Cutoff radius

Fig. 5. To generate an ensemble using Molecular Dynamics or Monte-Carlo simulation techniques the interaction between all pairs of atoms within a given cutoff radius must be considered. In contrast, to estimate changes in free energy using a stored trajectory only those interactions which are perturbed need be determined making the approach highly efficient.

C- cutoff radius method - all non-bonded forces between particles within angstroms of each other are computed explicitly... 

Calculating nonbonded interactions only to a certain distance imparts an error in the calculation. If the cutoff radius is fairly large, this error will be very minimal due to the small amount of interaction at long distances. This is why many bulk-liquid simulations incorporate 1000 molecules or more. As the cutoff radius is decreased, the associated error increases. In some simulations, a long-range correction is included in order to compensate for this error. 

Figure 2 A particle i interacts mainly with particles that are within the cutoff radius The neighbor list contains only those particles that are within a sphere of radius rj > Particles outside this sphere will not contribute to the force or energy affecting particleThe use of a neighbor list that is periodically updated during the simulation reduces the computer time required in calculating pairwise interactions.

Increasing the cation-solvent interaction radius from 8 to 10 A while the solvent-solvent interactions remain at 8 A results in only a small change (< 0.1 kcal/mol) in the free energy. However, if the solvent-solvent interaction radius is also increased to 10 A the change in the free energy becomes +0.4 kcal/mol which is much larger than would be expected from the water-image effect. It appears that for this mutation the choice of cutoff radius for the solvent-solvent interactions is more important than the radius for the cation-... 

Using the smaller van der Waals cutoff radius (3.0 2, the calculations gave three conformations Sickles l and 3, and Extended) totaling almost 93% of the total population (Table II). As expected, Sickle-1 and Sickle-3 were the dominant conformers, but the Extended conformer was also calculated to be present in... 

When a van der Waals cutoff radius of 3 A was used to calculate the conformational populations of JV,J -dihexylxYlaramide (2), similar results were obtained (Table III). Sickles-1 and 3 and the Extended conformation accounted for 94% of the total conformational population. Again, good agreement was obtained for calcd (3.66 Hz) and J2 3 xpt (3.32 Hz). 

The Fermi energy ej is found by imposing that at the cutoff radius the potential... 

We will adopt this model for e-j-pj) and pj-p from an inner radius r = Tq to the cutoff radius r=ri = bxj. In the inner region they will be replaced by quantum mechanical values than can be foimd from the solution of Schrodinger equation with the asymptotic expansion of the potential... 

We have carried out calculations for transitions for which empirical energy data were available [3,5,6,7], The core polarizabilities have been take from Fraga et al. [13], Since there is no analytical way of obtaining the cutoff radius r, we have chosen a value equal to the core mean radius, calculated in accord with an expression given by Chichkov Shevelko[14],... 

We ask how big are nuclei Our zero-order answer is that the radii of nuclei are in the range of 1 -10 fm. Our first-order answer to this question begins by assuming the nucleus is spherical with a uniform density out to some sharp cutoff radius, that is, the nucleus has the shape and density distribution of a billiard ball. This density distribution is shown in Figure 2.9. 

The computer simulations employed the molecular dynamics technique, in which particles are moved deterministically by integrating their equations of motion. The system size was 864 Lennard-Jones atoms, of which one was the solute (see Table II for potential parameters). There were no solute-solute interactions. Periodic boundary conditions and the minimum image criterion were used (76). The cutoff radius for binary interactions was 3.5 G (see Table II). Potentials were truncated beyond the cutoff. 

Thus uii is reduced from the classical plasma frequency by a factor 3-1/2. This has the effect of reducing the cutoff radius (response radius) by a factor 3-1 3 for a spherical atom. It has been shown that this resolves another difficulty with the plasma-response model, which implies response radii greater than the classical turning radius of the most weakly bound electron in an atom. The dielectric-response radius is in general less than the classical turning radius [12]. 

Beyond a chosen cutoff radius, the all-electron and pseudofunctions (potential and wavefunction) are identical, while inside the core region both the pseudopotential and pseudowavefunction are smoothly varying. After the construction of these pseudofunctions for a single atom and ensuring that their scattering properties are almost identical to those of the all-electron functions, they can be used in any chemical environment. 

It is to be stressed here that besides choosing a large enough cutoff radius one must pay attention to two further points (for any finite radius) ... 

The zeolite framework was described by a specific force field developed by van Santen et al. [11] while the hydrocarbon molecules and their interaction among themselves and with the zeolite lattice were described by the generic force field Drdding n [12]. All the internal coordinates of the alkane molecules were allowed to fully relax. The nonbonded interactions (electrostatic and van der Waals) were computed for aU atoms within a cutoff-radius of 12A. Periodic boundary conditions were imposed along the three axes of the zeolite model to simulate an infinite crystal. 

Figure 8 Coulomb energy for the a-quartz structure calculated as a function of cutoff radius.

A simple but primitive method is to use a cutoff radius the summation is carried out to a predefined interatomic distance only, the cutoff radius beyond that distance, all interactions are neglected. This method works reasonably well with potentials that decrease regularly and rapidly with increasing interatomic distance, e.g., the Lennard-Jones potential. In the case of a periodic lattice, as is the case with zeolites, it is also easy to improve the overly simple cutoff treatment by implementing an approximation for the summation of the interactions beyond the cutoff radius ... 

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