Applications of the Ab initio Method

An extremely useful book by Hehre [32] discusses critically the merits of various computational levels ab initio and others) for calculating molecular properties, and contains a wealth of information, admonitory and tabular, on this general subject. 

The main differences are between X-ray diffraction (which probes nuclear positions via electron location) on the one hand and electron diffraction, microwave spectroscopy and neutron diffraction (which probe nuclear positions more directly), on the other hand. The differences result from (1) the fact that X-ray diffraction measures distances between mean nuclear positions, while the other methods measure essentially average distances, and (2) from errors in internuclear distances caused by the non-isotropic (uneven) electron distribution around atoms. The mean vs. average distinction is illustrated here  

Suppose that nucleus A is fixed and nucleus B is vibrating in an arc as indicated. The distance between the mean positions is r (shown), but on the average B is further away than r. 

Differences resulting from nonisotropic electron distribution are significant only for H-X bond lengths X-rays see electrons rather than nuclei, and the simplest inference of a nuclear position is to place it at the center of a sphere whose surface is defined by the electron density around it. However, since a hydrogen atom has only one electron, for a bonded hydrogen there is relatively little electron density left over from covalent sharing to blanket the nucleus, and so the proton, unlike other nuclei, is not essentially at the center of an approximate sphere defined by its surrounding electron density  

Position inferred froni supposing it to be at center of sphere defined by electron density around proton, 

None of the three levels consistently over- or underestimates C-C bond lengths. HF/6-31G C-X (X = O, N, Cl, S) bond lengths tend to be underestimated slightly (ca. 0.015 A) while MP2/6-31G C-X bond lengths may tend to be slightly (ca. 0.01 A) overestimated. HF/3-21G 1 C-X bond lengths are not consistently over- or underestimated. 

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The following chapters will present applications of the ab initio method to different biochemical systems, such as amino acids, peptides, and anti-tumor drugs. 

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