HK Confusion

[Ruben Quiroz]

The gist of the HK theorem is that there is a one to one correspondence between the ground state density and the external potential.

What confuses me is the question whether we can also calulate exited states without a wave function and if so why did we ever bother learning about wave functions.

Furthermore I can’t wrap my head around how a 3N dimensional object can be truly 3N dimensional and only contatin as much information as a 3 dimensional object. (Which is what I think HK says…)

Thanks for any and all help!

[jmontgomery@flsouthern.edu]

I think we still bother with wave functions is that there is a prescription for getting the exact result given the computational resources. For example, the post HF methods are a prescribed way to get to the exact answer. For DFT, since we do not know the XC functional, we do not have the prescribed method for getting the exact result.

[Ruben Quiroz]

Ahh, ofcourse, in the beginning the emphasis was so much on the theorems that I took them to heart maybe a bit to much. As long as the black magic for the perfect XC functional is not performed densities will be approximate!

Thank you so much 🙂

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