Atom-pair interaction potentials

Atom-Pair Interaction Potentials. Affinities can be calculated based on ligand-receptor atom-pair interaction potentials that are statistical in nature rather than empirical. Muegge and Martin (320) derived these potentials from crystallographic data in the Protein... 

In the theory of the liquid state, the hard-sphere model plays an important role. For hard spheres, the pair interaction potential V r) = qo for r < J, where d is the particle diameter, whereas V(r) = 0 for r s d. The stmcture of a simple fluid, such as argon, is very similar to that of a hard-sphere fluid. Hard-sphere atoms do, of course, not exist. Certain model colloids, however, come very close to hard-sphere behaviour. These systems have been studied in much detail and some results will be quoted below. 

Consider first two simple spherical atoms, say argon atoms. The pair interaction potential has the general form depicted in Fig. 9.6. Note that for/ < the potential... 

A general theoretical approach to monolayer physical adsorption is discussed. In this theory, the isotherms and heats of adsorption at given T are given as functions of the interaction energies of the adsorbed atoms with the solid and with each other. The general equations reduce to localized and mobile adsorption when the potential variations over the surface are either very large or very small. Intermediate cases are also included. Gas atom-solid interaction energy functions are computed from the known pair interaction potentials for several rare gas systems, and it is shown that a considerable amount of information can be obtained about the adsorption properties of such systems from these potential functions. 

Figure 2 Atomic structure of a two-dimensional nanocrystallme material computed using pair interaction potentials. The atoms in the central portions of the nanocrystals are indicated in black atoms in the nanograin boundary regions are represented by open circles. (Ref 13. Reproduced by permission of Springer)...

Knowledge-based functions are based on the derivation of statistical preferences in the form of potentials for protein ligand atom pair interactions. Similar to potentials derived for protein folding and protein structure evaluation (e.g., Ref. 148), pair potentials akin to potentials of mean force (PMFs) are derived for various protein and ligand atom types using the PDB as a knowledge base. The PMF scoring function [118]... 

Van der Waals Interactions. The van der Waals term in (16.94) is usually taken as the sum of interactions involving all possible 1,4,1,5,1,6,... atom-pair interactions Kdw = 2i,s4 Kdw, /. where atoms i and j are in a 1,4 or greater relation.The 1,2 and 13 van der Waals interactions and electrostatic interactions are considered to be implicitly included in the bond-stretching and bond-bending parameters. Each van der Waals pair term Vvdw.iy the sum of an attraction due to London dispersion forces and a repulsion due mainly to Pauli repulsion. The AMBER, CHARMM, DREIDING, UFF, and TRIPOS force fields take as a Lennard-Jones 12-6 potential (Fig. 16.12 and... 

Another way of representing atom-pair interactions, which lends itself particularly well to computational methods is the spline potential. A least-squares calculation fits various accurately known sets of numerical interaction energies at certain interatomic regions (perhaps from various theoretical and/or empirical investigations) into a functional form under conditions of matching first and second derivatives, so that a potential and its derivatives may be invoked at an arbitrary atom separation. 

Except for the Coulombic contributions, which are computed by an Ewald-type summation, as described in Section 2.3, a potential cutoff distance is imposed to avoid unnecessary computing time calculating negligible contributions by short-range interactions from most of the V 2N N— 1) atom pairs in the system. In the commonly used nearest-image convention, if the cutoff obeys the condition re < VtJL, Then atom pair interactions included are between atom i in the central box and either atomj in the same box or one of its imagesf in an adjacent one, depending on whichever distance x/ - Xy or x/ - f is least (see Fig. 5.4). 

Non-bonded interactions. A distance-corrected Morse potential is used to describe atom-pair interactions, with excessively high repulsions between bonded atoms avoided by including a shielded interaction. 

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

Extensive computer simulations have been caiTied out on the near-surface and surface behaviour of materials having a simple cubic lattice structure. The interaction potential between pairs of atoms which has frequently been used for inert gas solids, such as solid argon, takes die Lennard-Jones form where d is the inter-nuclear distance, is the potential interaction energy at the minimum conesponding to the point of... 

Here r is the distance between the centers of two atoms in dimensionless units r = R/a, where R is the actual distance and a defines the effective range of the potential. Uq sets the energy scale of the pair-interaction. A number of crystal growth processes have been investigated by this type of potential, for example [28-31]. An alternative way of calculating solid-liquid interface structures on an atomic level is via classical density-functional methods [32,33]. 

The Finnis-Sinclair type potentials (Finnis and Sinclair 1984) are central-force potentials but have a many-body character in that the energy of a system of particles is not merely a sum of pair interactions between individual atoms. In this scheme, modified for binary alloys by Ackland and Vitek (1990), the total energy of a system of N atoms is written as... 

---