Nonbonded radii

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. 

This example shows the round particle in cell B,B with two possible nonbonded cutoffs. With the outer cutoff, the round particle interacts with both the rectangle and its periodic image. By reducing the nonbonded cutoff to an appropriate radius (the inner circle), the round particle can interact with only one rectangle—in this case, the rectangle also in cell B,B. ... 

Waals radius rj for each atom type and a hardness parameter ej that determines the depth of the attractive well and how easy (or difficult) it is to push atoms close together. There are interactions for each nonbonded ij pair, including all pairs. The parameters for a pair are obtained from individual atom parameters as follows ... 

To a first approximation, atoms in molecules may be regarded as hard spheres with a segment cut off in the bonding direction, as in the familiar space-filling models. The radius of the atom in a nonbonding direction is called the van der Waals radius. Half the distance between two atoms of the same kind in adjacent molecules at equilibrium is taken as the van der Waals radius (Figure 5.1). In assigning a fixed radius in this way, we assume that atoms... 

Element 1,3 Nonbonded Radius Van der Waals Radius Radius of Isolated Gas Phase Atom3... 

At the heart of the AIM theory is the definition of an atom as it exists in a molecule. An atom is defined as the union of a nucleus and the atomic basin that the nucleus dominates as an attractor of gradient paths. An atom in a molecule is thus a portion of space bounded by its interatomic surfaces but extending to infinity on its open side. As we have seen, it is convenient to take the 0.001 au envelope of constant density as a practical representation of the surface of the atom on its open or nonbonded side because this surface corresponds approximately to the surface defined by the van der Waals radius of a gas phase molecule. Figure 6.15 shows the sulfur atom in SC12. This atom is bounded by two interatomic surfaces (IAS) and the p = 0.001 au envelope. It is clear that atoms in molecules are not spherical. The well-known space-filling models are an approximation to the shape of an atom as defined by AIM. Unlike the space-filling models, however, the interatomic surfaces are generally not flat and the outer surface is not necessarily a part of a spherical surface. 

The hard sphere exclusion distances for this system were chosen as follows nonbonded backbone carbons, 4.60 R (twice the C-H bond distance plus van der Waals radius for H) non-neighboring fluorines, 2.70 R (twice van der Waals radius for F) neighboring fluorines, 6.39 R (distance across phenyl ring using dimensions of Table I and van der Waals radius for Hof... 

Vy The van der Waals radius. A useful measure of group size. The internuclear distance between two nonbonded atoms in contact is equal to the sum of their van der Waals radii. 

The van der Waals radius is defined as a nonbonded distance of closest approach, and these are calculated from the smallest interatomic distances in crystal structures that are considered to be not bonded to one another. Again, these are average values compiled from many crystal structures. If the sum of the van der Waals radii of two adjacent atoms in a structure is greater than the measured distance between them,... 

Nonbonded radii enable us to rationalize aspects of crystal chemistry that cannot be understood in terms of the ionic model. For instance, it is difficult to understand why silicon is four-coordinated in most oxides. This is unlikely to be because of the radius ratio of the classical ionic model 81 is too small to have four oxygens around it. Six-coordinated silicon is known in certain cases (e.g. SiP207) silicon is octahedrally coordinated in fluorides, although the ionic radii of and F are similar. The reason... 

Table 1.6. Nonbonded radius R and bond length to oxygen I in tetrahedral compounds and their ratio"...

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