Distance cutoffs

Ways to circumvent the above-mentioned problems have been to simply increase the cutoff distance to larger values, to use more than one cutoff value with different update frequencies, or to define more sophisticated cutoff schemes. In the last case, a truncation of the non-bonded interactions was replaced by shifting the interaction energies to zero or by additionally applying a switched sigmoidal func-... 

The function/c is a smoothing function with the value 1 up to some distance Yy (typically chosen to include just the first neighbour shell) and then smoothly tapers to zero at the cutoff distance, by is the bond-order term, which incorporates an angular term dependent upon the bond angle 6yk- The Tersoff pofenfial is more broadly applicable than the Stillinger-Weber potential, but does contain more parameters. 

In the reaction field method, a sphere is constructed around the molecule with a radius equal to the cutoff distance. The interaction with molecules that are within the sphere is calculated explicitly. To this is added the energy of interaction with the medium beyond the sphere, which is rnodelled as a homogeneous medium of dielectric constant g (Figure 6.23). The electrostatic field due to the surrounding dielectric is given by ... 

Table 7.1 presents us with something of a dilemma. We would obviously desire to explore i much of the phase space as possible but this may be compromised by the need for a sma time step. One possible approach is to use a multiple time step method. The underlyir rationale is that certain interactions evolve more rapidly with rime than other interaction The twin-range method (Section 6.7.1) is a crude type of multiple time step approach, i that interactions involving atoms between the lower and upper cutoff distance remai constant and change only when the neighbour list is updated. However, this approac can lead to an accumulation of numerical errors in calculated properties. A more soph sticated approach is to approximate the forces due to these atoms using a Taylor seri< expansion [Streett et al. 1978] ... 

The molecular mechanics force fields available include MM+, OPLS, BIO+, and AMBER. Parameters missing from the force field will be automatically estimated. The user has some control over cutoff distances for various terms in the energy expression. Solvent molecules can be included along with periodic boundary conditions. The molecular mechanics calculations tested ran without difficulties. Biomolecule computational abilities are aided by functions for superimposing molecules, conformation searching, and QSAR descriptor calculation. 

For the periodic boundary conditions described below, the cutoff distance is fixed by the nearest image approximation to be less th an h alf th e sm allest box len gth. With a cutoff an y larger, m ore than nearest images would be included. 

Figure 6 A schematic representation of two clustering methods, m which each point represents a single molecular conformation and the circles are the similarity cutoff distances used to define the clusters, (a) Three clusters are defined when overlapping clusters are grouped together, (h) Five clusters are defined when the overlaps are removed from one of the overlapping clusters.

Morse potential). The constant C is defined such that t/ (r) = 0 at the cutoff distance R. The interaction range is determined by the parameter a, which Viduna et al. choose very large, a = 24. Hence the cutoff distance can be made small (R = 1.25cr in [144]). This model was first used by Gerroff et al. [147] and is discussed in some detail in Chapter 12 of this book. 

These functions are truncated and shifted to zero at a cutoff-distance between the third and fourth nearest neighbor shell. N ai is the number of valence electrons and U4s is a parameter. Following Daw and Baskes further on we use cubic spline functions to represent the functions and Z(r). The splii s have been fitted to... 

This is similar to the simple atom-atom truncation except that dipolar groups will never be split by the cutoff distance. There is still the problem of discontinuities, but these are less extreme than in the case of atom-atom truncations. In cases where water is explicitly included, this approach exhibits the curious phenomena of hot water and cold protein if the entire system is coupled to a heatbath. This is because the more mobile atoms (the water) are subjected to more discontinuities which makes them hotter than the less mobile atoms (the protein) (Levitt, M., Weizmann Institute, personal communication, 1986.). It should be noted that this is one of the most commonly used methods of truncation for simulations where CHARMM is not used. For the group-group truncation, these calculations are in progress and will be reported elsewhere. For this type of truncation, both methods where the list is updated on... 

The RMS displacement as a function of time for the shifted potential simulations are shown in Figure 3. As expected for this functional form, the longer cutoff distances result in a smaller RMS deviation from X-ray. The results for the 100 picosecond analysis section of all of the simulations are summarized in Table IV. For Table IV, the term "rdie" indicates that a distant dependant dielectric was used, cdie indicates that a constant dielectric was used, and eps2 indicates that the electrostatic forces have been scaled by 0.5. 

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