Intermolecular forces force theory long range

The potential outside the charge distribution and due to it is simply related to the moments, as is the interaction energy when an external field is applied.14 The multipole moments are thus very useful quantities and have been extensively applied in the theory of intermolecular forces, particularly at long range where the electrostatic contribution to the interaction may be expanded in moments. Their values are related to the symmetry of the system thus, for instance, a plane of symmetry indicates that the component of n perpendicular to it must be zero. Such multipoles are worth calculating in their own right. 

This is a theory for the activity coefficients of dilute electrolyte solutes. Ions exert large forces on each other, and these forces are called long-range forces because they act over large distances compared with other intermolecular forces. The electrostatic force on a charge Qi due to a charge Q2 is given by Coulomb s law. 

In the previous chapters, the diffusion equation has been used extensively to model fast chemical reaction in solution. By addition of various correction factors (such as intermolecular forces, long-range transfer, solvent structure, hydrodynamic repulsion, etc.), the agreement between experiment and theory can be improved as the model becomes more realistic. Nevertheless, the reactants have been presumed to execute Brownian motion. This is only the long-time limit of their actual behaviour. 

In the field of intermolecular forces a book has been published by Kaplan241 which provides a coverage of the theory from long-range forces (including retardation effects) to short-range forces and nonadditivity. The determination of molecular potentials from experimental data is also considered in one chapter of this book. 

The relation between the supermolecule coupled cluster approach and the perturbation theory of intermolecular forces in even less obvious than the case of the Mpller-Plesset theory, and no formal analysis has been reported in the literature thus far. Rode et al.68 analyzed the long-range behavior of the CCSD(T) method65, and showed that this method, although very popular and in principle accurate, may lead to wrong results for systems with the electrostatic term strongly depending on the electronic correlation, e.g. the CO dimer. 

Stone AJ, Tough RJA (1984) Spherical tensor theory of long-range intermolecular forces. Chem Phys Lett 110 123-129... 

A. J. Stone and R. J. A. Tough, Chem. Phys. Lett., 110,123 (1984). Spherical Tensor Theory of Long-Range Intermolecular Forces. 

The Maier-Saupe theory of nematic liquid crystals is founded on a mean field treatment of long-range contributions to the intermolecular potential and ignores the short-range forces [88, 89]. With the assumption of a cylindrically symmetrical distribution function for the description of orientation of the molecules and a nonpolar preferred axis of orientation, an appropriate order parameter for a system of cylindrically symmetrical molecules is... 

The effect of the long-range intermolecular forces between the electrode and bacteria has been considered by Rutter and Vincent in terms of the DLVO theory.The total free energy of interaction comprises... 

Density functional theory (DPT) calculations [18] suggest the tangential pulling force Ft as a solid/liquid adhesion originated in long-range solid/liquid intermolecular attraction... 

Extrapolating continuous description of fluid motion to a molecular scale might be conceptually difficult but unavoidable as far as interfacial dynamics is concerned. Long-range intermolec-ular interactions, such as London-van der Waals forces, still operate on a mesoscopic scale where continuous theory is justified, but they should be bounded by an inner cut-off d of atomic dimensions. Thus, distinguishing the first molecular layer from the bulk fluid becomes necessary even in equilibrium theory. In dynamic theory, the transport in the first molecular layer can be described by Eq. (60), whereas the bulk fluid obeys hydrodynamic equations supplemented by the action of intermolecular forces. Equation (61) serves then as the boundary condition at the solid surface. Moreover, at the contact line, where the bulk fluid layer either terminates altogether or gives way to a monomolecular precursor film, the same slip condition defines the slip component of the flow pattern. 

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