Truncating potential

These functions allow- the nonbonded potential energy Lo turn off smoothly and systematically, removing artifacts caused by a truncated potential. With an appropriate switching function, the potential function is unaffected except m the region of the switch. 

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. 

Example For two atoms having point charges of 0.616 and -0.504 e and a constant dielectric function, the energy curve shows a switching function turned on (Ron) at a nonbonded distance of 10 A and off (Roff) at a distance of 14 A. Compare the switched potential with the abruptly truncated potential. 

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... 

Fig. 5. Values of h °(r) for dipolar hard spheres at p —0.4 and —2.75. The big dots are MC results for Af—256, Rf. —4.2d. The solid and dashed curves are the QHNC and LHNC approximations, respectively, for a spherically truncated potential. The dotted curve is the QHNC result for an infinite system with an untruncated potential. (Results from Ref. 58.)...

The other approximations described in Section III.C have not been solved for a spherically truncated potential, but an estimate of their accuracy can be obtained by comparing with the LHNC or QHNC theories for an infinite system. We are of course assuming that the LHNC and QHNC approximations remain accurate for the full (untruncated) dipolar interaction and lie close to the true infinite system result. The MSA, LIN, L3, and LHNC theories for a dense dipolar hard-sphere system are compared in... 

Fig. 13. Values of h"°(r) for hard spheres with dipoles and quadrupoles at p = 0.8 and H = Q = 1.0. The dots are MC results (N=256, R(. =3.4rf), and the solid, dashed, and dash-dot curves represent the QHNC, LHNC, and MSA, respectively, for a spherically truncated potential. (Results from Ref. 59.)...

Hard Spheres with Dipoles and Quadrupoles. The LHNC, QHNC, and mean spherical approximations have been solved for fluids of hard spheres with both dipole and quadrupole moments. Theoretical results for spherically truncated potentials have been compared with Monte Carlo (SC)... 

One clever approach to obtaining better convergence is to include asymptotic properties of the pair correlation functions (Lebowitz and Percus 1963). In particular, exact asymptotic expressions have been obtained by Attard and coworkers (Attard 1990 Attard et al. 1991), such as for dipolar fluids. Other work has extended simulation results for a system with a truncated potential to give those for the full potential (Lado 1964). The effects on pair distribution functions of potential truncations are important. 

The combination of a truncated potential function and periodic boundary conditions leads to an important programming simplification. Let L be the length of the molecular dynamics box and let r, be a molecule s interaction range. (In the case of an anisotropic potential, r, is the maximum distance of the... 

Shifting functions- 77 provide an alternative to smoothly truncated potential energies. As the name suggests, the true potential is shifted so as to make it zero at the cutoff distance. One form of a shifted potential is ... 

Truncated Potentials. In the interest of computing efficiency, site-site potentials are truncated at a cutoff distance, r, usually taken to be about 2.5 times the effective "diameter of the site. Interactions beyond this distance are neglected, and corrections to the calculated thermodynamic properties, due to the neglected "tail", are added using a simple perturbation scheme ( ). 

In Figure 1(a) the potential energy and force between two sites are plotted against distance for a typical truncated potential. It is the discontinuity in the force at r=rc that is the source of error in molecular dynamics simulations. To reduce the error we use a modified force, Fj, formed by subtracting from the usual expression for the force a constcint, H, equal to the magnitude of this discontinuity. The modified force is... 

The small changes to the force and potential energy, resulting from the change to a shifted force potential function, provide improved accuracy eind stcibility in computer simulations, with negligible changes to structure and time correlation functions, at short to moderate times, calculated from the usual truncated potential. Corrections to calculated thermodynamic properties to account for modifications to the potential can be calculated by a perturbation method similar to that used for the long tail corrections. This matter will be discussed in detail in a separate paper. 

LMTS system onto a different trajectory In phase space from that followed by the system evolved by the CMD method. Hence, there Is no strictly Newtonian connection between widely separated phase points but then, there Is no true Newtonian connection between widely separated phase points In the system generated by the CMD method due to round off errors and the truncated potential. The conclusion is that the phase space trajectories become different in the two calculations, but one is not necessarily more wrong (or right) than the other. Hoover and Ashurst have discussed this point In another context with similar conclusions (35). The restriction which this Imposes is that the LMTS method cannot be used to study very long-lived phenomena such as the long tail of the velocity autocorrelation function. 

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