Sigma theory equation

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

Equation (1.3) represents a sigma orbital (1(7), just like the ones described in Section 1.2.2.1. Both of these electron orbitals behave like waves, and therefore, according to wave theory, can interact constructively in the intemuclear region. This constructive interference intensifies the amplitude of the wavefunction, and this in turn, increases the probability of finding the electron between the two nuclei. Any electron located between the two hydrogen nuclei will interact strongly with both of them. As a result, the overall energy of the... 

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