Spin-coupled wave function

J. Gerratt, Adv. At. Mol. Phys. 7, 141 (1971). General Theory of Spin-Coupled Wave Functions for Atoms and Molecules. 

Rettrup S (1978) Spin-coupled wave functions in ab initio SCF and Cl calculations with application to the manganate ion. Dissertation, The Technical University of Denmark, DK-2800 Lyngby... 

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. 

A sequence of models and associated orthogonality restrictions based on the structural formula of the target molecule was introduced [107]. These models interpolate between the pair function model, which involves the most severe orthogonality, restrictions, and the spin-coupled wave function, in which all orbitals are nonorthog-onal. For example, the pair function description of the ground state of the BeH2 molecule with doubly occupied core orbitals, is based on a spatial function with the form... 

In the following section, the constmction of spin functions s Af will be briefly discussed and this will be followed by a description of the physical interpretation of the spin-coupled wave function. 

The Serber spin functions are particularly useful in displaying the spatial symmetry properties of spin-coupled wave functions, when it is obvious that those spin functions which do not lead to the required overall symmetry of the total wave function have zero spin-coupling coefficients. This has turned out to be of great utility in cases where the introduction of electron correlation leads to unexpected additional symmetries of, for example, the a electrons in a planar n system. Examples of this will be presented in due course. 

THE PHYSICAL INTERPRETATION OF THE SPIN-COUPLED WAVE FUNCTION... 

The development of a multi-configuration spin-coupled wave function in order to incorporate correlation effects not included in the single configurational wave function (equation 7) was already attempted with the earliest applications of SC theory. Since the SC wave function incorporates as much radial correlation as is possible within the framework of a single-configuration form, the main improvements to the wave function must stem from the inclusion of doubly excited configurations in which two occupied orbitals are replaced by orbitals which differ from them, in some sense, by symmetry. In the case of the very simple diatomic molecules H2, LiH, and Li2,i9,2o whose occupied orbitals are all of a symmetry, it is fairly clear that the main improvement is due to replacement of the two CT orbitals involved in the bond by two orbitals of 7T symmetry, if complex orbitals are used, or by... 

One disappointment was that the National Science Foundation refused to support the work started by J. Gerratt and me on spin-coupled wave functions. 

Gerratt and Lipscomb introduced spin-coupled wave functions in 1968 ". The energy expression for spin-coupled wave functions... 

The theory of spin-coupled wave functions was developed by Gerratt et al. and applied to a wide range of molecular systems including diborane . 

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