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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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