Relativistic methods for large systems

Fortunately the DHF method has particular features that can be exploited to reduce the computational cost to something closer to the classical HF method and to present it in a form which is amenable to the use of recently developed linear scaling or 0 N) methods. Visscher [117] observed that the charge density asociated with small components is highly localized near the nuclei, suggesting that the interaction energy involving small component densities may 

The electrostatic interactions in a molecule are determined by the structure of the density matrix D. In constructing D from an atomic orbital or atomic spinor basis, we incorporate a lot of redundant information in the Gaussian overlap charge distributions, since most of the electron density is concentrated near the nuclei. One should therefore try to transform D into a block diagonal form in which each dense block corresponds to a one-centre density so that the 

The MCDHF(B) method supposes that the eigenfunctions of the N-electron Hamiltonian, P, may be expanded in a basis of configuration state functions (CSF), J , which may themselves be written as linear combinations of N-electron determinants. We make no distinction between CSFs and determinants at this stage, and write 

The similarity of this formalism with that conventionally used in nonrela-tivistic quantum chemistry is obvious all we have done is to replace the usual spin-orbital basis by one comprising four-component spinors. Slater s rules for the construction of determinantal matrix elements are still applicable, so that any hamiltonian matrix element may be written in the form 

The total energy can thus be written directly in terms of the one-and two-electron integrals over spinors as 

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