Many-electron system, Hamilton

An important consequence of the only approximate treatment of the electron-electron repulsion is that the true wave function of a many electron system is never a single Slater determinant We may ask now if SD is not the exact wave function of N interacting electrons, is there any other (necessarily artificial model) system of which it is the correct wave function The answer is Yes it can easily be shown that a Slater determinant is indeed an eigenfunction of a Hamilton operator defined as the sum of the Fock operators of equation (1-25)... 

Let us now revisit the Hamilton operator for a many-electron system as given in Equation (2.5). It contains the kinetic energies of the electrons, their Coulomb potentials in the fields of the nuclei and, also, the electron-electron interactions which we have not further specified yet. Fortunately, the success of one-electron theories in chemistry is due to the fact that an explicit consideration of the electron-electron interactions may often be ignored for a qualitatively appropriate description, simply because these interactions are implicitly contained in some parameters for example, one might want to recall that the spatial extent of the atomic orbitals (see Section 2.2) depends on the amount of interelectronic screening. Nonetheless, the explicit inclusion of electron-electron interactions is needed for accurate calculations and, just as important, also for imderstanding. Here is a qualitative description. 

A fully relativistic treatment of more than one particle has not yet been developed. For many particle systems it is assumed that each electron can be described by a Dirac operator (ca ir + p mc ) and the many-electron operator is a sum of such terms, in analogy with the kinetic energy in non-relativistic theory. Furthermore, potential energy operators are added to form a total operator equivalent to the Hamilton operator in non-relativistic theory. Since this approach gives results which agree with experiments, the assumptions appear justified. 

Chemistry is a many-particle science, however, which we may illustrate by explicitly writing down another Hamilton operator for a system containing many nuclei and electrons, i.e., a given molecule or some crystalline material... 

Many MFO-catalyzed reactions possess characteristic similarities to model reactions and since these enzymatic reactions occur very fast and the intermediates are too short lived, non-enzymatic model systems have been developed to study oxene mechanism. One specific example is the Udenfriend system (272) which involves the hydroxylation of aromatic compounds under physiological conditions by a mixture of ascorbate, Fe(n), EDTA, and O2. According to Hamilton (105), the intermediate complex A formed during the oxidation reaction (Fig. 7), is believed to be an oxinoid species which transfers electrons to the oxygen atom in the transition state and probably, at the same time, allows the transfer of singlet oxygen from complex A to substrate in one step so that diradical intermediates would not be necessary (705). 

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