Pair potential for

In calculating a pair potential for dineon, we have to take the separated atom energy as one half of the pair energy for an arbitrarily large distance. 

The creation of the Gay-Berne potential owes much to the original work by Corner in his pioneering development of pair potentials for molecules [7]. He had noted that the Lennard-Jones 12-6 potential provided a good description of the interactions between atoms... 

Tobi D, Elber R. Distance-dependent, pair potential for protein folding results from linear optimization. Proteins 2000 41 40-6. 

Favorable coarse-graining results for CCI4 are not surprising because this molecule is spherically symmetric. Planar benzene presents a more stringent test for the force-matching approach. Figure 8-8 shows the effective pair-force and pair-potential for the benzene COM. 

Sordo, J. A., M. Probst, G. Corongiu, S. Chin, and E. Clementi. 1987. Ab Initio Pair Potentials for the Interactions Between Aliphatic Amino Acids. J. Am. Chem. Soc. 109,1702-1708. 

The first option involves the obtainement of an analytic function that reproduces the interaction energy between couples of molecules which has been calculated by solving the Schrodinger equation usually by means of an ab initio method. The advantge of this possibility is that information about any potential energy hypersurface point can be obtained from the calculation whereas experimentally this is not always possible. The practical procedure in order to build up an ab initio pair potential for the interaction between two molecules a and P can be divided in four steps. 

The cation-anion pair potential for a symmetrical salt may be written as the sum of the core repulsion and the coulomb interaction. For example, if the core repulsion is an inverse power potential, then ... 

High-temperature Effective Pair Potentials for the System N2-N and 02-0. 

Figure 3.16 The pair potential for rutile in ethylene glycol at infinite dilution as a function of diffuse layer potential. Background concentration 1 x 10 4 Ml ] electrolyte...

Fig. 6.7 Interatomic pair potentials for (a) Na, (b) Mg, and (c) Al as a function of the interatomic separation in units of the Wigner-Seitz radius / ws. The positions of the fee first and bcc first and second nearest neighbours are marked. Since fee and ideal hep structures have identical first and second nearest neighbours, their relative structural stability is determined by the more distant neighbours marked in the figures. (After McMahan and Moriarty (1983).)...

The resultant pair potentials for sodium, magnesium, and aluminium are illustrated in Fig. 6.9 using Ashcroft empty-core pseudopotentials. We see that all three metals are characterized by a repulsive hard-core contribution, Q>i(R) (short-dashed curve), an attractive nearest-neighbour contribution, 2( ) (long-dashed curve), and an oscillatory long-range contribution, 3(R) (dotted curve). The appropriate values of the inter-atomic potential parameters A , oc , k , and k are listed in Table 6.4. We observe that the total pair potentials reflect the characteristic behaviour of the more accurate ab initio pair potentials in Fig. 6.7 that were evaluated using non-local pseudopotentials. We should note, however, that the values taken for the Ashcroft empty-core radii for Na, Mg, and Al, namely Rc = 1.66, 1.39, and... 

Fig. 6.10 The phase shift, cc3, of the long-range contribution to the pair potential for sodium, magnesium, and aluminium as a function of their relative atomic volume, / ). (AfterWard (1985).)...

Ward, M. A. (1985). Analytic Pair Potentials for Simple Metals (Ph.D. thesis). 

The system studied here consists of one solute molecule of mass M and the N solvent molecules, each of mass m. The pair potential for the solvent-solvent pair and the solute-solvent pair is assumed to be given by the simple Lennard-Jones 12-6 potential. 

Figure 16 show the effective pair potential for the systems in Fig. 15, calculated from the Orstein-Zernike equation with three different closure relations, following the procedure of deconvoluting the experimental g(r). In both cases, the effective pair potential exhibits an attractive component, independent of the closure relation, which is not consistent with the DLVO potential. As pointed out, the DLVO potential has a short-range first mini-... 

Mas EM, Szalewicz K, Bukowski R, Jeziorski B (1997) Pair potential for water from symmetry-adapted perturbation theory. J Chem Phys 107 1207 1218... 

Curtiss LA, Woods Halley J et al (1987) Nonaddidivity of ab initio pair potentials for molecular dynamics of multivalent transition metal ions in water. J Chem Phys 86(4) 2319-2327... 

Based on this idea, Derjaguin and Landau, and Verwey and Overbeek, found the pair potential for the electrostatic repulsion of two identical spherical particles in an electrolyte solution to be... 

Morse MD, Rice SA (1982) Tfests of effective pair potentials for water predicted ice structures. J Chem Phys 76 650- 660... 

Preliminary inspection of Equation 2.16 reveals that the Gibbs pair potential leads to repulsion at small interplate separations and attraction at large distances. Because it is U°n and not 17 F that is the appropriate pair potential for describing the effective interaction between the mth and nth macroions in solution under isobaric conditions, the different analytic properties of and U, have profound implications for colloid science. 

Let us now apply the Sogami potential to the problem. As with the onedimensional problem, we get a good qualitative insight into the behavior of the system by simply equating the observed interparticle separation (b) with the position (Rm) of the minimum in UG(R), the Gibbs pair potential for spheres with separation R, namely [7]... 

Figure 7.17 Left Fluctuating density in a liquid phase near a solid surface, relative to the bulk density p0. The first maximum occurs at the hard-sphere contact distance from the surface, at r = a the molecular diameter. Right Pair potentials for two molecules in the liquid calculated from p(r) - p0exp[-w/kT]...

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