The van der Waals (more accurately, the Lennard-Jones) term comes in two versions, an exclusion list version (this version vdw-) and an inclusion list version (see vdw+ above). In the exclusion list version, every pair of atoms in the system is assumed to contribute to the total van der Waals interaction unless explicitly excluded in an exclusion list. In the inclusion list version, the pairs of atoms that contribute to this interaction are explicitly listed. The vdw- term is the correct choice if the majority of atom pairs contribute to the van der Waals interaction; the vdw+ term would have required a very long listing of pairs. The inclusion list version is the better choice if there is only a small number of interactions; the vdw- term will require a prohibitively large exclusion list. Only one version or the other should be used in a descriptor; it is unlikely to be useful (but it is not impossible) to use both versions in a single descriptor.

For a system of N_atom atoms, there will be a maximum of N_atom(N_atom-1)/2 van der Waals interactions, each interaction is of the form:

T[ rij ]{ A / rij12 - B / rij6 }

where T[ r_ij ] is a trimming function, which operates from zero or r_start and completes its transformation at r_finish. Trimming Function Details [will open in a separate window]. A and B are constants dependent on the atoms atom_i and atom_j and r_ij is the current distance between these two atoms.

Out of the maximum number of N_atom(N_atom-1)/2 pairs of van der Waals interactions, a number of these N_exclude will be excluded from consideration. (These are usually closely bonded pairs of atoms.) The van der Waals function decays very slowly to a zero value; the zero value is achieved only at infinity. The trimming function increases the decay so that the potential achieves a zero value at a finite distance, at r_finish. This reduces the number of atom pairs for which the van der Waals term has to be evaluated. Thus, the van der Waals interaction is evaluated from a list of atom pairs; the candidate list. The candidate list contains pairs of atoms that are not in the exclusion list and whose distance is within a distance r_cutoff which is slightly larger than r_finish. This list is updated regularly so that it remains accurate in between updates. The list update interval and r_cutoff is user selected. The list update interval should be as infrequent as possible but that will require a large value for r_cutoff. On the other hand, r_cutoff should be as small as possible to reduce the number of computations. A compromise has to be made to select optimal values for these two paramaters.

The vdw- record in the descriptor file has the form:

vdw-	trim	Nexclude	Ntype	rstart	rfinish	rcutoff
	A11	A12	...
		A22	...
			...
	B11	B12	...
		B22	...
			...
		atomi	atomj
		...	...

The record starts with the keyword vdw- followed by a code trim, then the number of atom pairs to be excluded N_exclude, the number of atom types N_type (it must be at least as large as the largest atom type number in the type record), the starting distance at which the trimming starts r_start, the distance at which trimming is complete r_finish and finally the cutoff distance r_cutoff.

Following the header line are N_type(N_type+1)/2 constants for the r^-12 term A₁₁, A₁₂, A₂₂, ... for interactions between all possible pairs of different atom types (not atom numbers). Since A₂₁ has the same values as A₁₂, only one of these values need to be specified, and these are listed in the order shown above. The values for the dissimilar atom type pairs must be listed because mimesis does not have any built-in combination rules. This also means the user has the flexibility to use any combination rule.

Following these are the same number of constants for the r^-6 term B₁₁, B₁₂, B₂₂, ...

The record concludes with N_exclude pairs of atoms atom_i and atom_j that are to be excluded from energetic considerations. The pairs must be listed in a strictly increasing order. atom_j must be larger than atom_i and each atom_i must be equal or larger than the previous atom_i. An atom cannot exclude itself.

trim is a code to select the trimming function as follows:

trim	1	2	3
Trimming Function	Truncate	Switch	Shift

Trmming modifies the van der Waals function. To minimize the effect, select the truncation function (trim=1) and set a very large value for r_finish (the largest linear dimension of the system for example). However this will result in a very large increase in memory usage and in the number of computations.

Example:

vdw-   2   15   3   12.5   15.0   17.5

107800   107800   120700
         1.254    12840
                  12790
5041     5060     6885
         10.87    1859
                  1845
1   2
1   3
1   4
1   5
1   6
2   3
2   4
2   5
2   6
3   4
3   5
3   6
4   5
4   6
5   6

A vdw- record with 5 terms. The Switching function is selected and it will operate from 12.5Å to 15Å. There is no built-in combination rules in mimesis. Values are supplied for the constants A and B for dissimilar pairs (off-diagonal elements) using a complex combination rule.