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Non-bonded interactions

NAMD has a number of options that control the way that non-bonded interactions are calculated. These options are interrelated and can be quite confusing, so this section attempts to explain the behavior of the non-bonded interactions and how to use these parameters.

Van der Waals interactions

The simplest non-bonded interaction is the van der Waals interaction. In NAMD, van der Waals interactions are always truncated at the cutoff distance, specified by cutoff. The main option that effects van der Waals interactions is the switching parameter. With this option set to on, a smooth switching function will be used to truncate the van der Waals potential energy smoothly at the cutoff distance. A graph of the van der Waals potential with this switching function is shown in Figure 1. If switching is set to off, the van der Waals energy is just abruptly truncated at the cutoff distance, so that energy may not be conserved.

Figure 1: Graph of van der Waals potential with and without the application of the switching function. With the switching function active, the potential is smoothly reduced to 0 at the cutoff distance. Without the switching function, there is a discontinuity where the potential is truncated.

The switching function used is based on the X-PLOR switching function. The parameter switchdist specifies the distance at which the switching function should start taking effect to bring the van der Waals potential to 0 smoothly at the cutoff distance. Thus, the value of switchdist must always be less than that of cutoff.

Electrostatic interactions

The handling of electrostatics is slightly more complicated due to the incorporation of multiple timestepping for full electrostatic interactions. There are two cases to consider, one where full electrostatics is employed and the other where electrostatics are truncated at a given distance.

First let us consider the latter case, where electrostatics are truncated at the cutoff distance. Using this scheme, all electrostatic interactions beyond a specified distance are ignored, or assumed to be zero. If switching is set to on, rather than having a discontinuity in the potential at the cutoff distance, a shifting function is applied to the electrostatic potential as shown in Figure 2. As this figure shows, the shifting function shifts the entire potential curve so that the curve intersects the x-axis at the cutoff distance. This shifting function is based on the shifting function used by X-PLOR.

Figure 2: Graph showing an electrostatic potential with and without the application of the shifting function.

Next, consider the case where full electrostatics are calculated. In this case, the electrostatic interactions are not truncated at any distance. In this scheme, the cutoff parameter has a slightly different meaning for the electrostatic interactions -- it represents the local interaction distance, or distance within which electrostatic pairs will be directly calculated every timestep. Outside of this distance, interactions will be calculated only periodically. These forces will be applied using a multiple timestep integration scheme as described in Section 7.3.4.

Figure 3: Graph showing an electrostatic potential when full electrostatics are used within NAMD, with one curve portion calculated directly and the other calculated using PME.

Non-bonded force field parameters

PME parameters

PME stands for Particle Mesh Ewald and is an efficient full electrostatics method for use with periodic boundary conditions. None of the parameters should affect energy conservation, although they may affect the accuracy of the results and momentum conservation.

MSM parameters

The multilevel summation method (MSM) [37] is an alternative to PME for calculating full electrostatic interactions. The use of the FFT in PME has two drawbacks: (1) it generally requires the use of periodic boundary conditions, in which the simulation describes an infinite three-dimensional lattice, with each lattice cell containing a copy of the simulated system, and (2) calculation of the FFT becomes a considerable performance bottleneck to the parallel scalability of MD simulations, due to the many-to-many communication pattern employed. MSM avoids the use of the FFT in its calculation, instead employing the nested interpolation in real space of softened pair potentials, which permits in addition to periodic boundary conditions the use of semi-periodic boundaries, in which there is periodicity along just one or two basis vectors, or non-periodic boundaries, in which the simulation is performed in a vacuum. Also, better parallel scaling has been observed with MSM when scaling a sufficiently large system to a large number of processors. See the MSM research web page ( for more information.

In order to use the MSM, one need only specify ``MSM on'' in the configuration file. For production use, we presently recommend using the default ``MSMQuality 0'' ($ C^1$ cubic interpolation with $ C^2$ Taylor splitting), which has been validated to correctly reproduce the PME results [37]. At this time, we discourage use of the higher order interpolation schemes (Hermite, quintic, etc.), as they are still under development. With cubic interpolation, MSM now gets roughly half the performance of PME. Comparable performance and better scaling for MSM have been observed with the optimizations described in Ref. [37], which will be available shortly.

