Bypassing the Energy Functional in Density Functional Theory: Direct Calculation of Electronic Energies from Conditional Probability Densities.

Density functional calculations can fail for want of an accurate exchange-correlation approximation. The energy can instead be extracted from a sequence of density functional calculations of conditional probabilities ($CP$ DFT). Simple $CP$ approximations yield usefully accurate results for two-electron ions, the hydrogen dimer, and the uniform gas at all temperatures. $CP$ DFT has no self-interaction error for one electron, and correctly dissociates ${\mathrm{H}}_{2}$, both major challenges. For warm dense matter, classical $CP$ DFT calculations can overcome the convergence problems of Kohn-Sham DFT.