# Electron correlation vs electron exchange

• I
• Rzbs
In summary, electron correlation and electron exchange are two different phenomena in quantum mechanics. Electron correlation occurs when the behavior of one particle is influenced by the behavior of another particle, while electron exchange is a result of the indistinguishability of particles. These concepts can be explained using correlation functions and are often combined into a single exchange-correlation term. In classical approximations, the Hartree product wavefunction is used, but to account for exchange symmetry, a Slater matrix must be considered. The fully correlated wavefunction cannot be expressed as a single determinant and is known as the full CI limit.

#### Rzbs

TL;DR Summary
What is difference between electron correlation and electron exchange?
What is the difference between electron correlation and electron exchange?
Which of them is due to the spin of electrons and which is due to charge of electrons?

All of this can be easily understood mathematically using the so-called correlation functions, but I'll try to explain with words.

First, consider two neutral (non interacting) classical particles. In this case the two particles basically ignore each others so the evolution in time of each particle is totally independent (uncorrelated) of the other.

Now let's add a little bit of quantum mechanics: suppose the two particles are now indistinguishable. This is a purely quantum mechanical phenomenon and it changes the system. The two particles are still non-interacting (so their time evolution is still independent from each other) but now you get all the quantum mechanical effects that follow from indistinguishability (ex. exclusion principle). This is roughly the electron-exchange.

Finally suppose the particles are charged. Now the evolution of one particle is dependent of the other in a pretty complicated way and we say the particles are correlated.

Schematically you can think it this way:
classical view + exchange + correlation = real qm description.

In some cases the exchange term and the correlation terms are unified into the so-called exchange-correlation term.

etotheipi and Rzbs
Thanks

The most classical approximation to a many electron problem is via a Hartree product wavefunction. To get exchange symmetry, you have to consider all permutations and end up with a Slater matrix. This is the most general wavefunction describing somehow non-correlated electrons (each electron sees only the average field of the other electrons). The fully correlated wavefunction cannot be expressed as a single determinant but only as a (in principle infinite) sum of these. This is called the full CI (configuration interaction) limit.

dRic2 and Rzbs
Thanks.

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