How Do Dipole-Dipole Interactions Influence Molecular Behavior?

[secret2]

Could anyone please provide (or start off) the proof of (2.4) of the following document?

http://www-its.chem.uva.nl/research/complex_fluids/Teaching/LectureNotes%202004%20vdWaals%202.pdf

Many thanks

 

[clive]

The scalar potential from a electric dipole is given by
\phi=\frac{\vec{p}\cdot \vec{r}}{4\pi \epsilon_0 r^3}
Then
\vec{E}=-\bigtriangledown \phi
and with
U=-\vec{p}\cdot \vec{E}

you'll get exactly Eq. (2.4)!

 

[secret2]

I don't think I get the 3 in the numerator, nor the p dot p term.

 

[clive]

You don't think you get it OR you didn't get it?

\partial_x (x^2+y^2+z^2)^{-3/2}=-\frac{3}{(x^2+y^2+z^2)^{5/2}}

Right?

 

[secret2]

Oh...I was working with spherical coordinates.

 

[wadewizard]

There should not be a problem whether it is a sphere coordinate or not. Every two coordinates can transform into each other.

 

[Vanadium 50]

It's been 4-1/2 years since he asked the question, I'm afraid,