Dirac spinors molecular integrals

By incorporating these symmetries in the 4-spinor basis functions, as we have done in our BERTHA code [50-54], we can make substantial computational economies in computing interaction integrals. The angular stracture of Dirac 4-spinors described here is also exploited by the major computer package TSYM, which utilizes projection operators to construct relativistic molecular symmetry orbitals for double valued representations of point groups [77-79]. 

An efficient approach to improve on the Hartree-Fock Slater determinant is to employ Moller-Plesset perturbation theory, which works satisfactorily well for all molecules in which the Dirac-Hartree-Fock model provides a good approximation (i.e., in typical closed-shell single-determinantal cases). The four-component Moller-Plesset perturbation theory has been implemented by various groups [519,584,595]. A major bottleneck for these calculations is the fact that the molecular spinor optimization in the SCF procedure is carried out in the atomic-orbital basis set, while the perturbation expressions are given in terms of molecular spinors. Hence, all two-electron integrals required for the second-order Moller-Plesset energy expression must be calculated from the integrals over atomic-orbital basis functions like... 

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