Subject: van der Waals surface summary

From: elewars <[email-masked]>
Date: Mon, 01 May 2000 19:00:34 -0400

2000 May 1

Here is the summary of  replies to my question:
------------
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
======
I thank all who responded. In addition, I wish to point out that on page
183 of Bader's book (_Atoms in Molecules_, Oxford, New York, 1990) it
says: for simple molecules (gases) a 0.001 au density surface, enclosing
98-99 per cent of the electron density, gives molecular sizes in good
agreement with second virial coefficient and viscocity measurements. For
presumably bigger molecules, crystal data molecular size is fitted
reasonably well by a 0.002 au isosurface (I don't know what fraction of
the total electron density the 0.002 surface encloses; maybe about 95
per cent).

Thanks again to all who replied.

EL

===========
#1
  Date:
         Tue, 25 Apr 2000 18:52:00 -0400 (EDT)
 thought the closest isosurface to the VdW surface was the 0.002
isodensity surface?  I don't know what percentage of the e- density
this contains, but I recall somebody like Warren in the early/min
(mid) 80's publishing this in a paper.

Joe

From:  Joe M Leonard <[email-masked]>

===========
#2
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:
             "Prof. Curt M. Breneman" <[email-masked]>
 Organization:
             Rensselaer Polytechnic Institute
 ===========
#3
Spartan's default value is 0.002 au, but some chemists like to use 0.001
(they
have always looked essentially the same in the few cases where I have
checked).

Re #2 -
I'll be interested to hear what you receive on this topic. The two
comments that I
(think I) can recall off the top of my head (not a very good place to
start) are one
>from Pauling and a much later one from Allinger. I seem to remember
Pauling in one of
his books (perhaps Nature of the Chemical Bond) using the intermolecular
distance
between chlorine atoms in a solid state chloroarene as a measure of the
nonbonding
distance for this atom. I don't recall if Pauling referred to this as a
"van der
Waals" distance. Allinger, in his book (Molecular Mechanics), talks at
some length
about the difficulty of using intermolecular distances obtained from
solid state
structures. For example, suppose one has a solid in which octadecane
molecules (or
something like it) are aligned side by side. Does the intermolecular
distance between
hydrogens tell us the "van der Waals" distance? Allinger says NO because
the
intermolecular distance arises from a sum of many interactions, bonded
and nonbonded.

Anyway, that's from the top of my head complete with the omissions,
distortions and
fabrications that this source often provides. Good luck,

-Alan

--------------
Alan Shusterman
Department of Chemistry
Reed College
Portland, OR
=============
#4
Dear Dr. Elewars : Kindly send me the replies to receive to
the above mentioned query. Thanks in anticipation!...Shridhar Gadre
www.reed.edu/~alan

===================
#5
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
>...................................................................
=============
#6
Hi,

I would just like to make a small comment on the side:

The van der Waals size applies to a very simple picture of a molecular
system. It is quite useful in many cases but (and this is my perhaps
misdirected warning) when it comes to scattering processes, e.g.
collisional energy transfer, the shape of the repulsive wall is of
course important.

How to go from electron density to the correct repulsive potential is
discussed in e.g.:

C. Nyeland, J. P. Toennies, Chem. Phys. 188 (1994) 205.

There is also work in progress in this field.

yours
:-)         The spring has finally come here in Goeteborg!
Harald

Harald Svedung (Ph.Lic.)                phone:          +46-31-7722816
Department of Chemistry                 fax:            +46-31-167194
Physical Chemistry                      home phone:     +46-31-240897,
+46-709223206
Goeteborg University                    home e-mail:
[email-masked]
SE-412 96 Goeteborg, Sweden             www.che.chalmers.se/~svedung/
==========
#7
Dear Dr. Lewars,
A colleague has just given me a copy of your message on the CCL
concerning electron densities. Part of your question is answered in my
paper J. Phys Chem. A 102, 6043-6051 (1998) "Behavior of Electron
Density Functions in Molecular Interactions", in which I suggest that
the 0.002 au electron density contour corresponds to the van der Waals
interaction distance in a number of weakly bound systems. The paper you
were possibly remembering is Bader, Henneker and Cade, J. Chem. Phys.
46, 3341-3363 (1967) which discusses many facets of the electron density

functions of diatomic molecules. I think they mention some percentage of

electron density being enclosed by the .001 or .002 contours. If not
there, check out other works of that period by Bader, or the more recent

Bader et al., JACS 109, 7968-7979 (1987). Regarding the question about
x-ray diffraction, if you look at (for instance) Bondi's paper (J. Phys.

Chem. 68, 441-51, 1964) I believe he used x-ray diffraction values
supplemented by other observations. However, if you consider crystalline

Cl2, the contact distance depends on the relative orientations of the
molecules. Molecular models consisting of two spherical Cl atoms with
Van der Waals radii do not account for this, but models based on the
electron density do. So the warning is: even for a single atom in a
molecule, the van der Waals radius is not a single value. How big a
problem this is depends om your application.
I hope this is of some value to you.
Sincerely yours,
John Bentley
Assistant Director
Notre Dame Radiation Laboratory
University of Notre Dame
Notre Dame, Indiana  46556-0579

e-mail: [email-masked]  telephone: 219-631-6117  fax: 219-631-8068
===============