Computational Chemistry

somewhat different than in the gas phase to which ab initio reactions usually apply
(although structures and energies can be calculated taking solvent effects into
account; see refs. [ 1 a, e, f, i, k, l]) and Section 8.1. X-ray diffraction depends on
the scattering of photons by the electrons around nuclei, while electron diffraction
depends on the scattering of electrons by the nuclei, and microwave spectroscopy
measures rotational energy levels, which depend on nuclear positions. Neutron
diffraction, which is less used than these three methods, depends on scattering by
atomic nuclei.
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 betweenmeannuclear positions, while the other methods
measure essentiallyaveragedistances, and (2) from errors in internuclear distances
caused by the nonisotropic (uneven) electron distribution around atoms. The mean
versus average distinction is illustrated here:

etc. A r B etc.

Suppose that nucleus A is fixed and nucleus B is vibrating in an arc as indicated.
The distance between the mean positions isr(shown), but on the average B is
further away thanr.
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, isnotessentially at the center of an approximate sphere defined by its
surrounding electron density:

H X

actual position of

proton

position inferred from

supposing it to be at

center of sphere defined by

electron density around proton

i.e. X-ray-inferred position

X nucleus

282 5 Ab initio Calculations