Computational Chemistry/Semiempirical quantum chemistry

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Semi-empirical Philosophies

There is a difference in philosophy between the Pople and Dewar schools. Dewar's parameterisation aims to absorb all the missing parts of the model where SCF is inadequate, (Correlation , relativity, algebraic approximation), into the semi-empirical parameters, whereas Pople's initial idea was to produce cheap practical equivalents of minimal Slater orbital basis SCF calculations which would have all the mathematical niceties and limits of Hartree-Fock theory. In recent times Dewar's ideas and programs have prevailed because computing power has increased to make the real SCF wavefunction routinely computable for all but the largest molecules so MOPAC style programs are used for the largest molecules where Hartree-Fock is still uncomputable.

Programs for linear scaling SCF, where small approximations are made to make the effort scale linearly with the size of the molecule rather than scaling to the power of 4 dictated by the integrals evaluation, are hoping to make uncomputable Hartree-Fock problems a thing of the past.

A Brief Technical Description of Semi-Empirical Methods

The ZDO approximation, (Zero Differential Overlap). The first approximation is core-valence separation. The core electron MOs are independent of molecular environment and can be parameterised out. This is a good approximation, the all valence approximation - effective nuclear charges (Za) adjust for the missing inner electrons.

Basis functions belong to individual atoms in semi-empirical methods. In all methods For NDDO, (the most complete approximation i.e. nearest the full Hartree-Fock solution) i.e. all 3 and 4 centre integrals disappear. In CNDO the least complete method the Kroneka deltas are so only integrals like survive. In INDO 1-centre exchange integrals are added to the CNDO set

Remember 2J - K in Hartree-Fock theory.

The Invariance Problem

To insure the values of calculated properties do not change with rotated orientations of the molecule:

         (sAsA|pxBpxB)  =  (sAsA|pyBpyB)

        and

         (sAsA|pxBpxB)  =  (sAsA|sBsB)

This is a considerable approximation.

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