Electrostatic long-range

Long-range forces are most conveniently expressed as a power series in Mr, the reciprocal of the intemiolecular distance. This series is called the multipole expansion. It is so connnon to use the multipole expansion that the electrostatic, mduction and dispersion energies are referred to as non-expanded if the expansion is not used. In early work it was noted that the multipole expansion did not converge in a conventional way and doubt was cast upon its use in the description of long-range electrostatic, induction and dispersion interactions. However, it is now established [8, 9, 10, H, 12 and 13] that the series is asymptotic in Poincare s sense. The interaction energy can be written as... 

Belhadj,M., Alper, H.A., Levy, R.M. Molecular dynamics simulations of wa ter with Ewald summation for the long-range electrostatic interactions. Chem. Phys. Lett. 179 (1991) 13-20. 

A very simple — and in fact quite widely used — approximation completely neglects long range electrostatic interactions beyond a certain cut-off distance [43] of typic ally 8 — 15 A. For systems which are significantly larger... 

The development of efficient algorithms and the sophisticated description of long-range electrostatic effects allow calculations on systems with 100 000 atoms and more, which address biochemical problems like membrane-bound protein complexes or the action of molecular machines . 

Smith P E and v an Gunsteren W F1993. Methods for the Evaluation of Long Range Electrostatic Forces. In van Gunsteren W F, P K Weiner and A J Wilkinson (Editors). Computer Simulation ofBiomolecular Systems. Leiden, ESCOM. 

In this model, reaction is considered to occur preferentially at that position in the aromatic molecule to which the approach of the electrophile causes the smallest increase in zero energy. In molecules possessing polar or dipolar groups, long range electrostatic forces will initially be the most important. 

The first modification is to simply scale the dielectric permittivity of free space (8 ) by a scale factor D to mediate or dampen the long range electrostatic interactions. Its value was often set to be between 1.0 and 78.0, the macroscopic value for water. A value of D=2.5, so that 8 =2.58q, was often used in early CHARMM calculations. 

In this final section, we recapitulate the relationship between long-range electrostatics and boundary conditions while attempting to assess the strengths and weaknesses of the three choices we have outlined. 

In Chapter 2 the curve of Fig. 7 was introduced, to show the mutual potential energy arising from short-range forces in contrast to that arising from long-range electrostatic forces. To account for the existence of molecules and molecular ions in solution, we need the same curve with the scale of ordinates reduced so as to be comparable with those of Fig. 

In simple systems such as nonpolar films wetting on surfaces, the van der Waals forces play a dominant role, but in more complex systems long-range electrostatic forces are also involved. 

A series of calculations on defect centers induced by radiation damage in alpha-quartz is reported. Ab initio SCF-MO calculations were carried out on a 21 atom cluster, Si50i6 % surrounded by 956 point-ions, designed to simulate alpha-quartz. This two-region approach made it possible to represent the long-range electrostatic effects, present in the crystal, in the SCF-MO cluster. 

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