Nonbonded cutoff distances

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. 

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... 

If one uses cutoff distances in MD for a system, one may acquire undesired border artifacts in which the energy jumps abnormally at the border when an atom moves in and out of this cutoff range. Inclusion and exclusion of the nonbonded energy term with respect to the cutoff distance are no longer valid. The direct method with fixed cutoff distance is also very slow for large cutoff distances. An improvement can be made to reduce the large jump of the direct method with the cutoff distance. In this method, called the spline- switching... 

Energy minimize using AMBER 3.1 with the heavy atoms fixed. (Distance dependent dielectric constant employed, 10 A nonbond cutoff.)... 

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. 

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. 

Cutoffs. The electrostatic and van der Waals interactions are called nonbonded interactions, and consume the largest part of the time needed to calculate V teric of a very large molecule. For a 3000-atom molecule, V"es and Kdw are each the sum of about j(3000)(2990) 4 X 10 terms. (The last factor is reduced to acknowledge that 1,2 and 1,3 interactions are omitted.) To speed up MM calculations on large molecules (and molecular dynamics calculations on systems containing many molecules), many programs use a cutoff, meaning that ij and Kdw.y terms are omitted for atom pairs that are farther apart than some chosen distance. 

If a cutoff is abruptly applied at a particular interatomic distance, this discontinuity can cause problems in energy minimization and molecular-dynamics calculations. To avoid this, one can use a cutoff that makes the nonbonded interactions go to zero gradually over a distance of, say, 1 A. This is done using what is called a switching function. 

Nonbonded terms include intramolecular interactiOTs between pairs of atoms separated by three or more bonds and those belonging to different molecules (i.e., intermolecular interactions). Interactions between pairs of atoms separated by one or two bonds are contained in the bonded energy terms of the bond-stretch and angle-bending terms, respectively. All interactions in a simulation system may be included (i.e., Ewald summation) or distance cutoffs, typically in the range from 8 to 12 A, may be used. 

The intramolecular van der Waal interactions were calculated only between atoms that were located at distances greater than their fourth nearest neighbors. A modified Ewald summation method (Karasawa and Goddard 1989) was used for calculating the nonbonded coulomb interactions, and an atom-based direct cutoff method was used for van der Waal interactions. Smart minimizer, as implemented in Cerius /Material Studio, was used for geometry optimization. The optimization was considered to be converged when a gradient of 0.0001 kcal/mole was reached. 

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