Optimization of local effective potentials that yield a target electron density in density functional theory (DFT) is of interest in two closely related areas. First, by solving this density-to-potential inversion problem, benchmark data can be obtained for developing improved exchange-correlation or non-interacting kinetic energy functionals. Second, most density-based embedding theories require non-additive kinetic potentials and embedding potentials as critical ingredients. It is important that these potentials are solved for accurately, especially for systems with strongly overlapping fragments.<br/>Although the forward potential-to-density problem of DFT is well-posed, <i>i.e.</i>, the Kohn-Sham potential uniquely determines the ground-state electron density, the inverse problem is ill-posed unless it is solved in the complete basis set limit. We introduce stable, efficient algorithms to perform density-to-potential inversions in DFT. When the target density is from non-interacting systems, the inverse problem can be solved by using atom-centered bases to represent both the electron density and the effective potential. However, the convergence behavior of the density and the potential largely depends on the choice of the basis functions. We focus on properly constructing the potential basis set to correctly reproduce the target density. The optimized effective potential is further regularized within the null space of the density matrix linear response, according to Koopmans' theorem and the smoothness of the potential. If the target density is from interacting systems, the inverse problem may not have solutions within finite basis sets. In such cases, we solve the inversion problem with multiwavelet bases, where both the density and the potential are effectively represented as continuous functions with guaranteed precision with respect to the complete basis set limit. Numerical examples are presented to compare the robustness of different inversion algorithms.

Density-to-potential inversions in density functional theory with atom-centered bases and multiwavelet bases

254th National Meeting (2017)

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