For now, NAMD's implementation of the MSM does not calculate the long-range electrostatic contribution to the virial, so use with a barostat for constant pressure simulation is inappropriate. (Note that the experiments in Ref. [37] involving constant pressure simulation with MSM made use of a custom version that is incompatible with some other NAMD features, so is not yet available.) The performance of PME is generally still better for smaller systems with smaller processor counts. MSM is the only efficient method in NAMD for calculating full electrostatics for simulations with semi-periodic or non-periodic boundaries.

The periodicity is defined through setting the cell basis vectors appropriately, as discussed in Sec. 7. The cutoff distance, discussed earlier in this section, also determines the splitting distance between the MSM short-range part, calculated exactly, and long-range part, interpolated from the grid hierarchy; this splitting distance is the primary control for accuracy for a given interpolation and splitting, although most simulations will likely want to keep the cutoff set to the CHARMM-prescribed value of 12 Å.

The configuration options specific to MSM are listed below. A simulation employing non-periodic boundaries in one or more dimensions might have atoms that attempt to drift beyond the predetermined extent of the grid. In the case that an atom does drift beyond the grid, the simulation will be halted prematurely with an error message. Several options listed below deal with defining the extent of the grid along non-periodic dimensions beyond what can be automatically determined by the initial coordinates. It is also recommended for non-periodic simulation to configure boundary restraints to contain the atoms, for instance, through Tcl boundary forces in Sec. 9.11.

Full direct parameters

The direct computation of electrostatics is not intended to be used during real calculations, but rather as a testing or comparison measure. Because of the $ {\mathcal O}(N^2)$ computational complexity for performing direct calculations, this is much slower than using PME or MSM to compute full electrostatics for large systems. In the case of periodic boundary conditions, the nearest image convention is used rather than a full Ewald sum.

Tabulated nonbonded interaction parameters

In order to support coarse grained models and semiconductor force fields, the tabulated energies feature replaces the normal van der Waals potential for specified pairs of atom types with one interpolated from user-supplied energy tables. The electrostatic potential is not altered.

Pairs of atom types to which the modified interactions apply are specified in a CHARMM parameter file by an NBTABLE section consisting of lines with two atom types and a corresponding interaction type name. For example, tabulated interactions for SI-O, O-O, and SI-SI pairs would be specified in a parameter file as:


Each interaction type must correspond to an entry in the energy table file. The table file consists of a header formatted as:

# multiple comment lines
<number_of_tables> <table_spacing (A)> <maximum_distance (A)>
followed by number_of_tables energy tables formatted as:
TYPE <interaction type name>
0 <energy (kcal/mol)> <force (kcal/mol/A)>
<table_spacing> <energy (kcal/mol)> <force (kcal/mol/A)>
<2*table_spacing> <energy (kcal/mol)> <force (kcal/mol/A)>
<3*table_spacing> <energy (kcal/mol)> <force (kcal/mol/A)>
<maximum_distance - 3*table_spacing> <energy (kcal/mol)> <force (kcal/mol/A)>
<maximum_distance - 2*table_spacing> <energy (kcal/mol)> <force (kcal/mol/A)>
<maximum_distance - table_spacing> <energy (kcal/mol)> <force (kcal/mol/A)>

The table entry at maximum_distance will match the energy of the previous entry but have a force of zero. The maximum distance must be at least equal to the nonbonded cutoff distance and entries beyond the cutoff distance will be ignored. For the above example with a cutoff of 12 Å the table file could look like:

# parameters for silicon dioxide
3 0.01 14.0
0 5.092449e+26 3.055469e+31
0.01 5.092449e+14 3.055469e+17
0.02 7.956951e+12 2.387085e+15
0.03 6.985526e+11 1.397105e+14
13.98 0.000000e+00 -0.000000e+00
13.99 0.000000e+00 -0.000000e+00
0 1.832907e+27 1.099744e+32
0.01 1.832907e+15 1.099744e+18
0.02 2.863917e+13 8.591751e+15
0.03 2.514276e+12 5.028551e+14
13.98 0.000000e+00 -0.000000e+00
13.99 0.000000e+00 -0.000000e+00
0 0.000000e+00 -0.000000e+00
0.01 0.000000e+00 -0.000000e+00
13.98 0.000000e+00 -0.000000e+00
13.99 0.000000e+00 -0.000000e+00

The following three parameters are required for tabulated energies.

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Next: Water Models Up: Force Field Parameters Previous: Potential energy functions   Contents   Index