Nonbonded interactions potential energy

Lennard-Jones potential As two atoms approach one another there is the attraction due to London dispersion forces and eventually a van der Waals repulsion as the interatomic distance r gets smaller than the equilibrium distance. A well-known potential energy function to describe this behavior is the Lennard-Jones (6-12) potential (LJ). The LJ (6-12) potential represents the attractive part as r-6-dependent whereas the repulsive part is represented by an r n term. Another often used nonbonded interaction potential is the Buckingham potential which uses a similar distance dependence for the attractive part as the LJ (6-12) potential but where the repulsive part is represented by an exponential function. 

In this section, we present a detailed discussion of methods relevant to counterion simulations of DNA. Electrostatic interactions dominate all energies involving the DNA and ions. The largest systems simulated to date typically require truncation of nonbonded interaction potentials at around ISA. Abrupt truncation of the potential has the adverse effect of creating an artificial boundary. In an MD simulation, the abrupt truncation produces a discontinuity in force because the first derivative of the interaction potential at the cutoff radius is infinity. Computer programs simply set the forces at the boundary to be zero instead of large values to represent infinity. 

United atom force fields (see United versus All Atom Force Fields on page 28) are sometimes used for biomolecules to decrease the number of nonbonded interactions and the computation time. Another reason for using a simplified potential is to reduce the dimensionality of the potential energy surface. This, in turn, allows for more samples of the surface. 

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

The classical force field represents the potential energy of a polymer chain, made of N atoms with coordinates given by the set r, as a sum of nonbonded interactions and contributions from all bond, valence bend, and dihedral interactions ... 

Polynitro derivatives of pentacyclo[5.4.0.0 .0 °.0 ]undecane have attracted interest as potential high-energy explosives. Molecular strain in this caged system could arise from both the constrained norbomyl moiety and the cyclobutane ring. Additional strain would be expected from nonbonding interactions if the S-endo and 1 l-endo positions were substituted with gm-dinitro groups. 

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