Dispersion energy molecular forces

The theory of molecular interactions can become extremely involved and the mathematical manipulations very unwieldy. To facilitate the discussion, certain simplifying assumptions will be made. These assumptions will be inexact and the expressions given for both dispersive and polar forces will not be precise. However, they will be reasonably accurate and sufficiently so, to reveal those variables that control the different types of interaction. At a first approximation, the interaction energy, (Ud), involved with dispersive forces has been calculated to be... 

There is another physical phenomenon which appears at the correlated level which is completely absent in Hartree-Fock calculations. The transient fluctuations in electron density of one molecule which cause a momentary polarization of the other are typically referred to as London forces. Such forces can be associated with the excitation of one or more electrons in molecule A from occupied to vacant molecular orbitals (polarization of A), coupled with a like excitation of electrons in B within the B MOs. Such multiple excitations appear in correlated calculations their energetic consequence is typically labeled as dispersion energy. Dispersion first appears in double excitations where one electron is excited within A and one within B, but higher order excitations are also possible. As a result, all the dispersion is not encompassed by correlated calculations which terminate with double excitations, but there are higher-order pieces of dispersion present at all levels of excitation. Although dispersion is not necessarily a dominating contributor to H-bonds, this force must be considered to achieve quantitative accuracy. Moreover, dispersion can be particularly important to geometries that are of competitive stability to H-bonds, for example in the case of stacked versus H-bonded DNA base pairs. ... 

The effect of induced dipoles in the medium adds an extra term to the molecular Hamilton operator. = -r R (16.49) where r is the dipole moment operator (i.e. the position vector). R is proportional to the molecular dipole moment, with the proportional constant depending on the radius of the originally implemented for semi-empirical methods, but has recently also been used in connection with ab initio methods." Two other widely available method, the AMl-SMx and PM3-SMX models have atomic parameters for fitting the cavity/dispersion energy (eq. (16.43)), and are specifically parameterized in connection with AMI and PM3 (Section 3.10.2). The generalized Bom model has also been used in connection with force field methods in the Generalized Bom/Surface Area (GB/SA) model. In this case the Coulomb interactions between the partial charges (eq. (2.19)) are combined... 

In addition to electrostatic, exchange, and induction (a.k.a. deformation) energy, the fourth principal contributor to the interaction energy is the so-called dispersion energy [39]. This quantity is closely related to the London forces that are well known from freshman chemistry texts that originate from instantaneous fluctuations of the electron density of one molecule, which cause a sympathetic series of instantaneous density fluctuations in its partner. Dispersion, by its very nature, is attractive. In terms of ab initio molecular orbital theory, the dispersion energy is not present at the SCF level, but is a byproduct of the inclusion of electron correlation into the calculation. The reader is hence alerted to the fact that calculations that do not include electron correlation (and there are many such, particularly in the early literature) cannot be expected to include this fourth, and sometimes very important, component of the noncovalent force. 

The difference in the composition and structure of phases in contact, as well as the nature of the intermolecular interactions in the bulk of these phases, stipulates the presence of a peculiar unsaturated molecular force field at the interface. As a result, within the interfacial layer the density of such thermodynamic functions as free energy, internal energy and entropy is elevated in comparison with the bulk. The large interface present in disperse systems determines the very important role of the surface (interfacial) phenomena taking place in such systems. 

While moving from the discussion of molecular interaction between condensed phases separated by a gap filled with dispersion medium to the analysis of molecular interactions between dispersed particles, it is necessary to outline that the interaction energy and force should be related to a pair of particles as whole, and not to the unit area of intermediate layer, as was done above. The interaction energy and force are not only the functions of distance between particles and the value of complex Hamaker constant, but also depend on size and shape of interacting particles. 

Very recently, Good [17] has extended the theory of interfacial energies [16] to include an explicit accoxmt of the different types of inter molecular forces dispersion, dipole induction, and dipole orientation. In the present paper, we will use the theory, as extended [17], to show how the actual surface free energies of certain solids can be calculated from contact angle data, including Fox and Zisman s critical surface tensions. 

Other induced, will interact in the same way as two dipoles. The strength of this interaction depends on the magnitude of the permanent dipole moment of the polar molecule, and on the polarizabiHty of the second molecule. Even if the two molecules are nonpolar, there can be attractive, low-energy molecular interactions between them. These are induced dipole-induced dipole interactions, also called London dispersion forces, in which a nonpolar molecule induces a small instantaneous dipole in another nearby polar molecule. The force F (in dynes) between two charges q and q (in electrostatic units) is expressed by Coulomb s equation ... 

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