Hartree-Foek approximation

Sueh partition is usually introdueed to get an effeetive Hamiltonian whose form resembles that of the standard Hamiltonian for the isolated system. In faet, if we limit our exposition to the Hartree-Foek approximation in whieh the moleeular orbitals are expressed as an expansion over a finite atomie orbital basis set, the Foek operators one defines for the two systems, the isolated and the solvated one, beeome (over the atomie basis set)... 

An experimental determination of the spin density distribution in the allyl radical recently has become available (30) and is in fair agreement with the results of the valence bond calculation and in somewhat better agreement with an extended Hartree-Foek calculation to be described below. It is seen that although the allyl radical possesses only a single unpaired electron, the total calculated ir-electron spin density on the molecule is % to % units depending on the approximation employed. However, the relationship (75)... 

However, the calculations were performed in terms of the restrieted Hartree-Foek method (i.e., with a strictly-defined zero spin) in the one-determinant approximation. This approach may account for a loss of solutions for cases of eomplex systems where the spin squared deviates from zero although all reagents are in the singlet state. Henee, this solution may have the physical meaning [21], as is the ease with ozone. In the literature, these cases are considered as unstable Hartree-Foek s solutions. In [22], ealeulations were performed with allowanee for this condition in terms of the unrestrieted Hartree-Foek (UHF) method the ealeulations showed that the reaction may proceed by non-coordinated addition but with the induction of higher-spin states (S = 0.7-1.2). 

Anomeric effect, 82, 310-311, 305 Antarafacial, 163 examples, 164 sigma bonds, 167 Anti-Bredt olefin, 102 Approximations of MO theory Born-Oppenheimer, 22 Hartree-Foek, 222 Huckel, 35, 86 independent electron, 35 LCAO, 229 nonrelativistic, 22 SHMO, 87... 

Now the non-relativistie hamiltonian is a semi-bounded, self-adjoint operator in Hilbert space. The algebraie approximation results in the restrietion of the domain of this operator to a finite-dimensional subspace S of Hilbert space. For an N-electron system, the algebraie approximation may be implemented by defining a suitable orthonormal basis set of M >N) one-electron spin-orbitals (usually solutions of the matrix Hartree-Foek equations) and then construeting aU unique A -electron determinants. The number of unique determinants that ean be formed is... 

A many-body perturbation theory (MBPT) approach has been eombined with the polarizable continmrm model (PCM) of the electrostatic solvation. The first approximation called by authors the perturbation theory at energy level (PTE) corrsists of the solution of the PCM problem at the Hartree-Foek level to find the solvent reaction potential and the wavefunction for the calcirlation of the MBPT correction to the energy. In the second approximation, called the perturbation theory at the density matrix level only (PTD),... 

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