The volume exclusion term comes in two versions, an inclusion list version (this version nbn+) and an exclusion list version (see nbn- next). In the inclusion list version, every atom pair that has a volume-exclusion interaction is explicitly listed. In the exclusion list version, every pair of atoms is assumed to have a volume-exclusion interaction unless a pair is explictly excluded. The nbn+ term is a good choice if there are few volume-exclusion interactions; using the nbn- term would require a very long exclusion list in this case. The nbn- term is a better choice if the majority of atom pairs have some kind of volume-exclusion interaction; using the nbn+ term would require a very long inclusion 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.

The nbn+ energy is the sum of N_include terms where each term has the form:

knb ( dij - do )n, if dij < do

0, everywhere else

---

where n is an integer greater than one, k_nb is a force constant, d_ij the current distance between atoms atom_i and atom_j and d_o is the exclusion radius for this pair of atoms. When the pair of atoms are more than d_o apart, there is no interaction. The interaction comes into play only when the atoms are closer together than d_o. Not all the pairs of atoms listed in this record will contribute anything to the total energy of the system. The interactions are calculated only from a portion of the list of non-bonds. This portion (the candidate list) consists of pairs of atoms from the larger list that are within r_cutoff d_o where the cutoff ratio r_cutoff is a number greater than one. The list of candidates is updated at regular intervals. In between updates, some of the candidate pairs move further apart while other pairs that are not in the candidate list move closer together. The list update interval and the value of r_cutoff are user controlled and have to be chosen so that r_cutoff is not too large (which requires more calculations) and the update interval is not too frequent but is frequent enough that the candidate list is always accurate.

The nbn+ record in the descriptor file has the form

nbn+	Ninclude	n	rcutoff
	atomi	knb	do	numij
		atomij
		...
	...	...	...	...

The volume exclusion record starts with the keyword nbn+ and is followed by three numbers: N_include, n and r_cutoff. Following this are N_include list of numbers. Each list consists of an atom number atom_i, a force constant k_nb, the exclusion radius d_o, the number of atoms that interact with atom_i with these parameters num_ij and finally the num_ij atom numbers atom_ij, ...

The atom numbers need not appear in any particular order and there may be more than one sub-list that starts with the same atom_i. Example:

nbn+   3   6   1.2

228   249275   50   4

288   303   318   333

231   249275   50   3

291   306   321

234   249275   50   3

294   309   324

An nbn+ record consisting of three lists. The first list is for interactions with atom number 228 and there are a total of four and these are atoms 288, 303, 318 and 333. The parameters for these interactions are a force constant of 249275 CEU/Å⁶ (495.4 kcal/mol/Å⁶) and an exclusion radius of 50Å. The other two lists contain three pairs of atoms each. The sixth power is chosen and the cutoff ratio r_cutoff is 1.2.