2020/07/03 by Aaron D. Kaplan, Kaplan, Aaron D., Biswajit Santra +19
Physics and Astronomy · Chemistry · Engineering · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Molecular Junctions and Nanostructures
paper · pdf · doi:10.48550/arxiv.2007.01917
Exact density functionals for the exchange and correlation energies are\napproximated in practical calculations for the ground-state electronic\nstructure of a many-electron system. An important exact constraint for the\nconstruction of approximations is to recover the correct non-relativistic\nlarge-Z expansions for the corresponding energies of neutral atoms with\natomic number Z and electron number N=Z, which are correct to leading order\n(-0.221 Z5/3 and -0.021 Z \ln Z respectively) even in the lowest-rung or\nlocal density approximation. We find that hydrogenic densities lead to\nEx(N,Z) \≈ -0.354 N2/3 Z (as known before only for Z \≫ N \≫ 1)\nand Ec \≈ -0.02 N \ln N. These asymptotic estimates are most correct\nfor atomic ions with large N and Z \≫ N, but we find that they are\nqualitatively and semi-quantitatively correct even for small N and for N\n\≈ Z. The large-N asymptotic behavior of the energy is pre-figured in\nsmall-N atoms and atomic ions, supporting the argument that widely-predictive\napproximate density functionals should be designed to recover the correct\nasymptotics. It is shown that the exact Kohn-Sham correlation energy, when\ncalculated from the pure ground-state wavefunction, should have no contribution\nproportional to Z in the Z\→ \∞ limit for any fixed N.\n