One-electron methods

In this chapter we have shown that the TDAN model gives a good description of the resonant charge-transfer process in atom-surface scattering. While it is unfortunate that exact solutions for the TDAN wavefunction cannot be obtained, the one-electron method can be used to find approximate solutions which allow qualitative predictions to be made. On the whole, these predictions are in reasonable accord with experimental Hndings. 

The result of these efforts, in both the organic and inorganic fields, was the gradual build-up of a set of rules to be used for the approximations in a one-electron all-valence orbital treatment of molecules. This culminated in Hoffmann s extended Hiickd theory where these and a few new rules were brought together in a very rational manner leading finally to a coherent one-electron method of wide application 22>. 

Daizadch I, Gehlen JN, Stuchebrukhof AA. Calculation of electronic tunneling matrix element in proteins comparison of exact and approximate one-electron methods for Ru-modified azurin. J Chem Phys 1997 106 5658-66. 

In present day quantum chemistry the linear-combination-of-atomic orbitals (LCAQ calculations play a predominant role including simple semi-empirical (SE) one electron methods up to sophisticated correlated ab initio ones. 

To begin this discussion, it is worthwhile to recognize that in the early days of organic photochemistry, the best methods were one-electron methods (i.e., Hiickel treatments). A good word needs to be put in for that methodology despite its... 

As we saw in the previous chapter, one-electron representation of the motion of electrons can never be exact. The best many-electron wave function is obtained if we put the spin orbitals into a Slater determinant. To obtain a good many-electron wave function, it is necessary to include other configurations, as demanded by the variation principle. We will first review the most popular one-electron methods, in particular the Hartree-Fock method. This method was used primarily for atoms for more than 30 years, until 1950. 

A third, but not negligible importance of second quantization is that this approach inherently deals with one-electron functions, although the theory is not restricted to one-electron methods. The occupancies of one-electron orbitals are the basic quantities one is dealing with in second quantization. This is a very descriptive picture which is in the mind of every chemist who tries to understand something about the electronic structure of molecules. 

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