Coulson-Fischer, wave-function theory

Keywords Coulson-Fischer wave function Coulson-Fischer analysis Coulson-Fischer theory Modern valence bond theory Multireference correlation problem Collaborative virtual environment... 

Hence the approximation (1), which is a prototype of multistructure valence bond theory, is equivalent to approximation (4), a prototype of molecular orbital configuration interaction theory, and both (1) and (4) are equivalent to (13), the Coulson-Fischer wave function. 

The generalization of a Coulson-Fischer type wave function to the molecular case with an arbitrary size basis set is known as Spin Coupled Valence Bond (SCVB) theory. ... 

Abstract The wave function of Coulson and Fischer is examined within the context of recent developments in quantum chemistry. It is argued that the Coulson-Fischer ansatz establishes a third way in quantum chemistry, which should not be confused with the traditional molecular orbital and valence bond formalisms. The Coulson-Fischer theory is compared with modern valence bond approaches and also modern multireference correlation methods. Because of the non-orthogonality problem which arises when wave functions are constructed from arbitrary orbital products, the application of the Coulson-Fischer method to larger molecules necessitates the introduction of approximation schemes. It is shown that the use of hierarchical orthogonality restrictions has advantages, combining a picture of molecular electronic structure which is an accord with simple, but nevertheless empirical, ideas and concepts, with a level of computational complexity which renders praetieal applications to larger molecules tractable. An open collaborative virtual environment is proposed to foster further development. 

Sixty years ago, in 1949, Coulson and Fischer published a seminal paper [18] in the Philosophical Magazine, entitled Notes on the Molecular Orbital Treatment of the Hydrogen Molecule. In this note, they presented a wave function for the hydrogen molecule, which, whilst retaining a simple physical picture, combines the advantages of the two rival theories of molecular electronic structure, mo and VB theories. Let us briefly summarize the discussion given by Coulson and Fischer. 

Wave function (4) is the standard configuration interaction expansion in mo theory. The parameter can take values from -1 to -1-1. Putting /r = 0 gives the pure molecular orbital description first considered by Coulson [49] in 1937. Table 1 summarizes the behaviour of the approximate wave functions as a function of the parameters k and /r. in the Coulson-Fischer analysis. (This table is taken from the work of Coulson and Luz [50].)... 

Evidence for this renaissance is seen in the number of monographs [53-55], edited volumes [56-58] and review articles [52, 59, 60, 62, 63, 61, 64-69] on valence bond theory published in recent years. These works display a rich variety of theoretical machinery inspired by the valence bond picture of molecular structure. Some of the methodologies - particularly in the so-called modern valence bond theories introduced by Gerratt and Lipscomb [70,71] under the name spin-coupled wave functions and developed by Gerratt [72,73] and his collaborators [68,74-86] over the past 40 years - exploit the Coulson-Fischer ansatz. As we have seen in Section 3 and will consider further in Section 6, the Coulson-Fischer theory presents a third way of constructing approximate molecular wave functions which combine many of the advantages of both molecular orbital theory and valence bond theory. 

In a paper pubhshed in 1953 as part of a series under the general title The molecular orbital theory of chemical valency, Hurley, Lennard-Jones and Pople [87] presented A theory of paired electrons in polyatomic molecules. The pah-function model of Hurley et al. employed a Coulson-Fischer-type wave function to describe each pair of electrons in a polyatomic molecule. Orthogonality constraints were imposed between orbitals associated with different pairs of electrons in order to render the theory practical, i.e. computationally tractable. Hurley presented the corresponding orbital equations in a subsequent paper [88] which was published in 1956. 

Here we are proposing the creation of an open collaborative virtual environment for the development of the Coulson-Fischer method for molecular wave functions. To this end we have created web pages at http //quantumsystems.googlepages.com/ cve theCoulson-Fischertheory, which is intended to form an element of a collaborative virtual environment for the further advancement of the Coulson-Fischer theory. In his recently published report, Karadakov [52] expresses his view that... 

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