Effective local potentials for density and density-matrix functional approximations with non-negative screening density.

A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. 136, 224109 (2012)]. As illustrated, a convenient variational quantity in that approach is the "screening" or "electron repulsion" density, ρrep, corresponding to the local, KS Hartree, exchange and correlation potential through Poisson's equation. Two constraints, applied to this minimization, largely remove self-interaction errors from the effective potential: (i) ρrep integrates to N - 1, where N is the number of electrons, and (ii) ρrep ≥ 0 everywhere. In this work, we introduce an effective "screening" amplitude, f, as the variational quantity, with the screening density being ρrep = f2. In this way, the positivity condition for ρrep is automatically satisfied, and the minimization problem becomes more efficient and robust. We apply this technique to molecular calculations, employing several approximations in DFT and in reduced density matrix functional theory. We find that the proposed development is an accurate, yet robust, variant of the constrained effective potential method.

Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT.

A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds upon the method of [Callow et al., J. Chem. Phys., 2020, 152, 164114.] and differs in the expansion of the screening density in orbital basis element products instead of basis functions of an additional auxiliary set. We demonstrated the method by applying it to densities from DFT, Hartree-Fock, CAS-SCF and RDMFT calculations. For RDMFT, we demonstrate that density inversion offers a viable single-particle description by comparing the ionization potentials for atomic and molecular systems to the corresponding experimental values. Finally, we show that with the present method, accurate correlation potentials can be obtained from the inversion of accurate densities.