Independent-particle model, wave function calculations

The various methods used in quantum chemistry make it possible to compute equilibrium intermolecular distances, to describe intermolecular forces and chemical reactions too. The usual way to calculate these properties is based on the independent particle model this is the Hartree-Fock method. The expansion of one-electron wave-functions (molecular orbitals) in practice requires technical work on computers. It was believed for years and years that ab initio computations will become a routine task even for large molecules. In spite of the enormous increase and development in computer technique, however, this expectation has not been fulfilled. The treatment of large, extended molecular systems still needs special theoretical background. In other words, some approximations should be used in the methods which describe the properties of molecules of large size and/or interacting systems. The further approximations are to be chosen carefully this caution is especially important when going beyond the HF level. The inclusion of the electron correlation in the calculations in a convenient way is still one of the most significant tasks of quantum chemistry. 

The major difficulty in wave function based calculations is that, starting from an independent-particle model, correlation between electrons of opposite spin must somehow be introduced into T. Inclusion of this type of electron correlation is essential if energies are to be computed with any degree of accuracy. How, through the use of multiconfigurational wave functions, correlation between electrons of opposite spin is incorporated into is the subject of Section 3.2.3. 

Is it really necessary to go through the calculations associated with the independent-particle model (which is the basis for the introduction of the correlation concept) as an essential step towards highly accurate wave functions ... 

The process of double photoionization in which one photon is absorbed and two electrons ejected is very interesting since it cannot occur in an independent particle model using orthogonal states. As a result, it is difficult to calculate this process, and there has been only a small number of calculations thus far. Early calculations by Brown and by Byron and Joachain used a correlated initial state wave function but neglected correlations in the final state. However, a recent MBPT calculation for He found that at low energies the final state correlations are larger but that there is much cancellation between terms representing correlations in the initial and final states. Calculations have also been carried out for Ne m, Be, and... 

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