SCF Hartree-Fock

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

The calculated deprotonation energies of ethane, ethylene and acetylene by SCF Hartree-Fock (FIF) and MP2 methods follow the expected order 456, 455 (basis... 

Our main reason for introducing the Slater atomic orbitals, however, is that linear combinations of them have often been used to approximate the SCF Hartree-Fock numerical orbitals. If x represents a set of analytical orbitals, such as the STOs of equation (6.56), then we may expand 0 in the Slater determinant (6.36) in terms of x,... 

Table 3,1. Equilibrium bond lengths (in a ) for a series of ten-electron molecules from (SCF) Hartree-Fock-Roothaan calculations using different basis sets, compared with experimental values...

Table 3.3. Equilibrium bond distance [R(O-H) in aj for H2O from an (SCF) Hartree-Fock-Roothaan calculation, and calculations using correlated wave functions (Cl and MBPT) compared with experiment...

Table 3.5. Comparison of metal-water bond lengths and binding energies calculated using (SCF) Hartree-Fock-Roothaan methods with...

Table 3.6. Comparison of the results of various types of (local) density-functional calculations (LCAO-Za, LMTO-Aa, DV-Aa) with ah initio SCF Hartree-Fock and multiple-scattering Xa calculations (using overlapping spheres, OS) and experimental data (expt.) for equilibrium bond distance [i e(fl )] and bond dissociation energy (D in eV) in the nitrogen molecule (Nj)...

Table 5.18. Calculated and experimental geometries in borate polyhedra. Bond lengths and bond angles for the borate clusters shown calculated using ab initio SCF Hartree-Fock-Roothaan methods with various basis sets, and the modified electron-gas and modified neglect of differential overlap method, and compared with experimental values (see text for data sources)...

There has been considerable effort directed towards the assessment of the covalency or ionicity of various solids. The output of standard ab initio (SCF) Hartree-Fock-Roothaan calculations contains Mulliken (1955) charge distribution analysis parameters such as the atomic-orbital populations, net atomic charges, and bond overlap populations deseribed earlier (Chapter 3), which are often used to discuss the relative covalency or ionicity of materials. Considerable caution is required in using such parameters, however, since net atomic charges and other such quantities are not quantum-mechanical observables that is, they cannot even in principle be measured, and are highly basis-set dependent, as noted by Hehre et al. (1986 pp. 336-41). This is illustrated for molecules more relevant to mineralogy in Table 7.1, in which a number of properties of CO2 and SiOj are shown calculated at various basis-set levels. It is clear... 

The development and efficient implementation of a parallel direct SCF Hartree-Fock algorithm, with gradients and random phase approximation solutions, are described by Feyereisen and Kendall, who discussed details of the structure of the parallel version of DISCO. Preliminary results for calculations using the Intel-Delta parallel computer system were reported. The data showed that the algorithms were efficiently parallelized and that throughput of a one-processor Cray X-MP was reached with about 16 nodes on the Intel-Delta. The data also indicated that sequential code, which was not a bottleneck on traditional supercomputers, became time-critical on parallel computers. 

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