Reproducibility of Density Functionals and the Role of Reusable Software in Quantum Chemistry

Susi Lehtola¹ ¹ Department of Chemistry, University of Helsinki, Finland Corresponding author: [email protected] Abstract: Density functional theory (DFT) is widely used across computational physics, chemistry, and material science to understand the behavior and properties of matter. As the exact functional is unknown and only some of its properties are known, practical calculations rely on density functional approximations (DFAs). Thanks to decades of advances in DFT, hundreds of DFAs have been published in the literature: over 600 DFAs are currently available in our Libxc library of density functionals [1], for example. In the traditional model of quantum chemistry software development, any new method such as a new DFA has to be reimplemented from scratch in every program package. As this model is essentially based on constantly reinventing the wheel, it has significant weaknesses. The duplicated effort across program packages causes a huge maintenance overhead, making it difficult to keep up the pace with the development of improved algorithms (such as new DFAs), as well as evolving computing hardware [2]. The reproducibility of scientific publications can also be questioned, as typical implementations of algorithms contain critical features that are not documented in scientific articles [3]. DFAs are an excellent example: as we have recently discussed [4], many DFAs have been ambiguously described in the original literature, and there has been little standardization with respect to naming of DFAs across various program packages; for instance, the Heyd‒Scuseria‒Ernzerhof (HSE) functionals having dissimilar definitions across various program packages. However, as exemplified by Libxc [1], an alternative model is possible: Libxc has (partially) replaced 40+ existing density functional implementations with a single reusable open source library. Libxc has become the standard DFA implementation in over 40 electronic structure packages, providing access to the exact same numerical implementation of any given density functional regardless of the numerical approach employed by these packages, which include both all-electron and pseudopotential approaches; target atomic, molecular, or solid state systems; and employ plane waves, finite differences, finite elements, or atomic basis sets to represent the orbitals, for example. Not only has Libxc greatly enhanced the scientific reproducibility of density functional calculations, but reliance on a shared implementation has also led to considerable synergies, reducing maintenance effort, enabling faster development cycles, and allowing following with the state of the art. In this contribution, I will discuss recent progress towards reusable libraries for quantum chemistry. I will also discuss pathological behaviors in a number of recent DFAs that have been recently observed already in atomic electronic structure calculations [5-7]. Keywords: electronic structure software, reusable software, density functional approximations Suggested Reading: S. Lehtola, C. Steigemann, M. J. T. Oliveira, and M. A. L. Marques, SoftwareX 7, 1 (2018). S. Lehtola, J. Chem. Phys. 159, 180901 (2023). S. Lehtola and A. Karttunen, Wiley Interdiscip. Rev. Comput. Mol. Sci. 12, e1610 (2022). S. Lehtola and M. A. L. Marques, J. Chem. Phys. 159, 114116 (2023). S. Lehtola and M. A. L. Marques, J. Chem. Phys. 157, 174114 (2022). S. Lehtola, J. Phys. Chem. A 127, 4180 (2023). S. Lehtola, J. Chem. Theory Comput. 19, 2502 (2023).