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Sorry, I now see that I completely misread the diff. I originally thought the ExchangeCorrelationEnergy PT was replacing the ExchangeCorrelationPotential PT, but that's not at all what happened. Making ExchangeCorrelationPotential a specialization of TwoCenterAOTensorRepresentation is the way to go.
As for making EXC a specialization of BraKet, we don't have to do this now (I'll open an issue to revisit this), but I do think it would simplify the code if we do so (in particular I think we get rid of the edge case in the energy evaluation). The name BraKet is perhaps not the greatest, but the BraKet property type covers matrix elements between two (possibly different) many-electron wavefunctions; so it's not just for expectation values. In the context of general DFT, there's no wavefunction so BraKet doesn't make sense, but at least for KS DFT there is a wavefunction so BraKet seems viable. BraKet is templated on the bra and ket wavefunction types, so if it doesn't make sense for BraKet to be defined for anything other than an expectation value we can restrict bra == ket
Originally posted by @ryanmrichard in #96 (comment)