Two-body interaction energies

This additional to the two-body interaction energies term originates from three-body interactions and is called the three-body interaction energy. 

Now we can decompose the m-body interaction energies, defined in previous section, into the PT series. For the two-body interaction energy, the expression directly follows from Eqs. (7), (8) and (13). 

The SMO-LMBPT method conveniently uses the transferability of the intracorrelated (one-body) parts of the monomers. This holds, according to our previous results [3-10], at the second (MP2), third (MP3) and fourth (MP4) level of correlation, respectively. The two-body terms (both dispersion and charge-transfer components) have also been already discussed for several systems [3-5]. A transferable property of the two-body interaction energy is valid in the studied He- and Ne-clusters, too [6]. In this work we focus also on the three-body effects which can be calculated in a rather straightforward way using the SMO-LMBPT formalism. 

Figure 6. Angular dependence of various two-body interaction energy components in the cyclic planar H2O trimer at R=3.0 A.

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 Van der Waals interactions are not easily accessible with ab initio methods, because the characterization of short-range intermolecular interactions requires a much higher level of theory than molecular structure or conformational energies. Moreover, at least a reasonably complete two-body interaction energy landscape is... 

Latajka and Scheiner analyzed their results also on the basis of a more rigorous definition of many-body effects in which relative geometries are frozen in the cyclic structure moreover, their prescription deals explicitly with BSSE [103]. They found that the three-body term is not negligible in either trimer. This term is approximately half as large as the two-body interaction energy in (HF)3 while about V4 as large in (HC1)3. The three-body term appears to be adequately described at the SCF level since correlation does not change it appreciably. 

The total interaction energy is then written as a sum of these two-body interaction energies plus a three-body interaction energy ... 

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