Hartree-Fock method conclusions

In conclusion, the above discussion suggests that geometry is reliably optimized by the DFT method but it is safe to evaluate the energy changes not only by the DFT method but also by the post-Hartree-Fock methods with sufficiently good basis sets. 

Thus, comparison of calculation results with experimental data demonstrates ab initio Hartree-Fock method in the 6-3 IG basis set provides qualitatively correct conclusion on hydrogen bond energies for systems considered. This model was applied to investigate the interaction between water and hydroxyfullerene cluster Qo. Hydroxyfullerene is a proper object for quantum-chemical modeling of interaction between activated carbon nanoparticle and water. At the same time hydroxyfullerene is of great interest because of its possible applications in medicine, for water disinfection, and for polishing nanosurfaces. 

The Hartree-Fock method gives an approximate wave funetion for the atom of any ehemieal element from the Mendeleev periodie table (orbital picture). The Hartree-Fock method stands behind the orbital model of atoms. The model says essentially that a single electron configuration can describe the atom to an accuracy that in most cases satisfies chemists. To tell the truth, the orbital model is in principle falsej but it is remarkable that nevertheless, the conclusions drawn from it agree with experimental results, at least qualitatively. It is exciting that... 

The second conclusion can be accepted, since it follows from the pairing of the spins, but the first conclusion is just absurd. Such nonsense is admitted by the Hartree-Fock method. In this chapter, we will ponder how can we introduce a correlation of electronic motions. 

However, first it should be stressed that within density-functional theory, in its most widespread formulation, it provides a method for calculating static groimd-state properties of a given atomic, molecular, crystalline, liquid,. .. system. This is the field where density-fimctional theory has found most applications and where the experience has shown that the results in by far the most cases are accurate and useftd. Typically, structural, energetical, and vibrational properties are as accurate as those obtained with Hartree-Fock methods augmented with perturbational inclusion of correlation effects at the MP2 level although there are exceptions (both for the case that the density-functional calculations are inaccurate and for the case that the Hartree-Fock-based calculations fail). In this report we have not attempted to review all the studies supporting this conclusion. Therefore, it is veiy important at this point to emphasize the importance and accuracy of such studies. 

This completes the proof of Koopmans theorem. The conclusion is that the orbital energy e, in the Hartree-Fock method may be interpreted as (approximately) the negative of the ionization energy. 

This mechanistic question is one of the examples of the success of density functional theory methods in organometallic chemistry. Earlier work on the reaction mechanism could not discriminate between the two alternatives. Analysis of the different orbitals based on extended Hiickel calculations came to the result that the [3+2] pathway is more likely, but could not exclude the possibility of a [2+2] pathway [13]. Similar conclusions where obtained from the results of Hartree-Fock calculations in combination with QCISD(T) single point calculations [21], Attempts to use Ru04 as a model for osmium tetraoxide indicated that the formation of an oxetane is less favorable compared to the [3+2] pathway, but still possible [22, 23],... 

However, until today no systematic comparison of methods based on MpUer-Plesset perturbation (MP) and Coupled Cluster theory, the SOPPA or multiconfigurational linear response theory has been presented. The present study is a first attempt to remedy this situation. Calculations of the rotational g factor of HF, H2O, NH3 and CH4 were carried out at the level of Hartree-Fock (SCF) and multiconfigurational Hartree-Fock (MCSCF) linear response theory, the SOPPA and SOPPA(CCSD) [40], MpUer-Plesset perturbation theory to second (MP2), third (MP3) and fourth order without the triples contributions (MP4SDQ) and finally coupled cluster singles and doubles theory. The same basis sets and geometries were employed in all calculations for a given molecule. The results obtained with the different methods are therefore for the first time direct comparable and consistent conclusions about the performance of the different methods can be made. 

Polarizability will be dealt with first because it is the easiest of the three properties to calculate and has certainly received the most attention. Many of the conclusions also apply to x and a, which are dealt with in much less detail. In each section we have tried to pick out the most important methods and consider them in detail at the expense of the less useful methods. Thus, for example, although the variational technique of Karplus and Kolker is simpler than the other uncoupled Hartree-Fock perturbation methods, it is not a very useful technique for calculating polarizabilities. It is very useful for calculations of magnetic susceptibility, however, where many other techniques are inappropriate. 

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