Spherical cutoff

HyperChem avoids the discontinuity and anisotropy problem of the implied cutoff by imposing a smoothed spherical cutoff within the implied cutoff. When a system is placed in a periodic box, a switched cutoff is automatically added. The default outer radius, where the interaction is completely turned off, is the smallest of 1/2 R, 1/2 R and 1/2 R, so that the cutoff avoids discontinuities and is isotropic. This cutoff may be turned off or modified in the Molecular Mechanics Options dialog box after solvation and before calculation. 

The MD simulations were carried out under standard temperature and pressure. A 1 fs time step was used with SHAKE25 applied to bonds. A 2 fs time step with SHAKE was used in the d(IC)6 d(IC)6 —> d(GC)6 d(GC)6 calculations. The non-bonded interactions for DNA complexes were subject to 10 -12 A spherical cutoff whereas no cutoff was applied to solute-solute interactions to avoid cutoff artifacts on coulombic interactions between sodium ions with phosphates. In the case of d(IC)6 d(IC)6 —> d(GC)6 d(GC)6 calculations an 8 A spherical cutoff was applied to non-bonded interactions. A weak harmonic restraint of 5.0 kcal/mol was imposed to avoid the disruption of terminal base pairs during FEP simulations of netropsin —> 0 and 2-imidazole-distamycin —> distamycin calculations. 

P. J. Steinbach and B. R. Brooks, New Spherical-Cutoff Methods for Long-Range Forces in Macromolecular Simulation, J. Comput. Chem., 15 (1994), 667-683. 

The reported results for equilibrium properties were obtained by means of the standard Monte Carlo (MC), molecular dynamics (MD), and Gibbs ensemble (GE) simulation methods [23, 24], For the trial systems of a finite range the simple spherical cutoff was used, whereas in simulations of the full systems either the Ewald summation or the reaction field method were used. For further technical details we refer the reader to the original papers. 

As computations with explicit solvent molecules are very time consuming in MD or MC simulations, spherical cutoffs are invariably applied to the list of nonbonded interactions. This leads to both unphysical discontinuities in the force field, which may lead to artefacts in the simulated structures, and the neglect of possibly important electrostatic interactions which decay slowly as q/r. Even in cases where it is practical to compute all of the nonbonded interactions, the total number of solvent molecules in a simulation is necessarily finite, so that the influence of the bulk has to be somehow modeled. 

The motion equations have been solved by the Verlet Leap-frog algorithm subject to periodic boundary conditions in a cubic simulation cell and a time step of 2 fs. The simulations have been performed in the NVT ensemble with the Nose-Hoover thermostat [62]. The SHAKE constraints scheme [65] was used. The spherical cutoff radius comprises 1.2 nm. The Ewald sum method was used to treat long-range electrostatic interactions. 

The Spherical Cutoff and Minimum Image Methods. Two commonly used and easily implemented approximations are the so-called spherical cutoff (SC) and minimum image (MI) methods. Both involve a simple... 

The computer simulations employ periodic boundary conditions as well as a spherical cutoff, hence do not exactly correspond to the system just described. Nevertheless, the situations are very similar, and we would not expect the periodicity to influence the formal results. It is clear that for the infinite system with a truncated potential is the mean square moment of the entire sample, or... 

Steinbach, P.J., Brooks, B.R. New spherical-cutoff methods for long-range forces in macromolecu-lar simulation, J. Comp. Chem. 1994,15(7), 667-83. 

The molecular dynamics simulation is performed using the MOTECC suite of programs (Sciortino, Corongiu and dementi, 1994) in the context of microcanonical statistical ensemble. The system considered is a cube with periodic boundary conditions, which contains 343 water molecules. Compatibility of this data with the water experimental density of0.998 g/cm requires a cube with a side length of 21.7446 A. In accordance with the polarizable model, a spherical cutoff with radium equal to half of the simulation cube side is imposed, together with a switching function to suppress energy drift. 

When tail corrections are to be added it is evidently easier to do the calculations with spherical cutoff rather than MI, at least for the continuum-type corrections. 

Evidently the MI method is less objectionable than cutoff from the standpoint of studying fluid structure. If one wants to add a tail correction to the results, however, a spherical cutoff truncation is much more convenient. One way around this difficulty might be to carry out a Markov chain based on the MI method, but simultaneously to keep track of the energy contributions from pairs within some cutoff distance, and finally to add a tail correction to the latter. A very attractive approach to approximating long-range effects in fluids is the reaction field (RF) method described above, which seems to be free of some of the faults of the Ewald method. It is, however, most convenient to use a spherical cavity in the continuum. If this is done one evidently does not entirely escape these problems associated with a spherical cutoff, however, and some way around them should be sought. 

The Importance of Electrostatic Interactions. A molecule with the high charge density of DNA requires special attention to the approximations used in the calculations. In particular, we were concerned about the effect that a finite cutoff would have on the ionic environment and on the DNA structure itself. To test the effect of the spherical cutoff, we repeated the simulation of mlp using the AMBER program 33) and AMBER... 

The simplest truncation of the interparticle interaction is to make a spherical cutoff (SC) at the particle separation Kcut- For a Coulomb system, this approach suffers from the observation that the net charge of the central particle and the other particles inside the cutoff region is not necessarily zero, which creates undesired artifacts (Sect. 6.1.2). 

Fig. 9 Macroion-macroion radial distribution functions for System I using a spherical cutoff at Rcut = 16Rm (SC, full curve), the minimum image convention (MI, dotted curve), and a magnification according 10(gMM(r) - 1) + 1 for r > 12Rm (MI, xlO, dotted curve), and the Ewald summation (Ewald, full curve). The RDFs have been analyzed beyond r = Ljl (arrow) by employing the appropriate volume elements in the normalization. The thin solid line corresponds to a uniform distribution. Nm = 80, L = 32.224Rm, and...

In the implementation of the Ewald summation according to Eq. 20, the value of the potential energy is controlled by three parameters a, the upper limit of m (ntcut), and the upper limit of n (ncut). At equal truncation error in the two spaces, the summation in the real space is often Umited to interactions involving only the nearest image (m = 0), and consequently a spherical cutoff distance i cut < in the real space can be applied. Moreover, the number of replicas in reciprocal space can be reduced by applying a spherical cutoff of n according to jnj < cut. 

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