic states of H were calculated using the relativistic complete active space MCSCF (CASMCSCF) Cl method [60]. 

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