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We use density-matrix renormalization group, applied to a one-dimensionalmodel of continuum Hamiltonians, to accurately solve chains of hydrogen atomsof various separations and numbers of atoms. We train and test amachine-learned approximation to $F[n]$, the universal part of the electronicdensity functional, to within quantum chemical accuracy. Our calculation (a)bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals,(b) includes the strong correlation of highly-stretched bonds without anyspecific difficulty (unlike all standard DFT approximations) and (c) is soaccurate that it can be used to find the energy in the thermodynamic limit toquantum chemical accuracy.

Pure density functional for strong correlations and the thermodynamic limit from machine learning