Pure Density Functionals for Efficient, Predictive Simulations

University Of Florida, Gainesville FL

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports computational and theoretical research, and education aimed to make the predictive simulation of the properties of materials faster and more efficient. Computational modeling of more complicated, subtle materials should be possible. The prediction of new materials for diverse devices and pharmaceuticals would also be accelerated. It would also advance our fundamental understanding of how electrons behave in materials and help train the next generation of computational materials researchers. The state of the art method for material properties simulation is molecular dynamics. In it, the motion of the constituent atoms of a material are calculated from the forces acting upon them. Those forces are from the electrons, which glue materials together and therefore determine many of their physical and chemical characteristics. Calculating forces on atoms is a formidable quantum mechanics problem. Kohn-Sham Density functional theory (KS-DFT) is a re-expression of that tough problem into a simpler one of individual electrons moving in a very special external field. KS-DFT in principle is exact. Though many properties of the KS-DFT external field have been proved, its exact form is unknown and must be approximated. Current workhorse models, known as GGAs (generalized gradient approximations) are simple and computationally cheap but lack generality. These models must be tuned to experimental data; they lack predictive power when such data is missing. This tuning is not needed for so-called "meta-GGAs" (for “beyond GGA”) – they make use of the spatial distribution of the kinetic energy (energy of motion) of electrons to make robust predictions of electronic forces. However, meta-GGA based calculations are notably slower than those based on GGA. A molecular dynamics simulation may need tens of thousands of KS calculations. So, the resulting slow-down is a major barrier to large-scale and high-throughput studies. In addition, the natural resolution of the density into specific contributions leads to so-called generalized KS equations, which differ from the original ones. Different materials physics is then imputed. This project addresses both problems. It replaces the resolved contributions appearing in the kinetic energy density contribution to a meta-GGA with combinations of spatial derivatives of the electron density. These are crafted from rigorous theoretical requirements to have well-defined physical content and be computationally stable. By replacing many contributions with a single quantity GGA-level efficiency is recovered. This leads to enhanced basic knowledge of electron behavior in materials and contributes insights for a number of computational approaches. The project supports education of a graduate, an undergraduate student, and a postdoctoral associate. Collaboration between the PI and co-PI will educate them as innovators, implementers, validators, and first users of advanced formulations of KS-DFT. They will engage with the developers of major community electronic structure computer codes. Societal benefits of this research project, if successful, will be faster simulations on larger systems of greater variety than currently possible leading eventually to likely advances in technological materials for devices, processing, and pharmaceuticals. TECHNICAL SUMMARY This award supports computational and theoretical research, and education aimed to cap the scale-up of computational costs for ab initio molecular dynamics (AIMD) simulations of complex materials, driven by Kohn-Sham density functional theory (KS-DFT) calculations. KS-DFT calculations of the electronic forces are the rate-limiters for AIMD, typically constituting more than 90% of the time of each AIMD nuclear step. Underlying this issue is that the best available exchange-correlation (XC) functionals for even-handed treatment of both materials and their molecular constituents are the meta-generalized gradient approximations, meta-GGAs. Since they depend explicitly on the KS orbitals, meta-GGAs significantly slow down AIMD simulations as compared to "lower-rung", orbital-independent XC functionals. The orbital dependence problem only worsens for "higher-rung" functionals popular in quantum chemistry. A closely related motivation is to develop true KS quantities with meta-GGA quality or better, rather than the generalized KS solutions that are almost always done with meta-GGAs because of their computational complexity. A third motivation is to push the utility of constraint-based approximate XC functionals dependent only on the electron density, and its derivatives as far as feasible. The resolution of the latter implicates long-standing issues of computational stability when higher-order derivatives like the Laplacian are used. The "de-orbitalization" of meta-GGAs is a novel route to affordable higher-rung DFT performance. It replaces orbital dependence in meta-GGAs with combinations of spatial derivatives of the density constrained to mimic the orbital-dependence. The project builds on the first successful de-orbitalization of modern meta-GGAs by the PI's group [Phys. Rev. A 96, 052512 (2017), Phys. Rev. B 98, 115161 (2018)]. The de-orbitalization of SCAN (called SCAN-L) works equally well for solids and molecules at 30% lower cost. With the exception of work of the co-PI and PI, little has been done on density Laplacians since the late 1990s. Prior de-orbitalization work proves the feasibility of the approach, but its limits are unknown. This project is focused on the systematic exploration of the practical limits of Laplacian-dependent functionals, including: development of theoretical constraints, construction of accurate, numerically stable exchange-correlation potentials, improved de-orbitalizations, and the construction of de novo functionals with higher accuracy than those from de-orbitalization. The expected consequence is the practical bounding of AIMD computational cost scaling, and a deeper understanding of the KS problem. The Division of Materials Research and Division of Chemistry contribute funds to this award. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.