Hartree-Foek method

A review of thermoehemieal results from the Hartree-Foek method is... 

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). 

A fiirther diflfieulty arises beeause the exaet wavefiinetions of the isolated moleeules are not known, exeept for one-eleetron systems. A eoimnon starting point is the Hartree-Foek wavefiinetions of the individual moleeules. It is then neeessary to inelude the eflfeets of intramoleeular eleetron eorrelation by eonsidering them as additional perturbations. Jeziorski and eoworkers [M] have developed and eomputationally implemented a triple perturbation theory of the syimnetry-adapted type. They have applied their method, dubbed SAPT, to many interaetions with more sueeess than might have been expeeted given the fiindamental doubts raised about the method. SAPT is eurrently both usefiil and praetieal. A reeent applieation [ ] to the CO2 dimer is illustrative of what ean be aehieved widi SAPT, and a rieh soiiree of referenees to previous SAPT work. 

The Seetion on More Quantitive Aspects of Electronic Structure Calculations introduees many of the eomputational ehemistry methods that are used to quantitatively evaluate moleeular orbital and eonfiguration mixing amplitudes. The Hartree-Foek self-eonsistent field (SCF), eonfiguration interaetion (Cl), multieonfigurational SCF (MCSCF), many-body and Moller-Plesset perturbation theories. 

The majority of routine ealculations in quantum chemistry are done with variational methods (mainly the Hartree-Foek scheme). If we consider post-Hartree-Foek ealeulations, then non-variational [CCSD, CCSD(T)] and perturbational approaehes (ineluding MBPT) take the lead. The perturbational methods are based on the simple idea that the system in slightly modified conditions is similar to that before the perturbation is applied (cf. p. 240). 

The situation is analogous to the unrestrieted Hartree-Foek (UHF) method, ef. p. 408. This extension of the DFT is known as spin density functional theory (SOFT). 

A self-eonsistent reaetion field method (SCRF) has been developed at the level of Hartree-Foek theory to solve the respeetive Sehrodinger equation ... 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

Fig. 8.11. The Hartiee-Fock method is variational. The better the wave function, the lower the mean value of the Hamiltonian. An extension of the AO basis set (i.e. adding new AOs) has to lower the energy, and the ideal solution of the Foek equations gives the Hartree-Tbck limit . The ground-state eigenvalue of the Hamiltonian is thus atwavs lower than the limit.

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