Pure Density Functionals for Efficient, Predictive Simulations

该奖项支持计算和理论研究，以及旨在使材料性能的预测模拟更快、更有效的教育。更复杂、微妙的材料的计算建模应该是可能的。对各种设备和药品新材料的预测也将加快。它还将推进我们对电子在材料中的行为的基本理解，并有助于培养下一代计算材料研究人员。最先进的材料性能模拟方法是分子动力学。在这个理论中，物质的组成原子的运动是根据作用在它们身上的力来计算的。这些力来自电子，电子将材料粘合在一起，从而决定了它们的许多物理和化学特性。计算作用于原子的力是一个棘手的量子力学问题。Kohn-Sham密度泛函理论（KS-DFT）是将这一棘手问题重新表述为单个电子在非常特殊的外场中运动的简单问题。原则上，KS-DFT是精确的。虽然KS-DFT外场的许多性质已被证明，但其确切形式尚不清楚，必须加以近似。目前被称为GGAs（广义梯度近似）的主力模型简单且计算成本低，但缺乏通用性。这些模型必须根据实验数据进行调整；当这些数据缺失时，它们就缺乏预测能力。这种调整对于所谓的“meta-GGA”（意为“超越GGA”）来说是不需要的——它们利用电子动能（运动能量）的空间分布来对电子力做出可靠的预测。然而，基于meta-GGA的计算明显比基于GGA的计算慢。分子动力学模拟可能需要数万次KS计算。因此，由此导致的慢速是大规模和高通量研究的主要障碍。此外，密度的自然分解为特定的贡献导致了所谓的广义KS方程，它与原始方程不同。然后推导出不同材料的物理特性。这个项目解决了这两个问题。它用电子密度的空间导数的组合取代了出现在动能密度对元- gga贡献中的分解贡献。它们是根据严格的理论要求精心设计的，具有良好定义的物理内容和计算稳定。通过用单个量代替多个贡献量，可以恢复gga水平的效率。这提高了材料中电子行为的基本知识，并为许多计算方法提供了见解。该项目支持培养1名研究生、1名本科生和1名博士后。PI和co-PI之间的合作将教育他们成为KS-DFT高级配方的创新者、实施者、验证者和第一批用户。他们将与主要社区电子结构计算机代码的开发人员接触。这个研究项目的社会效益，如果成功，将比目前可能更快地在更大的系统上进行更多样化的模拟，最终可能导致设备、加工和药品的技术材料的进步。该奖项支持计算和理论研究，以及旨在限制由Kohn-Sham密度泛函理论（KS-DFT）计算驱动的复杂材料从头算分子动力学（AIMD）模拟的计算成本扩大的教育。电子力的KS-DFT计算是AIMD的速率限制器，通常占每个AIMD核步骤时间的90%以上。这个问题的基础是，对于这两种材料及其分子成分进行公平处理的最佳可用交换相关（XC）泛函是元广义梯度近似（meta-GGAs）。由于它们明显依赖于KS轨道，与“低阶”、与轨道无关的XC泛函相比，meta- gga显著降低了aim模拟的速度。轨道依赖问题只会在量子化学中流行的“高阶”官能团中恶化。与此密切相关的动机是开发具有元- gga质量或更好质量的真正KS量，而不是由于计算复杂性而几乎总是使用元- gga完成的广义KS解。第三个动机是推动基于约束的近似XC泛函的效用，仅依赖于电子密度及其衍生物。后者的解决涉及长期存在的计算稳定性问题，当使用像拉普拉斯等高阶导数时。元- gga的“去轨道化”是实现可负担的更高阶DFT性能的新途径。它用密度约束的空间导数组合来模拟轨道依赖，取代了元gga中的轨道依赖。该项目建立在PI的团队首次成功的现代元gga去轨道化的基础上。[j] .生物工程学报，1997,11(2):451 - 451。[j].生物工程学报，2016,33(5):1181 - 1181。SCAN的去轨道化（称为SCAN- l）对固体和分子同样有效，成本降低30%。自20世纪90年代末以来，除了co-PI和PI的工作外，对密度拉普拉斯算子的研究很少。先前的去轨道化工作证明了该方法的可行性，但其局限性尚不清楚。本项目的重点是系统地探索拉普拉斯相关泛函的实际限制，包括：理论约束的发展，精确的、数值稳定的交换相关势的构建，改进的去轨道化，以及比去轨道化更高精度的从头泛函的构建。预期的结果是AIMD计算成本缩放的实际边界，以及对KS问题的更深入理解。材料研究部和化学部为该奖项提供资金。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis 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 SUMMARYThis 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.