Cutoff, nonbonded

Parallel molecular dynamics codes are distinguished by their methods of dividing the force evaluation workload among the processors (or nodes). The force evaluation is naturally divided into bonded terms, approximating the effects of covalent bonds and involving up to four nearby atoms, and pairwise nonbonded terms, which account for the electrostatic, dispersive, and electronic repulsion interactions between atoms that are not covalently bonded. The nonbonded forces involve interactions between all pairs of particles in the system and hence require time proportional to the square of the number of atoms. Even when neglected outside of a cutoff, nonbonded force evaluations represent the vast majority of work involved in a molecular dynamics simulation. 

It was also interesting to compare LN behavior as increases to trajectories that use nonbonded cutoffs for very large /c2, behavior of the LN trajectory begins to resemble the cutoff trajectory [88]. This observation suggests that the model itself, rather than the numerical scheme per se, is responsible for the deviations. 

Fig. 11. The Speedup of LN at increasing outer timesteps for BPTI (2712 variables), lysozyme (6090 variables), and a large water system (without nonbonded cutoffs 37179 variables). For lysozyme, the CPU distribution among the fast, medium, and slow forces is shown for LN 3, 24, and 48.

Fig. 2. Patches divide the simulation space into a regular grid of cubes, each larger than the nonbonded cutoff. Interactions between atoms belonging to neighboring patches are calculated by one of the patches which receives a positions message (p) and returns a force message (f). Shades of gray indicate processors to which patches are assigned.

Calculating nonbonded interactions only to a certain distance imparts an error in the calculation. If the cutoff radius is fairly large, this error will be very minimal due to the small amount of interaction at long distances. This is why many bulk-liquid simulations incorporate 1000 molecules or more. As the cutoff radius is decreased, the associated error increases. In some simulations, a long-range correction is included in order to compensate for this error. 

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. 

Choose the nonbonded cutoff carefully when using periodic boundary conditions. The cutoff must be small enough to prevent an atom from interacting simultaneously with another atom and with that atom s virtual image. 

This example shows the round particle in cell B,B with two possible nonbonded cutoffs. With the outer cutoff, the round particle interacts with both the rectangle and its periodic image. By reducing the nonbonded cutoff to an appropriate radius (the inner circle), the round particle can interact with only one rectangle—in this case, the rectangle also in cell B,B. ... 

For a rectangular box, the nonbonded cutoff should be less than one-half the smallest box dimension. 

HyperChem supplements the standard MM2 force field (see References on page 106) by providing additional parameters (force constants) using two alternative schemes (see the second part of this book. Theory and Methods). This extends the range of chemical compounds that MM-t can accommodate. MM-t also provides cutoffs for calculating nonbonded interactions and periodic boundary conditions. 

Use nonbonded (NB) tmncation methods to reduce size of NB pairHst it is a dominating term in the calculation. It is important to remember the pairHst i A/, consider tmncation of NBs at 100—120 nm (10—12E), and to experiment with electrostatic cutoffs independentiy of van der Waals. 

Performance. The total time for 500 steps of dynamics and 25 nonbond updates for the standard CHARMM benchmark (Brunger, A. T., Harvard University, personal communication, 1985.), a B-DNA eleven-mer duplex with 706 atoms and a 11.5 angstrom nonbond cutoff (77000 nonbond pairs) is found in Table II. 

For MM+ (energy calculations of small biomolecules or ligands) Choose either Bond dipoles or Atomic charges (assigned via Builds Set charge) for use in the calculations of nonbounded Electrostatic interactions. Select None (calculate all nonbonded interactions recommended for small molecules), Switched or Shifted for Cutoffs (for large molecules). 

The zeolite framework was described by a specific force field developed by van Santen et al. [11] while the hydrocarbon molecules and their interaction among themselves and with the zeolite lattice were described by the generic force field Drdding n [12]. All the internal coordinates of the alkane molecules were allowed to fully relax. The nonbonded interactions (electrostatic and van der Waals) were computed for aU atoms within a cutoff-radius of 12A. Periodic boundary conditions were imposed along the three axes of the zeolite model to simulate an infinite crystal. 

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. 

The nonbonded interaction energy was calculated for the new atom by summation over all nonbonded atoms within the set cutoff distance. The probability of acceptance was... 

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