London dispersion coefficients

In this way, for each H atom, the calculated dipole pseudospectra a, si] i = 1,2, , N of Table 4.2 can be used to obtain better and better values for the C6 London dispersion coefficient for the H—H interaction a molecular (two-centre) quantity C6 can be evaluated in terms of atomic (one-centre), nonobservable, quantities, a, (a alone is useless). The coupling between the different components of the polarizabilities occurs through the denominator in the London formula (4.19), so that we cannot sum over i or / to get the full, observable,12 aA oraB. 

Table 4.3 N-term results for the Cn dipole dispersion constant and the Cg London dispersion coefficients for the H-H interaction...

Permanent dipole moment Molecule (D) Polarizability (1 0 24cm3) Ionization potential (eV) London dispersion coefficient (1 0-79J m6) (Equation 80) Keesom polar orientation coefficient (1 0"79J m6) (Equation 86) Debye induced coefficient (1 0-79J m6) (Equation 88)... 

The first approximate value (6.47) of the Q, dispersion coefficient for the H-H interaction was obtained by Eisenschitz and London (1930) from a perturbative calculation using the complete set of H eigenstates following early work by Sugiura (1927). 

Magnasco, V. and Ottonelli, M. (1999) Long-range dispersion coefficients from a generalization of the London formula. Trends Chem. Phys., 7, 215-232. 

Vd = OO for r< a. For two dissimilar molecules, the London dispersion interaction coefficient Cd, from Equation (68), is... 

The way we have presented the one-dimensional dispersion model so far has been as a modification of the plug-flow model. Hence, u is treated as uniform across the tubular cross section. In fact, the general form of the model can be applied in numerous instances where this is not so. In such situations the dispersion coefficient D becomes a more complicated parameter describing the net effect of a number of different phenomena. This is nicely illustrated by the early work of Taylor [G.I. Taylor, Proc. Roy. Soc. (London), A219, 186 (1953) A223, 446 (1954) A224, 473 (1954)], a classical essay in fluid mechanics, on the combined contributions of the velocity profile and molecular diffusion to the residence-time distribution for laminar flow in a tube. 

It Is Interesting that In the Individual substituent positions molar volume (MR) was found to be the relevant parameter rather than ff. Eg or the STERIMOL descriptors. This fact and the positive coefficients for MR suggest that the enzyme-Inhibitor Interaction proceeds via London dispersion forces (31, ) and the binding to the enzyme Is favored If the bulky substituents are In meta or para positions, which Is In accordance with the earlier results (11). The parameter H-DO In position I seems to be Important In the regression. It systematically appears In each equation. Its path coefficient and partial r value, however. Is relatively low compared to those of Jit and MRjjj. In addition, the H-DOj variable Is not very useful because these Indicator parameters are the most poorly defined and the number of proton donor substituents (H-DO-1) Is rather small. 

In this equation rjkis a nonbonded interatomic distance between atoms j and k, q is the point electrostatic charge on an atom, and Aj Bj and are adjustable parameters that have been obtained from experimental measurements of unit cell dimensions, interatomic distances, and packing arrangements in crystal structures. Ajk represents the coefficient of ffie London dispersion attraction term between atoms j and k, while Bjk and Cjk are short-range repulsive energy terms. The summation is over all interatomic interactions (between all j atoms and all k atoms). For PAHs the terms in Eq. (1) represent forces between pairs of... 

Although this method is also empirical, it has a physical meaning, at least in the dispersion coefficient, and gives more accurate dispersion interactions than those of the London classical dispersion energy. 

We shall henceforth refer to (58) and (59) as of generalizations of the London formula [55] and the Casimir-Polder formula [56], respectively. The latter, in fact, refer to Cg dispersion coefficients for atoms expressed in terms of static (London) or dynamic (Casimir-Polder) polarizabilities, whereas (58) and (59) describe, in a completely general way, non-expanded dispersion between atoms or molecules. (59) expresses the coupling of two electrostatic interactions (l/ri2 and l/r ) involving four space points in the two molecules, with a strength factor which depends on how readily density fluctuations propagate between r and on A, r 2 and F2 on B (Fig. 4). 

Keywords REA Oscillator orbitals London dispersion energy Dispersion coefficient Local correlation method... 

The main purpose of the present work has been to describe the principal features of the formalism, without extensive numerical applications. However, the first rudimentary numerical tests on the molecular Ce coefficients have indicated that the results are quite plausible in spite of the simplifying approximations and it is reasonable to expect that more sophisticated variants of the method will improve the quality of the model. In view of the modest computational costs and the fully ab initio character of the projected oscillator orbital approach applied at various approximation levels of the RPA, which is able to describe dispersion forces even beyond a pairwise additive schane, the full numerical implementation of the presently outlined methodology has certainly a great potential for the treatment of London dispersion forces in the context of density functional theory. 

The no-bond wavefunction electrostatic forces such as those between permanent dipoles of A and B, the permanent dipole of A(B) and the induced dipole of B(A), and fluctuating dipoles of A and B (London dispersion forces). The dative-bond wavefunction I i corresponds to a structure, sometimes called a charge-transfer structure, in which an electron has been transferred from the base B (the donor) to the acid A (the acceptor). Equation 1.34 shows that, by varying the ratio of weighting coefficients a and b, all degrees of electron donation are possible. 

The theoretical foundations of these rules are, however, rather weak the first one is supposed to result from a formula derived by London for dispersion forces between unlike molecules, the validity of which is actually restricted to distances much larger than r the second one would only be true for molecules acting as rigid spheres. Many authors tried to check the validity of the combination rules by measuring the second virial coefficients of mixtures. It seems that within the experimental accuracy (unfortunately not very high) both rules are roughly verified.24... 

---