Operator Cowan-Griffin

Only recently has the work of Bauschlicher, Walch and Siegbahn showed the need to include d correlation, whereas the work of Werner and Martin and of Scharf, Brode and Ahlrichs stressed the importance of cluster corrections and relativistic corrections. The results of Werner et al. were obtained using CEPA-1 to account for cluster contributions, while Scharf et al. used the CPF approach. Both groups accounted for relativistic corrections by employing first-order perturbation theory, i.e. by evaluating the Cowan-Griffin operator which consists of the mass-velocity and the one-electron Darwin term of the Breit-Pauli Hamiltonian. 

Just as for the Cowan-Griffin operator, the potential is the atomic SCF potential and so includes both one- and two-electron spin-orbit effects. In this respect the integrals over this potential resemble the atomic mean-field spin-orbit integrals of Hess et al. (1996). 

This method yields good qualitative and, in some cases, quantitative results. It is especially useful in cases in which Cowan-Griffin orbital-based REPs, such as in this case, are employed because ab initio spin-orbit operators are not appropriate, since spin-orbit terms are not considered in the derivation... 

Shape-consistent pseudopotentials including spin-orbit operators based on Dirac-Hartree-Fock AE calculations using the Dirac-Coulomb Hamiltonian have been generated by Christiansen, Ermler and coworkers [161-170]. The potentials and corresponding valence basis sets are also available on the internet under http //www.clarkson.edu/ pac/reps.html. A similar, quite popular set for main group and transition elements based on scalar-relativistic Cowan-Griffin AE calculations was published by Hay and Wadt [171-175]. 

Griffin calculation in LS-coupling) and doing a similar averaging for the equations (8) and (9) can readily be evaluated. The steps leading to equations (8) and (9) have relevance not only for the relativistic operators but also for the core-valence interaction, equation (5) the first two terms in equation (5) are local operators anyway (i.e. multiplicative potentials), c Kc can be written as an /-dependent operator, for an atom as in equations (7) and (8), and the orbitals necessary for building up Jc and Kc can be taken from an LS Cowan-Griffin AE calculation as above. 

In the Cowan-Griffin-Wood-Boring Hamiltonian, the 7] and operators of Eq. (4) read ... 

In the case of the Cowan-Griffin method, the spin-free one-electron relativistic operators are incorporated into the spectral representation of the exchange potential ... 

The Cowan-Griffin Hamiltonian was developed for spin-free relativistic atomic calculations (Cowan and Griffin 1976). However, it has also found some use as a starting point for developing spin-free relativistic Hamiltonians for molecular application. Here, we show the form of this operator, and the associated spin-orbit correction. For atoms, the Cowan-Griffin Hamiltonian follows directly from the radial form of the atomic Dirac equation (7.29), which may be given as... 

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