Cutoffs, nonbonded potential

Fig. 8. The six intermolecular site-site radial distribution functions [60] for iPP (N = 48 C//x sites, p = 0.03282 A , T = 453K). g(r) between sites of the same type (a) and between sites of different type (b). SC/PRISM theory used repulsive Leonard-Jones nonbond potentials, and the MD used the full Lennaid-Jones potential with a 12 A cutoff. The curves were displaced vertically for clarity...

Force field calculations often truncate the non bonded potential energy of a molecular system at some finite distance. Truncation (nonbonded cutoff) saves computing resources. Also, periodic boxes and boundary conditions require it. However, this approximation is too crude for some calculations. For example, a molecular dynamic simulation with an abruptly truncated potential produces anomalous and nonphysical behavior. One symptom is that the solute (for example, a protein) cools and the solvent (water) heats rapidly. The temperatures of system components then slowly converge until the system appears to be in equilibrium, but it is not. 

Arelatively simple method for alleviating some of the nonphysical behaviors caused by imposing a nonbonded cutoff is to use a potential switching function (equation 14). 

In an attempt to remedy truncation problems, a shifting potential multiplies the nonbonded electrostatic potential by a function that goes to zero. That is, the potential is shifted to zero at the cutoff Roff. Unlike the switching function, the shifted potential does not apply to van der Waals interactions. 

To increase the speed of calculation in simulations of dense molecular systems, one may choose to neglect the interaction between nonbonded atoms if their separation exceeds some value that does not compromise the reliability of the simulation (i.e., a reasonable nonbonded cutoff). Either atom-based or group-based potential cutoffs may be chosen. Atom-based cutoffs are not the best choices for such systems, however, because significant errors may be introduced if the system under study contains atoms with large partial (or formal) charges. 

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. 

Coordinate, velocity, and energy data were collected every 0.05 ps. A nonbonded cutoff of 12 A was used in the calculations, and the nonbonded list was updated every 25 steps. The electrostatics and van der Waals potential energy terms were gradually switched to zero over the range of 9.0 to 11.0 A. Figure 12 is a snapshot from the molecular dynamics simulation. 

Figure 3 Sparse matrix structures resulting from the Hessian of the potential energy function of the protein BPTI (a) when 8 A cutoffs are used for the nonbonded terms, 13% nonzeros and (b) when only bond length, bond angle, and dihedral angle terms are included, with insets showing enlarged submatrices...

The par file begins with control variables for the present calculation, such as the choice of optimizer for an energy minimization, the temperature and pressure for an MC simulation, cutoff distances for the potential functions, and choices for distribution functions. Short descriptions are given on alternate lines and are mostly self-explanatory. An auxiliary program, parg38, is provided to create the par file for a new problem it asks the user a series of questions about the calculation, and outputs the appropriate par file. Otherwise, an old par file can be copied and edited for a new job. The bottom part of the par file contains the OPLS nonbonded and torsional parameters, as provided with the program, and/or additional user-supplied parameters. 

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