Single determinant SCF

It is found that, in general, the molecular charge densities obtained from single determinant SCF calculations carried essentially to the Hartree-Fock limit (see page 163) are accurate to within 2-5% of the total charge density at any point in space, except perhaps for very large distances from the nuclei. Coulomb electron correlation effects are relatively small in particular, the value of p(r) in the neighbourhood of a bond critical point calculated in that way exceeds the value obtained from a correlated wavefunction by only a few per cent. 

As in general all the y-coefficients do not vanish one has to assume a more general reference state than the single determinant SCF state. This is the rather well-known problem of finding the consistent reference state for the Random Phase Approximation (RPA). It also means that the field operator basis can be enlarged and can for instance include the iV-electron occupation number operators (in this discussion, electron field operators and their adjoints are used referring to a basis of spin orbitals that are the natural spin orbitals of the reference state, as will be discussed below, i.e., the spin orbitals that diagonalize the one-matrix)... 

In a previous note I gave an example of why an effective bond can exist when a real bond is absent within Single Determinant SCF-MO (SD-SCF-MO) theory. 

A set of standard type approximations (Born Oppenheimer approximation, group partition, simple Hartree factorization between the groups, single determinant SCF approximation i.e. 

DQMC calculations for atoms and molecules such as H2, H4, Be, H2O, and HF made by means of fixed-node structures obtained from optimized single-determinant SCF calculations typically recover more than 90% of the correlation energies of these species and yield total electronic energies lower than the lowest energy analytic variational calculations. These results suggest that optimized single-determinant wavefunctions have node structures that are reasonably correct. 

Greeff and Lester have carried out VQMC and DQMC calculations for a number of silicon hydride species SiH ( = 1-4), Si2, Si2Hg, and 8)2 Hg. The core electrons for Si were eliminated with use of a standard pseudopotential. The QMC calculations were carried out with importance sampling using a trial function composed of a single-determinant SCF function multiplied by a Jas-trow function of the type developed by Schmidt and Moskowitz." The statistical uncertainties in the energies determined were lower than 1.0 kcal/mol. 

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