Slater orbitals valence state theory

The choice of a single function from either set (36) or (37) does not permit such a useful physical interpretation, and may indeed lead to difficulties as the internuclear distance is varied. Thus if one chooses just the perfectly paired function from the set (36), as -R-> 00 one finds each N atom is described by a curious non-stationary state - the so-called valence state of the atom, about which there has been so much discussion in the literature.18 The choice of the set of functions (36) in which orbitals participating in a bond are directly coupled to each other is just the VB theory as proposed by Slater and Pauling,19 whereas the set (37) formed from atoms in specific L-S coupled states corresponds to the spin-valence theory employed by Heitler.20... 

The first of these methods was developed by Hoffmann in 1963 (1) and is known as extended Hiickel theory (EHT). Briefly, the method uses Hiickel formalism however, explicit consideration of non-bonded interactions and all overlap integrals are a refinement. Slater orbitals are used, and the computations require only one parameter, the valence state ionization potential for the Coulomb integral and indirectly for the reso-... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

Multiple line core spectra are produced also if the atom has an open valence shell, provided that the crystalline environment has not wiped out the J, L, S, M quantization of that shell the core vacancy is variously coupled to the open shell to yield a set of final states. For example, if the open shell has the one-electron orbital quantum numbers n and l and total spin S, a core s vacancy will be observed in two final states having spins (S +1/2) and (S — 1/2), with the latter spin state lying higher in energy. According to Condon-Slater-Racah theory, the energy separation is... 

Slater was one of the first scientists to realize that in qualitative discussions of molecule formation, the best procedure to follow was to compare critically the results of the two different methods developed—the valence bond and the molecular orbital viewpoint, and to point out, as already mentioned, that the choice between the two should be made on the basis of convenience rather than correctness. However, in Introduction to Chemical Physics, just a few lines are devoted to such a central topic in the context of Slater s contributions to quantum chemistry as well as in the development of the discipline itself. In the chapter on "Interatomic and Intermolecular Forces," in the section about "Exchange Interactions Between Atoms and Molecules," Slater stated that the problems of quantum chemistry are among the most complicated of quantum theory and that the theory itself will not be treated in an analytical manner. He considered the Heider-London approach and the molecular orbital approach as two different approximate methods of calculation used in wave mechanics. He believed that these two methods do not differ in their "fundamentals, but in the precise nature of the analytical steps used." And he proposed to study "the fundamental physical processes behind the intermolecular actions and we shall find that... 

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