Re: intermolecular forces

["John S. Denker" <jsd@MONMOUTH.COM>]

At 02:58 PM 2/11/01 +0200, Savinainen Antti wrote:

> I have a question on an intermolecular force between a pair of molecules.
> The force is electrostatic and it is a negative of the rate at which
> electric potential varies with respect to separation.

For typical molecules, that's not quite right.  Typical molecules are
uncharged, so they do not respond in proportion to the E-field (i.e. the
variation of potential w.r.t. separation).

In particular, an uncharged molecule in a constant E-field
(steadily-varying potential) would feel no force at all.

More commonly, the molecule develops an induced dipole moment.  This moment
is proportional to |E|.  And a dipole feels a force proportional to its
moment and proportional to the variation of E (and angular
factors).  Bottom line, roughly speaking you get a force proportional to
|E| del |E| which is equivalent to del (E^2).  If you write that in terms
of the potential it involves second derivatives as well as nonlinearities.

>   At equilibrium separation (= r0) there is no net force between the
> molecules and their potential energy has a minimum value. An increase in
> separation leads to an attractive force and a decrease in separation
> produces a repulsive force. It is easy to see this from the force against
> separation  graph. But is there a good qualitative explanation why the
> force is attractive if r > r0 and repulsive if r < r0 ?

The repulsive part has to do with quantum mechanics.  The key
misconceptions in the foregoing analysis have to do with
> The force is electrostatic
and
> their potential energy

The repulsive force has to do with kinetic energy, and it's not
electrostatic.  Think of an uncharged particle in a box.  As you decrease
the size of the box, the wavefunctions get more wiggles per unit length, so
their kinetic energy goes up.  This causes a repulsive force, i.e. a
pressure on the piston.

The same thing happens when molecules get too close.  The wavefunctions
have to have more wiggles per unit length, and .....


> The model described above is introduced in some high school books without
> explanation. Linus Pauling was the first one to apply quantum mechanics in
> chemical bonds.

Hardly the first.

> Is it even possible to understand a chemical bond using classical physics?

Not a chance.