Subject: van der Waals SURFACES/ELECTRON DEN

From: elewars <[email-masked]>
Date: Tue, 25 Apr 2000 18:35:22 -0400

2000 April 25

Hello,

I once read somewhere that an isosurface that encloses 97% of the total
electron density of a molecule corresponds best to the experimental van
der Waals surface.

(1) Has anyone a reference to this, or to any percentage of the electron
density?
(2) Is it correct to say that the usual way to measure the "van der
Waals size" of a molecule is by X-ray diffraction (the molecules in a
crystal being considered to be in contact)?

Thanks.

E. Lewars
======

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From: "Prof. Curt M. Breneman" <[email-masked]>
Date: Tue, 25 Apr 2000 20:03:09 -0400

elewars wrote:
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There is one convention that says that for condensed phases, the Van der
Waals surface is approximated by a 0.002 e/au3 isosurface, while the gas
phase VdW surface is represented by the 0.001 e/au3 isosurface.

Curt Breneman
RPI Chemistry

---

From: "C.F. Matta" <[email-masked]>
Date: Tue, 25 Apr 2000 21:40:42 -0400 (EDT)

Dear Dr. Lewars

In Prof. R.F.W.Bader's group, we integrate the properties densities of an
atom in a molecule over the atomic basin. The basin is the region of space
enclosed by the intersection of Inter-Atomic Surfaces (IAS) and and
envelope of the density choosen at some value. I will explain HOW AND WHY
we choose this value, with the hope of answering your question.

The IASs are not arbitrary. They must satisfy a quantum condition that
arises from the application of Swinger's principle of stationary action to
a subsystem (e.g. an atom in a molecule). An IAS is the unique surface
separating 2 atoms in a molecule so that the flux in the gradient vectror
field of the density vanishes.

If one integrates atomic properties up to the 0.001 a.u. isodensity 
envelope, these atomic values sum-up to the corresponding molecular (total
system) values with reasonable accuracy. 

For example, summing atomic energies of medium-sized molecules
such as the 20 naturally occuring amino acids recovers the SCF energy to
within 1 kcal/mol (typically 0.5 kcal/mol). The sum of the atomic populations
(or the corresponding atomic charges) is typically 0.001 e for a neutral
molecule (or within 0.001 e of the molecular charge). The sum of the atomic 
volumes (molecular vol.) of the 20 amino acids integrated up to 0.001
a.u. envelope corrrelates highly with the experimental partial molar
volumes (r^2=0.971).

These results are not surprising given that the 0.001 a.u. envelope 
encloses over 98% of the electronic charge of H atoms in hydrocarbons, and
over 99% of the electronic charge of atoms Carbon to Neon.

The 0.001 a.u. isodensity envelope has been shown to yield values of
molecular diameters of several gases in good agreement with the
equilibrium diameters of these molecules determined experimentally
(e.g. by viscosoity measurements fitted to a 6-12 potential).

The 0.002 a.u. may be a more realistic measure of the molecular size in
crystal, however.

   CONCLUSION
   ==========

The 00.1-00.2 a.u. isodensity envelopes are good approximation to the
experimentally determined van der Walls sizes of molecules.

   REFERENCES
   ==========

[1]	Bader RFW. Atoms in molecules: A quantum theory. Oxford,
	U.K.: Oxford University Press, (1990). pages 182,183,199,202.
	And references therein.
	(Radii of isolated ground-state atoms and ions is given in page
	432, for both the 0.001 and 0.002 envelopes). 

[2]	Matta CF, Bader RFW. Atoms-in-molecules study of the
	genetically-encoded amino acids. I. Effect of conformation on 
	geometric,atomic, and bond properties. Proteins: Structure, 
	Function and Genetics, (2000) [In Press].
 
.......................................................................
 Cherif F. Matta		  	tel. (905) 525-9140 ext. 22502
 Chemistry Department                   fax  (905) 522-2509
 McMaster University                      
 Hamilton, Ontario, CANADA L8S 4M1.

 Member of the Board of Governors of the University
.......................................................................