Hartree-Fock Treatment

The term ( iv X.o) in Equation 32 signifies the two-electron repulsion integrals. Under the Hartree-Fock treatment, each electron sees all of the other electrons as an average distribution there is no instantaneous electron-electron interaction included. Higher level methods attempt to remedy this neglect of electron correlation in various ways, as we shall see. 

Let us now turn to the density functional methods. All of them correctly predict the para-ortho ordering, but considering that this is the case even for a Hartree-Fock treatment this is a somewhat hollow victory. Without exception, all functionals wrongly predict p-protonation. Arguably, this small energy difference falls within the error margin of any type of calibration for (semi-) empirical DFT functionals. 

It is dear, therefore, that as the atoms are pulled apart the Hartree-Fock MO solution does not go over to that of two neutral-free atoms H°H°, but instead goes over to a mixed configuration, schematically represented by [2H°H° + H+H" + H H+]. Since the energy cost for the ionic configuration is / — A = (13.6 — 0.8) eV = 12.8 eV, the Hartree-Fock MO solution dissociates incorrectly to +6.4 eV rather than zero (We have assumed the Hartree-Fock treatment of H is exact.) The Heitler-London VB solution avoids this problem by working with only the covalent configurations in the first square bracket of eqn (3.37), so that it dissodates correctly. 

Hartree-Fock treatment which predicts the triplet to be at least 21 kJ mol"1 below the singlet state (2, 345). 

The approximations used in EH theory have included (1) neglect of core electrons, (2) use of atomic basis functions, (3) use of effective Hamiltonian resulting in arbitrariness in choice of matrix elements, (4) lack of explicit accounting for electron-electron and nuclear-nuclear repulsion, and (5) approximate energy calculation procedure. Although these approximations seems severe in light of Hartree-Fock treatments of MO theory, the important feature to remember is that EH theory has proved useful in several systems. 

Up to now most quantum mechanical studies of the ground and excited states of model heme complexes have focused primarily on diamagnetic systems (36), with less frequent treatment of heme systems with unpaired spins (37-42). With the inclusion of a restricted Hartree-Fock treatment (37, 38) within an INDO formalism parameterized for transition metals (39, 40, ), it is now possible to calculate the relative energies of different spin states of ferric heme complexes in an evenhanded fashion at a semiempirical level. 

C. Pisani, R. Dovesi and C. Roetti, Hartree—Fock treatment of crystalline systems, Springer, Berlin, 1988. 

The most rigorous way of incorporating relativity in the calculations is achieved by using four-component methods. However, for many applications a full Dirac-Hartree-Fock treatment is not feasible and reduced schemes are preferred keeping the numerical effort much lower. We... 

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