Induction/dispersion interactions

For the evaluation of the averaged induction-dispersion interaction we here... 

For the evaluation of the averaged induction-dispersion interaction -Ce/ " , we here accept based on the Slater-Kirkwood formnla valne Ce=23.2 from the work [23], In order to create more reliable estimations of the anisotropy of Ce term, one can again resort to the RSOF method by Meyer et al. [6] and to the related calculations of the fragment dynamic polarizabilities [20, 30], The FFC basis of Eq.25 consists of 36 functions transforming upon time inversion as... 

Long-range forces are most conveniently expressed as a power series in Mr, the reciprocal of the intemiolecular distance. This series is called the multipole expansion. It is so connnon to use the multipole expansion that the electrostatic, mduction and dispersion energies are referred to as non-expanded if the expansion is not used. In early work it was noted that the multipole expansion did not converge in a conventional way and doubt was cast upon its use in the description of long-range electrostatic, induction and dispersion interactions. However, it is now established [8, 9, 10, H, 12 and 13] that the series is asymptotic in Poincare s sense. The interaction energy can be written as... 

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

The idea of solvent polarity refers not to bonds, nor to molecules, but to the solvent as an assembly of molecules. Qualitatively, polar solvents promote the separation of solute moieties with unlike charges and they make it possible for solute moieties with like charges to approach each other more closely. Polarity affects the solvent s overall solvation capability (solvation power) for solutes. The polarity depends on the action of all possible, nonspecific and specific, intermolecular interactions between solute ions or molecules and solvent molecules. It covers electrostatic, directional, inductive, dispersion, and charge-transfer forces, as well as hydrogen-bonding forces, but excludes interactions leading to definite chemical alterations of the ions or molecules of the solute. 

The characterization of a solvent by means of its polarity is an unsolved problem since the polarity itself has, until now, not been precisely defined. Polarity can be understood to mean (a) the permanent dipole moment of a compound, (b) its dielectric constant, or (c) the sum of all those molecular properties responsible for all the interaction forces between solvent and solute molecules (e.g., Coulombic, directional, inductive, dispersion, hydrogen bonding, and EPD/EPA interaction forces) (Kovats, 1968). The important thing concerning the so-called polarity of a solvent is its overall solvation ability. This in turn depends on the sum of all-specific as well as nonspecific interactions between solvent and solute. 

The solvent reaction potential can be partitioned into several contributions of different physical origin, related to electrostatic, repulsive, induction and dispersion interactions between solute and solvent. In the original polarizable continuum approach only the electrostatic and induction terms are explicitly considered as an interaction potential... 

Table 2.4 lists the individual contributions or partial polarities for the solutes that appear in table 2.2. From this table, it is clear that a distinction can now be made between molecules of similar overall polarity. Much of the cohesive energy of toluene is due to dispersion interaction, whereas dipole orientation is more important in ethyl acetate. Orientation interaction is of more relevance in methylene chloride than it is in dioxane, which shows a considerable contribution from induction interaction. 

Depending on the nature of interacting molecules, some interactions may be negligible or equal to zero. Direct electrostatic, induction and dispersion interactions are combined in a general concept of van der Waals nonspecific interactions which are not related to the electron shell overlap. 

Van der Waals interactions are noncovalent and nonelectrostatic forces that result from three separate phenomena permanent dipole-dipole (orientation) interactions, dipole-induced dipole (induction) interactions, and induced dipole-induced dipole (dispersion) interactions [46]. The dispersive interactions are universal, occurring between individual atoms and predominant in clay-water systems [23]. The dispersive van der Waals interactions between individual molecules were extended to macroscopic bodies by Hamaker [46]. Hamaker s work showed that the dispersive (or London) van der Waals forces were significant over larger separation distances for macroscopic bodies than they were for singled molecules. Through a pairwise summation of interacting molecules it can be shown that the potential energy of interaction between flat plates is [7, 23]... 

Since the single-center multipole expansion of the interaction energy is divergent, one could use a kind of multicenter expansion. One can hope that the multipole expansion will provide better results if multipole moments and polarizabilities localized at various points of a molecule are used instead of global multipole moments and polarizabilities. This idea forms the basis of the so-called distributed multipole analysis of the electrostatic, induction, and dispersion interactions between molecules187 195. 

In this section we will review the symmetry-adapted perturbation theory of pairwise nonadditive interactions in trimers. This theory was formulated in Ref. (302). We will show that pure three-body polarization and exchange components can be explicitly separated out and that the three-body polarization contributions through the third-order of perturbation theory naturally separate into terms describing the pure induction, mixed induction-dispersion, and pure dispersion interactions. 

The induction-dispersion contribution, in turn, can be interpreted as the energy of the (second-order) dispersion interaction of the monomer X with the monomer Y deformed by the electrostatic field of the monomer Z (note that we have six such contributions). In particular, when X=A, Y=B, and Z=C the corresponding induction-dispersion contribution in terms of response functions is given by,... 

We wish to end this section by saying that similarly as in the two-body case, nonadditive induction, induction-dispersion, and dispersion terms have well defined asymptotic behaviors from the multipole expansions of the intermolecular interaction operators. For instance, the leading term in the multipole expansion of the three-body dispersion energy for three atoms in a triangular geometry is given by the famous Axilrod-Teller-Muto formula311,312,... 

Equation (1-239) relates the interaction-induced part of the dipole moment of the complex AB to the distortion of the electron density associated with the electrostatic, exchange, induction, and dispersion interactions between the monomers. The polarization contributions to the dipole moment through the second-order of perturbation theory (A/a, A/a, and A/a ) have an appealing, partly classical, partly quantum, physical interpretation. The first-order multipole-expanded polarization contribution (F) is due to the interactions of permanent multipole moments on A with moments induced on B by the external field F, and vice versa. The terms... 

Sadlej AJ (1980) Long range induction and dispersion interactions between Hartree-Fock subsystems. Mol Phys 39 1249-1264... 

The dispersion interaction arises from fluctuations in the charge distribution of <2, leading to transient induction in S and vice versa. By applying the multipole expansion in the dipole approximation in both Q and S, I4uf sp is reduced to... 

Additional excited configurations that generate induction and dispersion interactions contribute to eq.(45) when X k. These are examined in refs.[55(a)],... 

As the understanding of chemical bonding was advanced through such concepts as covalent and ionic bond, lone electron pairs etc., the theory of intermolecular forces also attempted to break down the interaction energy into a few simple and physically sensible concepts. To describe the nonrelativistic intermolecular interactions it is sufficient to express them in terms of the aforementioned four fundamental components electrostatic, induction, dispersion and exchange energies. 

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