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

Abstract

We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to $F[n]$, the universal part of the electronic density 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 any specific difficulty (unlike all standard DFT approximations) and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.

10 figures, 9 pages

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• DFT: A Theory Full of Holes?
• Infinite size density matrix renormalization group, revisited
• Kohn-Sham calculations with the exact functional
• Density functional theory in one-dimension for contact-interacting fermions

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