Longuet-Higgins basis

Longuet-Higgins [7] also reinforces the discussion by tbe following qualitative demonstration of a cyclic sign change for the LiNaK like system subject to Eq. (3), in which rows and columns are labeled by the basis functions... 

Accepting the Longuet-Higgins rule as the basis for the search of conical intersection, it is necessary to look for the appropriate loop. The -type degeneracy of a Jahn-Teller system is removed by a nonsymmetric motion. 

Longuet-Higgins has extended the Teller proof by considering the eigenvalues of the symmetric matrix obtained from a general orthonormal basis ofN states a, ... 

It is of interest to point out the role of primitive period isometric transformations (cf. Sect. 2.2.2.) in both the isometric and the Longuet-Higgins groug. According to Eq. (2.41) this type of transformations is represented on the basis X <( ) by... 

After the discovery of the metallic behaviour of PAc (Shirakawa et al., 1977) most of the work on theoretical models concentrated on this polymer. This built on the earlier studies of Longuet-Higgins and Salem (1959) and others who used the Hiickel model to demonstrate that the backbone of PAc in its ground state has a bond alternated structure, Fig. 9.8(b), rather than one with equal length C-C bonds, Fig. 9.8(a). In 1979 a Hiickel tight binding model was introduced that provided the basis for much of the subsequent discussion of themolecular and electronic structure of PAc (Su, Schrieffer and Heeger, 1979 and 1980). It is now usually referred to as the SSH model. In the adiabatic... 

More recently, molecular orbital theory has provided a basis for explaining many other aspects of chemical reactivity besides the allowedness or otherwise of pericyclic reactions. The new work is based on the perturbation treatment of molecular orbital theory, introduced by Coulson and Longuet-Higgins,2 and is most familiar to organic chemists as the frontier orbital theory of Fukui.3 Earlier molecular orbital theories of reactivity concentrated on the product-like character of transition states the concept of localization energy in aromatic substitution is a well-known example. The perturbation theory concentrates instead on the other side of the reaction coordinate. It looks at how the interaction of the molecular orbitals of the starting materials influences the transition state. Both influences on the transition state are obviously important, and it is therefore important to know about both of them, not just the one, if we want a better understanding of transition states, and hence of chemical reactivity. 

Cyclobutadiene complexes afford a classic example of the stabilization of a ligand by coordination to a metal and. indeed, were predicted theoretically on this basis by H. C. Longuet-Higgins and L. E. Orgel (1956) some 3 y before the first examples were synthesized. In the (hypothetical) free cyclobutadiene molecule 2 of the 4 rr-electrons would occupy and there would be an unpaired electron in each of the 2 degenerate orbitals 2. P l- Coordination to a metal provides further interactions and avoids this unstable configuration. See also the discussion on ferra-boranes (p. 174). 

Currie and Ramsay (8) discovered a diffuse system of absorption bands between 370 and 410 m/x during the gas phase photolysis of a number of allyl compounds. This absorption probably represents the weak absorption predicted by Longuet-Higgins and Pople (12) on the basis of their quantum mechanical calculations. Longuet-Higgins and Pople had also predicted a strong absorption band of the allyl free radical at 234 m/x. This last value is very close to the observations of Hamill et al. for the unsubstituted allyl free radical given in Table I. 

In between, the relationship of the two main quantum-chemical methods was established in the general sense by Slater [86] and later by Longuet-Higgins [87]. The fact that molecular orbital and valence bond methods must, if used with the same basis set and the... 

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