Coulson-Fischer analysis

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

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].)... 

The results of a valence bond treatment of the rotational barrier in ethane lie between the extremes of the NBO and EDA analyses and seem to reconcile this dispute by suggesting that both Pauli repulsion and hyperconjugation are important. This is probably closest to the truth (remember that Pauli repulsion dominates in the higher alkanes) but the VB approach is still imperfect and also is mostly a very powerful expert method [43]. VB methods construct the total wave function from linear combinations of covalent resonance and an array of ionic structures as the covalent structure is typically much lower in energy, the ionic contributions are included by using highly delocalised (and polarisable) so-called Coulson-Fischer orbitals. Needless to say, this is not error free and the brief description of this rather old but valuable approach indicates the expert nature of this type of analysis. 

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