Empirical pair potentials

To find appropriate empirical pair potentials from the known protein structures in the Brookhaven Protein Data Bank, it is necessary to calculate densities for the distance distribution of Ga-atoms at given bond distance d and given residue assignments ai,a2- Up to a constant factor that is immaterial for subsequent structure determination by global optimization, the potentials then ciiiergo as the negative logarithm of the densities. Since... 

There are many empirical and semi-empirical pair potentials which describe quite satisfactorily the properties of liquids and solids, see chapter 5 in book The parameters in these potentials are not real parameters of a true two-body interaction, their values depend upon properties of a medium. So these effective two-body potentials include nonadditive interactions through their parameters. The latter can not be directly related to the definite physical... 

Now, because computer resources are, after all, finite, all phase space points can be found in the first octant, below and to the left of a plane. Acknowledging this state of affairs it is appropriate to call this plane the horizon of the MD simulation world [21], or simply the computational horizon. The major part of all production calculations are still extended over a moderate number of time-steps (corresponding to a few hundred picoseconds), using empirical pair potentials-on systems with sizes, much smaller than what could maximally be possible. So, in fact, the vast majority of the points should be simply found in a region to the left of a plane we call the average computational horizon. The truly large scale simulations can be found between the two planes. 

F. Barocchi and M. Zoppi. Determination of collision induced polarizability in Ar, Kr, and Xe by means of collision induced scattering Analysis and empirical pair potentials. J. Chem. Phys., (57 901-905 (1976). 

Figure 1 Comparison of argon interaction-potentials. The solid line is the empirical pair potential 100 the dashed line is the van der Waals + dispersion model of Dion et al. 485 the dot-dashed line is a CCSD(T) ab initio potential 77 and the dotted lines with circle and square symbols are the SAPT (DFT) potentials of Podeszwa and Szalewicz97 with different functionals. Reprinted from, 97, Copyright (2005) with permission from Elsevier...

Fig 1. Potential energy curve of the Au2- Circles represent the relativistic density functional theory (RDFT) results, full line represents the fitted empirical pair potential energy function (PEF). 

The first term represehts the repulsive branch and the second term represents the attractive branch of the interaction potential between two atoms. By performing a non linear least square fit procedure the parameters (Al, ai, Ai A2, a2, A2) of the empirical pair potential are determined. In the fit procedure we have used the binding energy values of Au-dimer calculated at various interatomic distances by RDFT. The estimated points by RDFT and the fitted function are shown in Fig. 1. The potential parameters for the gold dimer interaction are determined as Ai = 1222.86345, A2 = -3.93623329, Ai = 2.94056151, A2 = -1.30223862, ai = 0.806351693, 2 = 0.216139972. In these parameters energy is in eV, and distance is in... 

Empirical Potential Based Modeling Schemes. Degrees of freedom in large-scale models can be reduced by incorporating prior information. One way to do this is to specify empirical pair potentials as a function of separation between each atom type. Then the number of atoms the model can be increased but the number of parameters depends only on the number of atomic species. In principle the pair potentials themselves should give the equilibrium structure of... 

The theory of empirical pair potentials is that since they are derived from observations they will incorporate the dominant thermodynamic effects without explicitly having to partition and quantify the effects. Empirical pair potentials have been widely used in protein structure prediction, particularly in fold recognition following their introduction by Sippl [13] and their use... 

Although there have been a fairly large number of first-principle simulations of condensed phase published to date, this number is completely dwarfed by simulations based on empirical potentials. The popular empirical pair potentials for water [76-78] have been used in many (thousands) research projects. The empirical potentials are usually fitted in simulations for liquids to reproduce measured properties of this phase. Thus, these potentials mimic the nonadditive effects by distortions of two-body potentials... 

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