Volume 1 Chapter 7 Using van der Waals Radii for Distance Testing

In all the non-bonded searches conducted so far, a distance range has been given to define whether two atoms form a contact. By default, the non-bonded search mechanism provides a van der Waals distance search.

Suppose that:

the distance between two non-bonded atoms i and j is dij
the van der Waals radii for these atoms are ri and rj

The two atoms are considered to be in contact if:

dij < ri + rj +t where t is a tolerance limit, set by default to 1.0Å

The default van der Waals radii are taken from A. Bondi (1964) "van der Waals Volumes and Radii" J.Phys.Chem. 68, 441-451. These values are shown in the table below (all values in Å).

If an element does not appear in the table it is assigned a value of 2.0Å.

   Ag  1.72      Ar  1.88     As  1.85     Au  1.66
   Br  1.85      C   1.70     Cd  1.58     Cl  1.75
   Cu  1.40      F   1.47     Ga  1.87     H   1.20
   He  1.40      Hg  1.55     I   1.98     In  1.93
   K   2.75      Kr  2.02     Li  1.82     Mg  1.73
   N   1.55      Na  2.27     Ne  1.54     Ni  1.63
   O   1.52      P   1.80     Pb  2.02     Pd  1.63
   Pt  1.72      S   1.80     Se  1.90     Si  2.10
   Sn  2.17      Te  2.06     Tl  1.96     U  1.86
   Xe  2.16      Zn  1.39

If the van der Waals radii and/or tolerance are to be changed from the standard values then the VDW-RAD command must be used before the CONTACT command is defined.

It should be noted that these van der Waals radii are provided merely as a starting point for non-bonded searches. Indeed, the revision of van der Waals radii is a vitally important area of research (see Nyburg and Faerman (1985) "A revision of van der Waals atomic radii for molecular crystals" Acta Crystallogr. B41, 274-279).

Ex. 5 If we try the hydrogen bonding example again with the default van der Waals distance search

CONTACT INTER 2 A 4 A

the result is shown in below.

The VDW-RAD command provides a way to modify the standard van der Waals radii and/or tolerance limit used in a search. If a VDW-RAD command is used, it must be invoked before the CONTACT command to which it is to apply.

Ex. 6 Suppose we wish to try out the example again but with a van der Waals radius of 1.6Å for oxygen and a tolerance of 0.0Å.

The VDW-RAD command must be entered before the CONTACT command as follows:

Select VDW-RAD

Please type an element symbol and radius, or press <RETURN>

Type O 1.60 <RETURN>

Please type an element symbol and radius, or press <RETURN>

Press <RETURN>

If you want to change the TOLERANCE value, type a number and press <RETURN>
Otherwise just press <RETURN> [No change]

Type 0.0 <RETURN>

The complete instruction set to conduct the search consists of

VDW O 1.6 TOL 0.0
CONTACT INTER 2 A 4 A

The result from the search is shown below.

van der Waals distance searching is particularly useful when a contact can have more than one element type as would happen when an ELDEF instruction is used.

Ex. 7 Consider the non-bonded search that follows, where TZ is either an oxygen or sulfur.

In constructing the search fragments we use: ELDEF TZ = S O
```
VDW TOL 0.0
CONTACT INTER 1 A 3 A
```

Oxygen and sulfur atoms differ greatly in size, such that a distance range suitable for one element would be inappropriate for the other. If van der Waals distance searching is used, the test distance will depend on whether TZ has been matched to an oxygen or sulfur. Combined with the VDW-RAD command this provides great flexibility in defining contacts.

Since the search above uses van der Waals distance testing it will locate fragments where the H...O and H ...S distances are less than 2.72Å and 3.0Å, respectively. An example of a hit registered by this search is shown below.

Back to Table of Contents

Volume 1 Chapter 7 Searching with Functional Groups .

7.14.3 Using van der Waals Radii for Distance Testing