Resonance integral molecular basis

The concepts of hybridisation and resonance are the cornerstones of VB theory. Unfortunately, they are often misunderstood and have consequently suffered from much unjust criticism. Hybridisation is not a phenomenon, nor a physical process. It is essentially a mathematical manipulation of atomic wave functions which is often necessary if we are to describe electron-pair bonds in terms of orbital overlap. This manipulation is justified by a theorem of quantum mechanics which states that, given a set of n respectable wave functions for a chemical system which turn out to be inconvenient or unsuitable, it is permissible to transform these into a new set of n functions which are linear combinations of the old ones, subject to the constraint that the functions are all mutually orthogonal, i.e. the overlap integral J p/ip dT between any pair of functions ip, and op, (i = j) is always zero. This theorem is exploited in a great many theoretical arguments it forms the basis for the construction of molecular orbitals as linear combinations of atomic orbitals (see below and Section 7.1). 

We note that much care has to be taken when Koopman s theorem is used to estimate the transfer integrals in asymmetric dimers, as has been extensively discussed elsewhere [58,59], In such instances, part of the electronic splitting can simply arise from the different local environments experienced by the two interacting molecules, which create an offset between their HOMO and LUMO levels prior to their interaction due to polarization and/or electrostatic effects. In order to evaluate the effective couplings, this offset can be accounted for by performing calculations using molecular orbitals localized on the individual units as basis set [59] or by applying an electric field to promote the resonance between the electronic levels, as done by Jortner and coworkers [56], This artifact can also be prevented when... 

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