The adiabatic connection and coordinate scaling are both productively utilized to help obtain approximate exchange-correlation functionals. With this in mind, the lecture will begin with an outline of the derivation of the adiabatic connection formula. Then this formula will be combined with coordinate scaling to arrive at properties of the electron repulsion energy at different coupling constants along the adiabatic connections. With this knowledge, high and low density constraints for the exchange-correlation energy will be given and the incorporation of the adiabatic connection perturbation theory will be discussed.
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