Hartree-Fock methods, for

So far, we have considered only the restricted Hartree-Fock method. For open shell systems, an unrestricted method, capable of treating unpaired electrons, is needed. For this case, the alpha and beta electrons are in different orbitals, resulting in two sets of molecular orbital expansion coefficients ... 

All the early work was concerned with atoms, with Sir William Hartree regarded as the father of the technique. His son, Douglas R. Hartree, published the definitive book, The Calculation of Atomic Structures, in 1957, and in this he derived the atomic HF equations and described numerical algorithms for their solution. Charlotte Froese Fischer was a research student working under the guidance of D. R. Hartree, and she published her own definitive book. The Hartree—Fock Method for Atoms A Numerical Approach in 1977. The Appendix lists a number of freely available atomie structure programs. Most of these can be obtained from the Computer Physics Communications Program Library. 

Fischer, C. F. (1977) The Hartree-Fock Method for Atoms A Numerical Approach, Wiley, New York. 

In the case of the Hartree-Fock method for a closed shell systems, the new Fock matrix is written as... 

The C02 insertion into the Rh(I)-H bond of the square planar RhH(PH3)3 complex was investigated with the Hartree-Fock method for geometry... 

FFi77] Froese Fischer Ch 1977 The Hartree-Fock method for atoms (John Wiley Sons, New York). [FGW74] Fellner-Feldegg H, Gelius U, Wannberg B, Nilsson AG, Basilier E and Siegbahn K 1974 J. Electron. Spectrosc. Relat. Phenom. 5 643. 

P.J. Stephens et al., Ab initio prediction of optical rotation A comparison of density functional theory and Hartree-Fock methods for three 2,7,8-trioxabicyclo[3.2.1] octanes. Chirality 14, 288-296 (2002)... 

Slater JC (1951) A simplification of the Hartree-Fock method for the exchange energy (Ex[p]) in the uniform electron gas, Phys Rev, 81 385-390... 

Hobza P, Kabelac M, Sponer J, Mejzlik P, Vondrasek J (1997) Performance of empirical potentials (AMBER, CFF95, CVFF, CHARMM, OPS, POLTEV), semiemprical quantum chemical methods (AMI, MNDO/M, PM3) and ab initio Hartree-Fock method for interaction of DNA bases comparison of nonempirical beyond Hartree-Fock results, J Comp Chem, 18 1136-1150... 

E.A. McCullough, Numerical Hartree-Fock methods for diatomic molecules A partial wave expansion approach. Comp. Phys. Rep. 4 (1986) 265. 

A. C. Wahl, PJ. Bertoncini, G. Das, T.L. Gilbert, Recent progress beyond the Hartree-Fock method for diatomic molecules The method of optimized valence configurations, Int. J. Quantum Chem. S1 (1967) 123. 

An overview of the development of the finite difference Hartree-Fock method for diatomic molecules has been presented. Given the power of the currently available workstations the exact solutions of the HF equations for systems containing 20-25 electrons can be obtained routinely. The approach has been successfully used to calibrate even-tempered gaussian basis sets the discrepancies between the finite difference and the finite basis set results for a number of diatomic molecules (including a 40-electron system GaF) could be narrowed to a couple of iHartree. 

Hartree-Fock Methods for Large Systems Linear Scaling Methods... 

C. Froese-Fisher, "The Hartree-Fock Method for atoms" Wiley, New-York, 1977... 

C. F. Fischer, The Hartree-Fock method for atoms, John Wiley Sons, New York, 1977. 

In practice, using currently available exchange and correlation potentials, this path leads to results [113] worse than those obtained with the Hartree-Fock method. This is illustrated for momentum moments in Table 19.2 which shows median absolute percent errors of (p ) for 78 molecules relative to those computed by an approximate singles and doubles coupled-cluster method often called QCISD [114,115]. The molecules are mostly polyatomic, and contain H, C, N, O, and F atoms. The correlation-consistent cc-pVTZ basis set [110] was used for these computations. Table 19.2 shows the median errors for the Hartree-Fock method, for second-order Mpller-Plesset permrbation theory (MP2), and for DFT calculations done with the B3LYP hybrid density functional... 

Froese-Fischer, C. (1977), The Hartree-Fock Method for Atoms, Wiley, New York. Gallusser, R. (1976), Thesis, Physical Chemistry Laboratory, ETH Zurich, Switzerland. Gallusser, R., and Dressier, K. (1982), J. Chem. Phys. 76, 4311. 

For a closed shell system there is only one Hartree-Fock method. For non-closed shells, however, various H.F. methods are possible. Different orbitals for the same non-closed configuration are obtained depending on which term [e.g. P or or in C(ls 2s 2 )] is used. Also, different approximations are possible to avoid the off-diagonal energy parameters which cannot be transformed away as in the closed shell case. About nine variants of such H.F. methods have been discussed in the literature. To list and discuss... 

Further work and applications are needed on Hartree-Fock methods for dealing with portions of large systems, on the many-electron theory of non-closed shells and on mfm-molecular van der Waals forces. 

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