Point charges, intermolecular interaction calculations

Following from formula (4.54), the transfer of energy on excitation of molecules has a noticeable probability even in the case where the impact parameter is much greater than their size d. Since the intermolecular spacings in a condensed medium are of order of d, a charged particle interacts with many of its molecules. The polarization of these molecules weakens the field of the particle, which, in its turn, weakens the interaction of the particle with the molecules located far from the track. This results in that the actual ionization losses are smaller than the value we would get by simply summing the losses in collisions with individual molecules given by formula (5.1). This polarization (density) effect was first pointed out by Swann,205 while the principles of calculation of ionization losses in a dense medium were developed by Fermi.206... 

Electrostatic term for each component, an ab initio calculation is carried out to obtain the wavefunction. The charge distribution is then written as a sum of multipolar, multicentric terms, up to quadrupole. It has been shown that the system can be represented by a relatively small number of point charges, one for each atom and one for each chemical bond [25]. The electrostatic term is the sum of all intermolecular multipole-multipole interactions. 

In the molecular mechanical force fields, the intermolecular interactions are most often described by the electrostatic and Van der Waals interactions. The MM atoms are normally represented by point charges and Lennard-Jones parameters (usually centered on atoms) in the calculation of intermolecular interactions. Therefore, a simple coupling can be established as shown schematically in Figure 2 and the corresponding Hamiltonian as in eq.(7). [12]... 

When attempting to treat ensembles of molecules it is essential to be able to represent the intermolecular interactions, at least beyond some cut-off distance, by pre-determined functions of distance so that high level quantum mechanical calculations do not have to be extended to larger and larger clusters. Masia et a/.88 have addressed the question of how the interaction of a water or carbon tetrachloride molecule interacting with a point charge can be represented. They monitor the molecular dipole as a function of the charge-molecule distance for various orientations of the molecule as calculated by ab initio methods. They find that the most satisfactory method is to represent the molecule by a small number of induced point dipoles with different orientations. In the case of water the ab initio induced dipoles are reproduced at all distances. 

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