Towards Verifying Exact Conditions for Implementations of Density Functional Approximations

Sameerah Helal, Zhe Tao, Cindy Rubio-González, François Gygi, Aditya V. Thakur

Abstract: Density Functional Theory (DFT) is used extensively in the computation of electronic properties of matter, with applications in solid state physics, computational chemistry, and materials science. Approximating the exchange-correlation (XC) functional is the key to the Kohn-Sham DFT approach, the basis of most DFT calculations. The choice of this density functional approximation (DFA) depends crucially on the particular system under study, which has resulted in the development of hundreds of DFAs. Though the exact density functional is not known, researchers have discovered analytical properties of this exact functional. Furthermore, these exact conditions are used when designing DFAs.This paper presents XCVerifier, the first approach for verifying whether a DFA implementation satisfies the DFT exact conditions. XCVerifier was evaluated on five DFAs from the popular Libxc library and seven exact conditions used in recent work by Pederson and Burke. XCVerifier was able to verify or find violations for a majority of the DFA-condition pairs, demonstrating the feasibility of using formal methods to verify DFA implementations. However, it timed out on all conditions of the recent SCAN functional, revealing directions for future work.