Interaction long range

The long range interaction between ions is given by Coulomb s law as  

The electronegativity equalisation method [30] and the charge equilibration method [31] were designed to introduce charges which depend on the atomic environment and the local electric field. The atomic charges predicted by these methods agree well with the experimental values and with the ones determined by quantum mechanical methods for ionic crystals and organic molecules. 

Electrostatic models including multipoles have also been developed. The multipoles are often deduced from the electronic structure determined by ab initio methods, for example, by using Wannier functions [32]. The dependence of the multipoles on the local electric field is accounted for by including polarisability in the model. An example of a polarisable model is the shell model, where a charge is attached to the atom by a spring, hence the dipole of the atom reacts to changes in the local electric field. 

---

To first order, the dispersion (a-a) interaction is independent of the structure in a condensed medium and should be approximately pairwise additive. Qualitatively, this is because the dispersion interaction results from a small perturbation of electronic motions so that many such perturbations can add without serious mutual interaction. Because of this simplification and its ubiquity in colloid and surface science, dispersion forces have received the most significant attention in the past half-century. The way dispersion forces lead to long-range interactions is discussed in Section VI-3 below. Before we present this discussion, it is useful to recast the key equations in cgs/esu units and SI units in Tables VI-2 and VI-3. 

It is thus seen that the dipole-induced dipole propagation gives an exponential rather than an inverse x cube dependence of U x) with x. As with the dispersion potential, the interaction depends on the polarizability, but unlike the dispersion case, it is only the polarizability of the adsorbed species that is involved. The application of Eq. VI-43 to physical adsoiption is considered in Section XVII-7D. For the moment, the treatment illustrates how a long-range interaction can arise as a propagation of short-range interactions. 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

For example, this is tire dominant long-range interaction between a neon atom and a fluoride anion F. ... 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

The long-range interaction V(R) between two atomic/molecular species can be decomposed into... 

Jordan K D and Paddon-Row M N 1992 Long range interactions in a series of rigid noncon]ugated dienes J. Phys. Chem. 96 1188-96... 

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. 

If the simulated system uses periodic boundary conditions, the logical long-range interaction includes a lattice sum over all particles with all their images. Apart from some obvious and resolvable corrections for self-energy and for image interaction between excluded pairs, the question has been raised if one really wishes to enhance the effect of the artificial boundary conditions by including lattice sums. The effect of the periodic conditions should at least be evaluated by simulation with different box sizes or by continuum corrections, if applicable (see below). 

Tasaki, K., McDonald, S., Brady, J.W. Observations concerning the treatment of long range interactions in molecular dynamics simulations. J. Comput. Chem. 14 (1993) 278-284. 

Esselink, K. A comparison of algorithms for long-range interactions. Comput. Phys. Comm. 87 (1995) 375-395. 

This hierarchical extrapolation procedure can save a significant amount of computer time as it avoids a large fraction of the most time consuming step, namely the exact evaluation of long range interactions. Here, computational... 

Helmut Grubmuller, Helmut Heller, Andreas Windemuth, and Klaus Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6 121-142, 1991. 

Brock A. Luty and Wilfried F. van Gunsteren. Calculating electrostatic interactions using the particle-particle particle-mesh method with nonperiodic long-range interactions. J. Phys. Chem., 100 2581-2587, 1996. 

Charles L. Brooks III, B. Montgomery Pettitt, and Martin Karplus. Structural and energetic effects of truncating long ranged interactions in ionic and polar fluids. J. Chem. Phys., 83(ll) 5897-5908, December 1985. 

One of the most expensive parts of a MD or MC simulations is the computation of long range interactions. Since the CPU time required for the... 

Grubmiiller, H., Heller, H., Windemuth, A., Schulten, K. Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions. Molecular Simulation 6 (1991) 121-142... 

This basic LFER approach has later been extended to the more general concept of fragmentation. Molecules are dissected into substructures and each substructure is seen to contribute a constant inaement to the free-energy based property. The promise of strict linearity does not hold true in most cases, so corrections have to be applied in the majority of methods based on a fragmentation approach. Correction terms are often related to long range interactions such as resonance or steric effects. 

Sutton and Chen extended the potential to longer range to enable the study of certain problems such as the interactions between clusters of afoms [Sutton and Chen 1990]. Their objective was to combine the superior Fiimis-Sinclair description of short-range interactions with a van der Waals tail to model the long-range interactions. The form of the Sutton-Chen potential is ... 

Long-range interactions and extended electrostatics—Chapter 5. 

---