At what frequency does a non-polar molecule acquire a dipole able to participate in London Dispersion forces?

London Dispersion forces are forces between non-polar non-ionic molecules that the random fluctuation of their electrons makes them temporarily dipoles.


* What is the frequency that this occurs?
* Every how many milliseconds does a molecule like this becomes a dipole?
* Are there such numbers for some specific molecules out there?




According to [Prof. Loren Williams of Georgia Tech](http://ww2.chemistry.gatech.edu/~lw26/structure/molecular_interactions/mol_int.html#DF), the fluctuations occur on the femtosecond $\left(10^{-15}\ \mathrm{s}\right)$ time scale:



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> [![Figure 13 from website of Prof. Loren Williams](https://i.stack.imgur.com/zkfvE.jpg)](https://i.stack.imgur.com/zkfvE.jpg)
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> Figure 13 shows how fluctuating dipoles of liquid Xenon (or Helium or Neon, etc) are coupled. Darker blue indicates higher electron density. The fluctuations are correlated and are very fast, on the femtosecond ($10^{-15}$ second) timescale. Adjacent Xenon atoms experience electrostatic attraction from the transient dipoles. Two different representations of fluctuating dipoles are shown.
> 
> 
> 


This corresponds to a frequency of $1\ \mathrm{PHz}$ ([petahertz](https://en.wikipedia.org/wiki/Metric_prefix)), which is about five hundred thousand times faster than most modern [computer processors](https://en.wikipedia.org/wiki/Central_processing_unit).


Another estimate of the time scale (albeit one devised by me and thus of potentially suspect validity), is the SI value of the [atomic unit](https://en.wikipedia.org/wiki/Atomic_units) for time, derived by dividing the reduced Planck constant by the atomic unit for energy, the [Hartree](https://en.wikipedia.org/wiki/Hartree) (values are rounded a bit):


$$
\left\{atomic\ time\right\} = \frac{\hbar}{E\_\mathrm{h}} = \frac{1.05457\times 10^{-34}\ \mathrm{J\cdot s}}{4.3597\times 10^{-18}\ \mathrm{J}} = 2.41888\times 10^{-17}\ \mathrm{s} \approx 0.024\ \mathrm{fs} = 24\ \mathrm{as}
$$


That last value is $24$ [*attoseconds*](https://en.wikipedia.org/wiki/Metric_prefix), which is a well and truly short span of time. For comparison, this corresponds to a frequency of $41\ \mathrm{PHz}$.


Whatever the exact value, I have to believe the fluctuations are fast enough so as to be impossible to measure directly. (I would be fascinated to learn otherwise, though!) Thus, even if different atoms/molecules do actually have different frequencies of London dipole oscillation, we have no way of finding out these values.


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While dispersion forces dominate in non-polar, non-ionic systems, they are actually felt by all chemical species that contain electrons. But, for simplicity's sake, let's use the example of a non-polar, non-ionic atom or molecule to describe these forces in this answer.


Surprisingly, these molecules are almost never completely "non-polar". There is almost always a dipole moment, but the strength and direction are random. The electron densities around these atoms and molecules are always shifting, which almost always leaves an uneven distribution of electron density around the nucleus.


The London dispersion forces are simply the sum of interactions between the constantly fluctuating dipoles of one particle, and the induced dipoles within the neighboring particles. The influence of the electrostatic force is directly proportional to the product of polarizabilities for each participating particle.


To summarize: Molecules or atoms with no permanent dipole are almost never in a completely "non-polar" state, due to the constantly fluctuating electron cloud. This negates the question of instantaneous dipole frequency, because it is never not a dipole.


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The electron rich/ electron poor regions tend to oscillate at a period of about 1-10 femtoseconds.


[Logothetidis, Stergios. *Nanostructured Materials and Their Applications*. N.p.: Springer, 2012.](http://www.springer.com/us/book/9783642222269).


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