Core electrons valence bond theory

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

In Chapter 5, we examined chemical bonding from the standpoint of MO theory, valence bond theory, and local bonding, always focusing on the electrons involved in the bond formation the valence electrons. To accurately predict the geometries and properties of molecules with many electrons, however, we have to take into account all of the electrons, including the core electrons. 

The opposite conclusion that correlation increases the dimerization reached in PPP valence bond (VB) theory [36] holds only in comparison to Hiickel theory which is not the semiempirical equivalent to ab initio HF. In fact Hiickel theory would correspond to diagonalization of the one-electron part of the ab initio Fock matrix rather than to HF itself although in Hiickel theory correlation may appear implicitely via the parameters. And indeed, if one considers only the one-electron part of the ab initio Fock matrix (core diagonalization) in a 6-31G basis set the equidistant geometry for trans-butadiene is favored. Inclusion of electron-electron interactions on one-particle level (HF), which corresponds to PPP theory yields an increase of the bond-alternation beyond its experimental value. The inclusion of Jt-n correlations (CCD-level) decreases this value again to the experimental one [16]. 

The disadvantage of the pseudopotential (plane-wave) approach can be summarized as follows. First, all information for the core-like wavefunctions and their associated electron density is lost, trivially so. Second, an essentially delocalized plane-wave basis set poses difficulties when it comes to questions of chemical interpretation in terms of atoms and bonds. In addition, there has always been some concern about the arbitrariness of pseudopotentials because there is certainly more than one pseudopotential (in fact, an infinite number) for a given atom. Recall that the partitioning of a quantum-mechanical system into subsystems is invalid because the electrons cannot be distinguished in principle, there are no "core" or "valence" electrons. Nonetheless, pseudopotential plane-wave calculations have established themselves as accurate and powerful tools for electronic-structure theory, both for molecules and, in... 

The first quantum-mechanical treatment of the hydrogen molecule was by Heitler and London in 1927. Their ideas have been extended to give a general theory of chemical bonding, known as the valence-bond (VB) theory. The valence-bond method is more closely related to the chemist s idea of molecules as consisting of atoms held together by localized bonds than is the molecular-orbital method. The VB method views molecules as composed of atomic cores (nuclei plus inner-shell electrons) and bonding valence electrons. For H2, both electrons are valence electrons. 

Attempts have been made to make the choice of core/valence/virtual orbital partition into a black box. In particular the unrestricted natural orbitals can provide a good starting point for MC-SCF as as suggested by Pulay[17]. We now explore this point in some detail since it also gives us some additional insight into MC-SCF theory. As discussed by Pulay[17] in his paper one can understand the problem with a two electron example. In UHF wavefunction for a two electron localized bond, one seeks the optimum energy of a wavefunction of the form... 

The electrons responsible for bonding are those in the outer shell, or valence shell, of an atom. Valence shell electrons are those that were not present in the preceding noble gas orbitals. We will focus attention on these electrons in our discussion of covalent bonding. The electrons in the lower energy nohle gas configuration are not directly involved in covalent bonding and are often referred to as core electrons. Lewis formulas show the number of valence shell electrons in a polyatomic molecule or ion (see Sections 7-5 through 7-9). We will write Lewis formulas for each molecule or polyatomic ion we discuss. The theories introduced in this chapter apply equally well to polyatomic molecules and to ions. 

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