Charge transfer - components

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. 

CT = charge-transfer terms (excluding the one-body charge-transfer components)... 

The A scp term is calculated using the standard CP-method. At the correlated MP2 level, we have shown for several systems [7-10], that the AE terms are usually and systematically smaller than the dominant ( )+ Ecj) terms. The sum of these two terms provides a good approximation to the total interaction energy at the correlated level. It is important to emphasize that the AE values were obtained by making the difference with the values of the CP-corrected subsystems i.e. taking into consideration the "benefit effect" of the superposition of the basis set [3, 6]. As the charge-transfer components are of importance in the two-body interaction, (see a discussion in ref. 10), we will also investigate them separately for the three-body terms in the studied systems. 

In order to have an insight into the three-body effect,we continue the study of the He-clusters. Fortunately, there are published examples for several He-clusters, as cited above. All of these studies, however, were performed in the canonical representation. The use of the localized representation allows us to separate the dispersion and the charge transfer components of the interaction energy for the three-body effects as it was similarly done for the two-body effects. The calculation of the interaction energy in the SMO-LMBPT fiumework has been discussed in detail in several papers [8-10] The formulae given at the correlated level, however, were restricted to the two-body interaction. 

Various methods have been suggested for this partitioning [89, 310-313], When applied to O-H 0 bonds in the water dimer [50], and the complexes of water-formamide and water-cyclopropenone [312], the electrostatic component provides 80% of the total attractive energy for Ow-H Ow, see Fig. 2.1, and about 75% for O-H 0=C bonds. This is balanced by the repulsive energy, while the polarization and charge-transfer components provide less than 5% for moderate strength bonds. 

Hydrogen bonding must have an effect on the electron density distribution of a molecule. In principle, this should be observed in the deformation density distributions discussed in Chapter 3. There are, in fact, two methods available. One is purely theoretical, in which the calculated deformation density for a hydrogen-bond dimer or trimer is compared with that of the isolated molecule. The other method compares the experimental deformation density of a hydrogen-bonded molecule in a crystal structure with the theoretical deformation density of the isolated molecule. Formamide has been studied by both methods [298, 380], and there appear to be significant differences in the results which are not well accounted for. Theoretical difference (dimer vs. monomer) deformation density maps have been calculated for the water dimer and the formaldehyde-water complex [312]. When those for the water dimer are decomposed into the components described in Chapter 4, a small increase in the charges on the atoms in the O-H -O bond due to the charge-transfer component is predicted [312]. 

The authors go on to conclude that the red shift of the v, band in this H-bonded complex can be directly attributed to the lengthening of the Oj—H bond. By partitioning the interaction energy into various components, they show how the stretch of this bond makes it both more polar and polarizable, which in mrn, increases the induction and charge transfer components of the interaction energy. Although the authors did not include correlation in their treatment, the same could be said for dispersion energy which is directly related to polarizabilities of the individual monomers. It is for this reason that a nearly linear relation-.ship is observed between Av and Ar. Zilles and Person have reached a similar conclusion that the polarity and polarizability of the O—H bond increases upon formation of the H-... 

In the expansion 22 the expressions in parentheses represent zeroth-order excitations localized at the carbonyl or cyclopropane moieties, respectively. The term CT includes charge-transfer components and depends upon the extent of mesomeric interactions between the subunits. The sum in equation 22 is over all the HOMO - LUMO (3e, 4e ) transitions of cyclopropane (cf. Subsection III.A). Actually, of course, more excitations have to be included into expansion 22. In particular, expansion 22 does not include Rydberg excitations. 

The first term (Eer) is the exchange-repulsion component, a combination of the Pauli repulsion that two electrons feel when forced to be in the same region of the space, and the attractive exchange component (overall, it has a net repulsive character). The second term (Ee ) is the electrostatic component, associated to the electrostatic interaction of two fragments whose electronic distribution is frozen to their values when isolated. The next two terms (Ep and Ef) are the polarization and charge-transfer components, respectively. The first one is associated to the polarization of the electronic distribution of the fragments due to the presence of... 

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