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The Three—Body Force

Intermolecular forces are commonly believed to be pair-wise
additive. That is, the energy of an assembly of atOms or molecules
is equal to the sum of the interaction energies of all pairs of
interacting particles. However, this aSSumption has been challenged.
It is certainly not strictly valid for condensed systems, namely
also for systems of interest in molecular biology. The reason is
that when an atom is polarized simultaneously by two other neigh—
bouring atoms, its polarization is proportional to the vectorial
Sum of the electrostatic forces, thus the dispersion energy of
three neighbouring atoms must depend not only on the three inter-
atomic distances but also on the three angles between them.
According to Axilrod and Teller?, this three body interaction
potential, namely the correction to the pairwise additive potential
energy of the dispersion interaction,is

" -3
v3 — Cabc(l+3 cosfia coseb cosecxrabracrbc) (15)

where Cabc is a constant and the r's and 6's are the sides and
angles of the triangle formed by the atoms a,b and c. While it is
common practice to neglect this term in calculations of nonebonded
interactions, we should realize that they are by no means always
negligibly small. For example, Kestner and Sinanoglua concluded
that three body forces reduced the dispersion interaction between
base pairs in the DNA double helix by 28%.

Electrostatic Interactions

 

Most chemical bonds are not purely covalent, but possess a
partial electrostatic character. Whenever the electronegativitieS 0f
two bonded atoms are different, the charge distribution of the
bonding electrons is shifted partly towards the more electronegative
atom, thus making the total charge (nucleusand electrons) in the
vicinity of this atom equivalent to a partial negative charge, while
the less electronegative atom obtains a partial positive charge.

The detailed charge distribution may be obtained from the wave
functions of the Schrddinger equation. However, the calculation

of electrostatic interactions frOm continuous charge distributions
is extremely cumbersome, involving multidimensional integrals.

Since the available solutions to the Schrddinger equation are
approximate and so are the charge distributions, there is no reason
to attempt such calculations. A major simplification of the problem
is obtained if the continuous charge is represented approximately

by point charges located on the atoms. This is done, for example,
by the so called Mulliken population analysisg, where the charges

in a given molecular orbital are assigned to the individual atoms,
according to the extent to which the atomic orbitals of each atom
contribute to the molecular orbital. There is a vast literature on
the Mulliken analysis of various molecules, and also on other similar

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