n2v: A density-to-potential inversion suite. A sandbox for creating, testing, and benchmarking density functional theory inversion methods

Abstract

From the most fundamental to the most practical side of density functional theory (DFT), Kohn–Sham inversions (iKS) can contribute to the development of functional approximations and shed light on their performance and limitations. On the one hand, iKS allows for the direct exploration of the Hohenberg–Kohn and Runge–Gross density-to-potential mappings that provide the foundations for DFT and time-dependent DFT. On the other hand, iKS can guide the analysis and development of approximate exchange–correlation and noninteracting kinetic energy functionals, and diagnose their errors. iKS can also play a similar role in the development of nonadditive functionals for modern density-based embedding methods. Various strategies to perform iKS calculations have been explored since the inception of DFT. We introduce n2v, a density-to-potential inversion Python module that is capable of performing the most useful and state-of-the-art inversion calculations. Currently based on NumPy, n2v was developed to be easy to learn by newcomers to the field. Its structure allows for other inversion methods to be easily added. The code offers a general interface that gives the freedom to use different software packages in the computational molecular sciences (CMS) community, and the current release supports the Psi4 and PySCF packages. Six inversion methods have been implemented into n2v and are reviewed here along with detailed numerical illustrations on molecules with numbers of electrons ranging from ~10 to ~100.

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