How Do Dipole-Dipole Interactions Influence Molecular Behavior?

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SUMMARY

The discussion centers on the mathematical proof of Equation (2.4) from the lecture notes on van der Waals forces. The scalar potential from an electric dipole is defined as φ = (p·r)/(4πε₀r³), leading to the electric field E = -∇φ and potential energy U = -p·E. Participants express confusion regarding the numerator's factor of 3 and the p dot p term in the equation. The conversation highlights the importance of coordinate systems in deriving these equations, specifically addressing the transition between Cartesian and spherical coordinates.

PREREQUISITES
  • Understanding of electric dipole moments and their scalar potential.
  • Familiarity with vector calculus, particularly gradient operations.
  • Knowledge of potential energy in electrostatics.
  • Proficiency in coordinate transformations, especially between Cartesian and spherical coordinates.
NEXT STEPS
  • Study the derivation of electric dipole potential in detail.
  • Learn about vector calculus operations, focusing on gradients and divergences.
  • Research the implications of coordinate transformations in electrostatics.
  • Examine the role of van der Waals forces in molecular interactions.
USEFUL FOR

This discussion is beneficial for physicists, chemists, and students studying electrostatics, particularly those interested in molecular interactions and the mathematical foundations of dipole-dipole interactions.

secret2
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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
 
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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)!
 
I don't think I get the 3 in the numerator, nor the p dot p term.
 
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?
 
Oh...I was working with spherical coordinates.
 
There should not be a problem whether it is a sphere coordinate or not. Every two coordinates can transform into each other.
 
It's been 4-1/2 years since he asked the question, I'm afraid,
 

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