Dispersion energy definition

Note the appearance of the AB equilibrium geometry (Rm, which can be obtained by a self-consistent procedure136) and Le Roy s parameter142 [R0, which represents the smallest value of the internuclear distance for which the asymptotic series of the dispersion energy is still a good representation of the damped series (49)] in the definition of the reduced coordinate x represents the expectation value of the square of the radial coordinate for the outermost valence electrons, which is tabulated in the literature143 for atoms with 1 120. Other important parameters in the dispersion damping... 

The second-order dispersion energy is defined as the difference between the second-order polarization and induction energies, E = E j — E J. One can also use the following direct definition... 

Although the spherical form of the multipole expansion is definitely superior if the orientational dependence of the electrostatic, induction, or dispersion energies is of interest, the Cartesian form171-174 may be useful. Mutual transformations between the spherical and Cartesian forms of the multipole moment and (hyper)polarizability tensors have been derived by Gray and Lo175. The symmetry-adaptation of the Cartesian tensors of quadrupole, octupole, and hexadecapole moments to all 51 point groups can be found in Ref. (176) while the symmetry-adaptation of the Cartesian tensors of multipole (hyper)polarizabilities to simple point groups has been considered in Refs. (172-175). 

We recognize on the right side (the first two terms) the complete first-order contribution i.e., the electrostatic energy (Feist) and the valence repulsion energy (F pj,). From the definition of the induction and dispersion energies [Eqs. (13.13) on p. 808], as well as fi-om the reduced resolvent Rq of Eq. (10.76) on p. 644. (applied here to the individual molecules), one may write... 

In both these continuous processes medium to high energy disperse dyes should be used to avoid the risk of dye subliming to contaminate the atmosphere of the fixation unit and then staining the print by vapor-phase dyeing, or to produce a loss of definition of the printed mark due to diffusion from the appHed thickened paste. 

The partitioning of free energy contributions in the explanation (and for design, the prediction) of binding constants is a subjective matter. Different workers choose different definitions, e.g. of hydrophobic binding, which may or may not include dispersion interaction, and different approaches to factorization of enthalpic and entropic components. 

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