The adiabatic connection formalism in DFT – theory and practice

The adiabatic connection formalism yielding an exact expression to exchange–correlation functional, has been instrumental in building DFT approximations. Here, we derive and analyze the density-fixed adiabatic connection (AC), which gives an exact expression of the DFT’s exchange–correlation functional. We give an outline of the exact features of the key AC quantities, yielding physical constraints for constructing approximations to the exchange–correlation functional. Lastly, inspired by recent progress in the AC developments in wave function theories, we discuss the similarities and differences between the AC in DFT and wave function formalisms.