Hartree-Fock self-consistent-field

There are two ways to improve the accuracy in order to obtain solutions to almost any degree of accuracy. The first is via the so-called self-consistent field-Hartree-Fock (SCF-HF) method, which is a method based on the variational principle that gives the optimal one-electron wave functions of the Slater determinant. Electron correlation is, however, still neglected (due to the assumed product of one-electron wave functions). In order to obtain highly accurate results, this approximation must also be eliminated.6 This is done via the so-called configuration interaction (Cl) method. The Cl method is again a variational calculation that involves several Slater determinants. 

The most commonly used ab initio method is the self-consistent field Hartree-Fock (SCF-HF) scheme with or without configuration interaction (Cl). 

F. LCAO Self-consistent Field (Hartree-Fock) Molecular Orbitals I. Slater-type atomic orbitals... 

Difficulties arise in the band structure treatment for quasilinear periodic chains because the scalar dipole interaction potential is neither periodic nor bounded. These difficulties are overcome in the approach presented in [115] by using the time-dependent vector potential, A, instead of the scalar potential. In that formulation the momentum operator p is replaced by tt =p + (e/c A while the corresponding quasi-momentum Ic becomes k = lc + (e/c)A. Then, a proper treatment of the time-dependence of k, leads to the time-dependent self-consistent field Hartree-Fock (TDHF) equation [115] ... 

The self-consistent field Hartree-Fock (HF) method is the foundation of AI quantum chemistry. In this simplest of approaches, the /-electron ground state function T fxj,. X/y) is approximated by a single Slater determinant built from antisymmetrized products of one-electron functions i/r (x) (molecular orbitals, MOs, X includes space, r, and spin, a, = 1/2 variables). MOs are orthonormal single electron wavefunctions commonly expressed as linear combinations of atom-centered basis functions ip as i/z (x) = c/ii /J(x). The MO expansion coefficients are... 

MO calculations for the azide group have involved a variety of approaches and degrees of sophistication. Probably the most reliable wave functions are obtained from recent self-consistent-field Hartree-Fock MO calculations. These are reviewed here. For a discussion of other calculations [10-17], reference is made to the excellent review by Treinin [18]. 

The pseudo-local presentation of the self-consistent-field Hartree-Fock equation nicely shows how closely these one-particle equations formulated for a many-electron atom resemble the Schrodinger equation for one-electron atoms. Hence, the SCF equation for a given orbital of given angular momentum I is formally like the Schrodinger equation for the electron in the... 

Here, this interaction is treated within the self-consistent field Hartree-Fock approximation which gives the following mean-field spin-polarized electron-electron interaction Hamiltonian ... 

---