Electron-Electron Correlations

[Modey3]

Hello,

The "holy grail" for people who do electronic structure research is to obtain a exact expression for the correlation of the electrons. What are the physical aspects of correlation? How is the correlation energy different that the coulombic energy given exactly in the hartree-fock equations? Aren't both energies electron-electron interaction energies? Thanks.

Best Regards

modey3

 

[Gokul43201]

An important aspect of correlations - one that is missed by HF theory - is that they have a frequency (or time) dependence. If I'm not mistaken, HF theory deals with only what are known as "equal time correlations", which makes it only an approximation, which in some cases, is very poor. So, I'd guess that it is the static nature of HF that is its biggest weakness.

For instance, in the case of the high density (i.e., weakly interacting) electron gas living in a positive background, the HF calculation fails pretty badly. It predicts a dispersion that diverges logarithmically at the Fermi surface (making the Fermi velocity blow up and electron effective mass vanish there, in strong contradiction to measurements).

As we learn from QFT, there are a whole host of interactions with a vacuum state that is continuously spitting out particle-antiparticle pairs that are themselves interacting in a myriad ways that contribute to the overall picture of many-body interactions. The HF calculation is just a partial sum over interaction terms of 2 particular kinds (a forward scattering, or Hartree interaction and an exchange, or Fock interaction term). To avoid the divergence of HF theory for the electron gas, one must go to the next order of interactions, which gives rise to what is known as the Random Phase Approximation.

PS: It would be prudent of you to wait to get a second opinion on this. A theorist's perspective will, no doubt, be more accurate and useful.