I apologize to did some mistake in my Monte-Carlo algorithm when replying
to Wen-Shyong Tzou about article 744 of bionet.molec-model (void volume).
The void volume and its standard deviation are of course proportional
to the volume W of the window, not to the volume Vc of the cell, and
of course, Vc=Det (not Det/6) .
I also reply to Gerard J. Kleywegt (article 758 of bionet.molec-model):
the volume occupied by the solvent is not the volume of the cell minus
the volume occupied by the molecules of the chemical in the cell.
There is empty parts.
The Monte-Carlo algorithm is the simplest able to evaluate any of these
volumes. It handles situations where molecules are shared between two
ore more cells.
The algorithm to evaluate the void volume of a molecule in its cell is:
(J.Comput.Chem.1994,15[5],507-523, appendix 3).
1) Insert the cell in a parallelepipedic window (the smallest is the better)
Let W be the volume of the window.
2) Generate N uniformly distributed random points in the window
3) Let Nv be the number of points falling both inside the cell and outside
all of the atomic spheres (solvent+chemical or only chemical, depending on
what you are looking to). Let be: p=Nv/N and q=1-p.
The void volume is estimated as Vv=W*p, and its standard deviation is
estimated as s=W*sqrt(p*q/N).
Michel PETITJEAN, Email: petitjean at itodys.jussieu.fr
ITODYS (CNRS, URA34), ptitjean at ccr.jussieu.fr
1 rue Guy de la Brosse, Phone: +33 (1) 44 27 48 57
75005 Paris, France. FAX : +33 (1) 45 84 98 25