Libxc - functionals for density-functional theory

• Applicant: Professor Dr. Miguel Marques
• Subject Area: Theoretical Condensed Matter Physics ; Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 327644371

• Final Report Year: 2021

Final Report Abstract

L IBXC is a library of exchange-correlation and kinetic energy functionals for density-functional theory. The original aim was to provide a portable, well tested and reliable set of these functionals to be used by all the codes of the European Theoretical Spectroscopy Facility (ETSF), but the library has since grown to be used in several other codes as well (more than 30 at the moment, including most relevant codes in Quantum Chemistry and Solid-State Physics). With this project we had a few practical and pragmatic goals for this project. The first regarded the maintenance and further development of LIBXC. We continued our work on both the interface to LIBXC and in the test suite. Nowadays, and besides the native C interface, we developed a F ORTRAN 2013, and PYTHON , and a C++ interface. Furthermore, now all functionals in the library are consistently tested and we included automated tests to check the numerical stability of the implementations and the appearance of floating point exceptions. We also added more than 100 new functionals to the library, from the standard LDAs passing through the GGAs, metaGGAs and hybrid functionals. The second regarded implementing automatic differentiation techniques to ease the future development of LIBXC and to open the way for the use of this library to calculate high-order response functions using density-functional perturbation theory. With this is mind, LIBXC was almost entirely rewritten, with all functionals being translated to MAPLE. A driver script then translates the MAPLE code into C that can be compiled directly into LIBXC. Needless to say that this approach speeds up considerably the introduction of new functionals in LIBXC and increases the reliability of the library. Furthermore, it enabled us to generate all derivatives up to 4th order of the large majority of functionals. This allows the use of the LIBXC not only for linear response, but also second- and third-order response within density-functional perturbation theory. Finally, the last task was designed to harness the power of LIBXC in order to benchmark a large selection of functionals (including many of the lesser known ones). We compiled a large dataset designed for the efficient benchmarking of exchange-correlation functionals for solids, and used it to benchmark 33 functionals, ranging from standard local and semilocal functionals, passing through meta-generalized-gradient approximations, and several hybrids. All in all, this was an extremelly successful project that allowed the further development of LIBXC, and that will have a massive impact in the ab initio community.

Publications

• Recent developments in libxc — A comprehensive library of functionals for density functional theory.” In: SoftwareX 7 (2018), pp. 1–5
  S. Lehtola, C. Steigemann, M. J. Oliveira, and M. A. Marques
  
• “Efficient first-principles prediction of solid stability: Towards chemical accuracy.” In: npj Computational Materials 4.1 (2018)
  Y. Zhang et al.
  
• “Large-Scale Benchmark of Exchange–Correlation Functionals for the Determination of Electronic Band Gaps of Solids.” In: Journal of Chemical Theory and Computation 15.9 (2019), pp. 5069–5079
  P. Borlido, T. Aull, A. W. Huran, F. Tran, M. A. L. Marques, and S. Botti
  
• “Exchange-correlation functionals for band gaps of solids: benchmark, reparametrization and machine learning.” In: npj Computational Materials 6.1 (2020)
  P. Borlido, J. Schmidt, A. W. Huran, F. Tran, M. A. L. Marques, and S. Botti