Empirical potential energy functions

The additional penalty function that is added to the empirical potential energy function in restrained dynamics X-ray refinement has the form ... 

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

Schlenkrich, M., Brickmann, J., MacKerell Jr., A. D., and Karplus, M. (1996) An empirical potential energy function for phospholipids criteria for parameter optimization and application. In Biological membranes a molecular perspective from computational and experiment, Merz Jr., K. M. and Roux, B. (eds.), Birkhauser, Boston, 31-81. 

The most famous three-parameter empirical potential-energy function is... 

A considerably more accurate empirical potential-energy function is the Varshni function ... 

The CHARMM code, version c25bl, was chosen for integration with the metal potential. CHARMM is a multi-purpose molecular dynamics program [35], which uses empirical potential energy functions to simulate a variety of systems, including proteins, nucleic acids, lipids, sugars and water. The availability of periodic boundary conditions of various lattice types (for example cubic and orthorhombic) makes it possible to treat solids as well as liquids. 

The location of extra framework cations is a major problem in characterising zeolites. Simulation is becoming an increasingly powerful tool for the exploration and rationalisation of cation positions, since it not only allows atomic level models to be compared to bulk experimental behaviour, but can also make predictions about the behaviour of systems not readily accessible to experimental probing. In the first part of this work we use the Mott-Littleton method in conjunction with empirical potential energy functions to predict and explore the locations of calcium cations in chabazite. Subsequently, we have used periodic non-local density functional calculations to validate these results for some cases. 

Numerous computational techniques are available to study receptor-ligand interactions that are based on an explicit evaluation of the interaction energies between receptor and ligand molecules. These techniques generally utilize an empirical potential energy function to describe the energy hypersurface for receptor-ligand interactions, such as that shown in Equation 1 ... 

In this study we have parameterised a semi-empirical potential energy function (PEF) for the gold element which is discussed in part two and three. Using the semi-empirical PEF we performed molecular-dynamics (MD) simulations to predict the optimum geometries of gold microclusters. Results and discussions are given in part four. 

A possible choice of Echem is an empirical potential energy function [25-30]... 

Conformational analysis is becoming a widely utilized tool in drug design, molecular modeling, and the determination of structure-activity relationships. Of the many techniques presently available for conformational studies, classical, empirical potential energy functions hold great promise in providing relatively inexpensive explorations of conformational hyperspace in various simulated solvent environments. An excellent example of the application of these classical techniques is embodied in the CAMSEQ Software System (1,2.,3.). 

By using classical-type empirical potential energy functions, accurate conformational calculations which account for experimentally observed phenomena can be performed. Geometry optimization is employed to improve the efficiency of the calculations. In this way, only those atoms whose positions change as a function of conformation are recalculated. 

Displacements derived from temperature factors have been compared with those obtained from molecular dynamics. In these calculations, an empirical potential energy function is expressed as a function of the positional co-ordinates of the atoms. This function is then used to o,.. ain the force on each atom (energy is a generalised force X a generalised displacement) and the Newtonian equations of motion are solved for a small time interval, usually a fraction of a picosecond. Good agreement has been obtained for BPTI [195] and cytochrome c [196]. There are likely to be significant developments in this field as the sophistication of both refinement and simulation methods is increased. 

Although the energy calculations described here are of interest, they have a number of limitations. The first of these is inherent in the inaccuracies of the empirical potential energy functions that are being used. These are known to be significant, as indicated by the sizable difference found between the minimum-energy structure obtained from the potential functions and the observed crystallographic structure, even when the calculations are done for the full crystal system.161,1613 Such errors can be reduced, in principle, by further refinements of the form of the potential function and the associated parameters. 

For molecules with central finite attractive and repulsive forces (Fig. 2-4c), we may take S v ) = n9 Xmm where b Xmin) is the impact parameter corresponding to a minimum angle of deflection selected as an arbitrary cutoff to prevent S Vr) from going to infinity as x goes to zero when classical collision theory is used. The specific dependence of h(Xmin) on will vary with the magnitude of the parameters s and t or a and b in the empirical potential-energy functions. A realistic calculation for this model, i.e., one which avoids an arbitrary cutoff Xmiw must be carried out quantum mechanically. 

Molecular modeling and computer simulation with empirical potential energy function (force field) are now routinely carried out to help understand and predict structures and dynamics of proteins and other macromolecules of biological relevance in water and membrane environments. After over 40 years of development, popular force fields such as AMBER, CHARMM, OPLS and GROMOS have been widely employed in biomolecular simulations. These force fields are used dominantly in highly optimized molecular dynamics... 

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