Two-body interaction energy the dimer

We have kept the parameter R=Rab to underline that this potential depends both on the relative position of the two molecules and on their mutual orientation it is a 6-dimensional function depending on these two sets of 3 parameters each, in the following indicated. 

Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli 

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Figure 1 Angular variation of components of the two-body interaction energy in (HF)3 in a planar Cii, configuration. SCF components are labeled as follows ES = electrostatic, EX = exchange, def = deformation energy (AE - - ES - EX). The dispersion energy 6cjisp ° computed by perturbation theory is denoted disp. The curve representing the complete two-body interaction through third-order Mpller-Plesset perturbation theory is labeled as full. All terms have been computed in the dimer-centered basis set. (Data taken from ref. 120.)...

The two-body interaction energy can be calculated directly through O Eq. 6.4 as the difference in energies of the dimer and the monomers. This approach, known as the supermolecnlar method, has the advantage of allowing Bint to be calculated using a variety of electronic structure methods. We will only briefly describe some aspects of this method below for a more complete description see Chalasinski and Szczesniak (2000). 

It indicates that, the physical sense of the 2-body SCF energy in trimers is the same as the SCF interaction energy in dimers it is predominantly the exchange interactions which are repulsive for two interacting atoms with closed subshells. The attractive contributions from the electrostatic and induction energies are less than the repulsive exchange contribution. This is the reason that CF(A3) is positive for the alkaline trimers in all calculated distance regions [22]. 

AE j yn) at various levels. The data clearly indicate the cooperativity as the binding energy rises from 1.9 kcal/mol (at the SCF level) for the dimer up toward 5.4 as the number of molecules reaches six. (However, the data for the dimer may be misleading as the complex is not cyclic and so contains only a single H-bond.) This study concludes that two and three-body interactions can provide most of the total interaction. Correlation is recommended, but the MP2 level appears satisfactory. 

The difference may arise from the radical character of the monomers versus the closed-shell electronic structure of the dimer Nj O4. In the former, because of the high electron afhnity, a harpooning process is expected, while in the dimers the interaction is short range with covalent character. It is important to realize that for collision energies of more than 10.5 kcal the cross section for the N2O4 reaction exceeds that of the monomeric process. It is difficult to conclude on the third-body effect in this reaction because of the differences in the electronic structure between the two species NO2 and N2O4. Usually one would like to investigate the cluster s effect where only small perturbations exist. 

We now wish to extend the dimer model to encompass an infinitely large three-dimensional crystal lattice this is very similar to the transition from the covalent bonding of two atoms to the band structure of a metal or a semiconductor with delocalised states. Starting from the more or less sharp energy levels in the two-body system, we arrive at a band of energy states whose width depends on the interactions of the individual molecules or the overlap of the molecular orbitals in the lattice. We must then take the interaction of an excited molecule with aU the other molecules in the crystal and with the periodic lattice potential into account The levels and E in the dimer model of Fig. 6.7 are transformed into a more or less broad band of energy levels. These are the excitonic bands of the crystal, which we shall treat in this section. 

The pair potential functions for the description of the intermolecular interactions used in molecular simulations of aqueous systems can be grouped into two broad classes as far as their origin is concerned empirical and quantum mechanical potentials. In the first case, all parameters of a model are adjusted to fit experimental data for water from different sources, and thus necessarily incorporate effects of many-body interactions in some implicit average way. The second class of potentials, obtained from ab initio quantum mechanical calculations, represent purely the pair energy of the water dimer and they do not take into account any many-body effects. However, such potentials can be regarded as the first term in a systematic many-body expansion of the total quantum mechanical potential (dementi 1985 Famulari et al. 1998 Stem et al. 1999). 

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