Of London dispersive energy

The last important contribution to intermolecular energies that will be mentioned here, the dispersion energy (dEnis). is not accessible in H. F. calculations. In our simplified picture of second-order effects in the perturbation theory (Fig. 2), d mS was obtained by correlated double excitations in both subsystems A and B, for which a variational wave function consisting of a single Slater determinant cannot account. An empirical estimate of the dispersion energy in Li+...OH2 based upon the well-known London formula (see e.g. 107)) gave a... 

The over-riding significance of gas-phase measurements is that in the gaseous state the contributions of electrostatic and even of London dispersion forces can be reasonably estimated this allows of more significant comparison with the observed AH values. At this point it may be appropriate to emphasize the variation in AH with the medium in which it is observed. If the free energy increase (AG) attending the dissociation of the dimer were to vary with the dielectric constant (D) according to... 

In the absence of electron donor-acceptor interactions, the London dispersive energy is the dominant contributor to the overall attractions of many molecules to their surroundings. Hence, understanding this type of intermolecular interaction and its dependency on chemical structure allows us to establish a baseline for chemical attractions. If molecules exhibit stronger attractions than expected from these interactions, then this implies the importance of other intermolecular forces. To see the superposition of these additional interactions and their effect on various partitioning phenomena below, we have to examine the role of dispersive forces in more detail,... 

See R. H. French, "Origins and applications of London dispersion forces and Hamaker constants in ceramics," J. Am. Ceram. Soc., 83, 2117-46 (2000) K. van Benthem, R. H. French, W. Sigle, C. Elsasser, and M. Rtihle, "Valence electron energy loss study of Fe-doped SrTiOs and a E13 boundary Electronic structure and dispersion forces," Ultramicroscopy, 86, 303-18 (2001), and the extensive literature cited therein. Energy E" in those papers is written as hco" here. 

By time averaging Ej t> nt>, the London dispersion energy is obtained. Recently a book on the theory of intermolecular forces that treats the subject in a comprehensive manner [153] has been published. 

Here a and b are occupied MO s of systems A and B. Equation (6,32) is easily expressible in terms of integrals over atomic basis functions and elements of the density matrix. In eqn. (5.31) two terms may be distinguished. The first one is due to single electron excitations of the type a r") and (b —->s"), where a and r", respectively, are occupied and virtual MO s in the system A, and b and s" are occupied and virtual MO s in the system B, Contribution of these terms corresponds to the classical polarization interaction energy, Ep, Two-electron excitations (a r", b — s"), i.e. simultaneous single excitations of either subsystem, may be taken as contributions to the second term - the classical London dispersion energy, Ep, If the Mjiller-Ples-set partitioning of the Hamiltonian is used, Ep may be expressed in... 

As a final test of the influence of correlation, the CC geometry was reoptimized at the MP2 level, using a 6-31G basis set. The resulting changes, with respect to the Hartree-Fock structure, accounted for a further stabilization of only 1.1 kcal/mol, or a 6% increase, despite the contraction of one of the H-bonds from 3.05 to 2.92 A, a full 0.13 A. It was noted that an estimate of the dispersion energy by the empirical London formulation does not reproduce the correlation contribution to the interaction as computed by MP2. 

These jr-bonding effects are part of the theory of the HSAB Principle. We can also imagine that London dispersion energies between atoms or groups in an A B complex could stabilize it. Since these dispersion energies, or van der Waals energies, depend on the product of the polarizabilities of the two groups, soft-soft combinations would be stabilized in this way. The hydride ion is very polarizable, and its softness depends on this factor, presumably. 

Since, London dispersion energy is the potential energy between non-polar molecules, Equations (68) and (69) show that Vd is independent of temperature. On the other hand, the first ionization potentials of most substances do not differ very much from one another, so London s equation is more sensitive to the polarizability than it is to the ionization potential. We can rewrite Equations (68) and (69) ... 

A parameter with indices that are identical is just the pure-component parameter, i.e., fl = A and bii = b,. The fly with i j i a cross-interaction parameter, and is found only in mixtures containing i and j, but never in a pure substance. Since a expresses the effect of intermolecular attractive energy, for similar molecules i and j, fly is approximated by the geometric mean of and Ujj in analogy to the London dispersion energy. But the geometric mean becomes worse as the i and j molecules become more dissimilar. It is generally useful to represent fly by... 

A Short Survey of the Theory of the London Dispersion Energy... 

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