Switching function, potential

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). 

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. 

An alternative way to eliminate discontinuities in the energy and force equations is to use a switching function. A switching function is a polynomial ftmction of the distance by which the potential energy function is multiplied. Thus the switched potential o (r) is related to the true potential t> r) by v r) = v(r)S(r). Some switching functions are applied to the entire range of the potential up to the cutoff point. One such function is ... 

The switching function has a value of 1 at r = 0 and a value of 0 at r = r., the cutoff distcince. Between these two values it Vciries as shown in Figtire 6.19, which also shows how the potential function is affected. 

Fig. 6.20 A switching function that applies over a narrow range near the cutoff and its effect on the Lennard-Janes potential.

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. 

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. 

Display electrostatic potential maps for water, ethanol, formic acid and propanoic acid, and examine the value of the electrostatic potential at the most electron-poor site. What causes a larger change in electrostatic potential, switching the alkyl group for H, or changing the structure of the acidic functional group ... 

Figure 4.—Continued. Potential energy of the 7.5 A cutoff potentials (truncate, shift, switch) and the no cutoff potential on the heating portion of the trajectories of (c) the 6.5 to 7.5 A switching function simulation and (d) the 7.5 A simple truncation simulation.

The ab initio and interpolated potential functions are coupled using a smooth switching function, written in terms of the energy difference between the electronic states ... 

The first two terms are Morse potentials for A-B and B-C bonds. The third term attenuates the alteration between B and C as A approaches by means of switching function. The last term supplies a repulsive interaction between A and C. The switching function tends from 0 to unity as rAB varies from large to smaller value. 

The focus in the reaction dynamics studies was on the N02 elimination channel, but they also studied the HONO elimination reactions [70]. They based the potential energy surface on experimental data but performed some minimal basis set ab initio calculations to determine geometries, force fields, torsional potentials, and some information about the reaction paths. The representations of the global potential energy surfaces were based on valence force fields for equilibrium structures with arbitrary switching functions operating on the potential parameters to effect smooth and (assumed) proper behavior along the reaction paths. Based on the available experiments [71-73], they assumed that the primary decomposition reaction is simple N-N bond rupture to eliminate N02. 

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