A New Real-Space Finite Element Method to Solve the Kohn-Sham Equations of Density Functional Theory

求解密度泛函理论Kohn-Sham方程的新实空间有限元方法

• 批准号: 0811025
• 负责人: Natarajan Sukumar
• 金额: $ 4.8万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-10-01 至 2011-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0811025&HistoricalAwards=false
• 关键词: New; Real; Space; Finite; Element

First principles (ab initio) quantum mechanical simulations based on Kohn-Sham density functional theory (DFT) are a vital component of modern materials research. The parameter free, quantum mechanical nature of the theory facilitates both fundamental understanding and robust predictions across the gamut of materials systems, from metallic actinides to insulating organics.However, the solution of the equations of DFT (coupled Schrodinger and Poissonequations) is a formidable task and this has severely limited the range of materials systems that can be investigated by such rigorous, quantum mechanical means. Current state-of-the-art approaches for DFT calculations extend to more complex problems by adding more grid points (finite-difference methods) or basis functions (planewave and finite-element methods) without regard to the nature of the complexity, leading to substantial inefficiencies in the treatment of highly inhomogeneous systems such as those involving first-row, transition-metal or actinide atoms. This project will overcome this basic limitation of current approaches by employing partition-of-unity techniques in finite-element analysis to build the known atomic physics into the solution process, thus substantially reducing the degrees of freedom required and increasing the size of problems that can be addressed.The electronic structure and fundamental properties (mechanical, electrical, magnetic, and optical) of materials are obtained via efficient and accurate solutions of the equations of density functional theory. By virtue of its generality, the proposed partition-of-unity finite element method for electronic-structure calculations has the potential to change the way the largest, most complex quantum mechanical calculations are done, thereby paving the way for new applications in metallic, biological, and nanostructural materials that were not possible before. The external collaboration with Dr. John Pask at LLNL will lead to the development of an optimized, fully self-consistent implementation, well-suited to large-scale parallel computational platforms. This collaboration greatly strengthens the likelihood of maximum impact with the realization of faster computational times on complex simulations, such as melting of d- and f-electron systems, equation of state studies, and structure and energetics of defects in new materials.

基于Kohn-Sham密度泛函理论（DFT）的第一性原理（ab initio）量子力学模拟是现代材料研究的重要组成部分。 该理论的无参数量子力学性质有助于对从金属锕系元素到绝缘有机物的所有材料系统的基本理解和可靠预测。然而，DFT方程（耦合薛定谔方程和泊松方程）的求解是一项艰巨的任务，这严重限制了可以通过这种严格的量子力学手段研究的材料系统的范围。目前最先进的DFT计算方法通过添加更多的网格点（有限差分法）或基函数（平面波和有限元法）而不考虑复杂性的性质，从而扩展到更复杂的问题，导致在处理高度不均匀的系统时效率低下，例如涉及第一行，过渡金属或锕系原子的系统。该项目将克服目前方法的这一基本限制，在有限元分析中采用单位分割技术，将已知的原子物理学纳入求解过程，从而大大减少所需的自由度，增加可以解决的问题的规模。通过密度泛函理论方程的有效和精确的解，可以获得材料的力学、电学、磁学和光学性质。由于其通用性，所提出的用于电子结构计算的单位分割有限元方法有可能改变最大，最复杂的量子力学计算的方式，从而为金属，生物和纳米结构材料中的新应用铺平了道路。与LLNL的John Pask博士的外部合作将导致开发一个优化的，完全自洽的实现，非常适合大规模并行计算平台。这种合作大大加强了最大影响的可能性，实现了更快的计算时间对复杂的模拟，如熔化的d-和f-电子系统，状态方程的研究，以及结构和能量的缺陷在新材料。