New Numerical Solutions for Density Functional Theory

描述（申请人提供）：第一性原理（从头算）量子化学方法广泛应用于生物学、化学和材料科学的计算研究。在各种量子化学模型中，密度泛函理论（DFT）在计算成本和精度之间取得了很好的平衡，因此在包括生物研究在内的许多科学领域中应用最为广泛。在这个项目中，我们建议开发和实施两种新方案，这将显著降低DFT计算的计算成本，可能降低3倍或更多。首先，我们将实现傅立叶变换库仑（FTC）方法来评估库仑对DFT的贡献。FTC已经被证明能够将库仑相互作用的计算速度提高一到两个数量级，并且通过将其与Q-Chem中已经存在的其他有效的库仑方法相结合，我们将实现显着的性能改进。其次，我们提出了一种新的数值格式来提高交换相关（XC）对DFT的贡献的计算效率。这种新方法被称为多分辨率XC (mrXC)，它认识到一个基集中的高斯函数具有不同的分辨率，而那些低分辨率（在空间上缓慢变化）的高斯函数可以在一个更宽的数值网格上进行评估。由于大多数XC网格点位于网格密度较高的区域，因此可以显著减少CPU时间。计算库仑和XC项是DFT计算中最耗时的步骤，因此本项目的改进将大大减少执行时间并提高研究人员的生产力。这些改进将使DFT更接近我们的目标，即能够取代目前在分子动力学或蛋白质和其他大分子系统的蒙特卡罗模拟中使用的精度较低但计算要求较低的模型。

DESCRIPTION (provided by applicant): First principle (ab initio) quantum chemistry methods are widely used for computational studies in biology, chemistry and material science. Among the various quantum chemistry models, density functional theory (DFT) offers a good balance between computational cost and accuracy and accordingly is the most widely used method in many scientific fields, including biological research. In this project, we are proposing to develop and implement two new schemes that will significantly reduce the computational cost of DFT calculations, possibly by a factor of 3 or more. First, we will implement the Fourier Transform Coulomb (FTC) method to evaluate the Coulomb contribution to DFT. FTC has been shown to be capable of speeding up computation of the Coulomb interaction by one to two orders of magnitude, and by combining it with other efficient Coulomb methods already in Q-Chem, we will achieve significant performance improvements. Secondly, we propose a novel numerical scheme to improve the computational efficiency of the exchange-correlation (XC) contribution to DFT. The new method, called multiresolution XC (mrXC), recognizes the fact that the Gaussian functions in a basis set have different resolutions, and those with a low resolution (slowly-changing in space) can be evaluated on a courser numerical grid. The CPU time can be significantly reduced since most of the XC grid points are in the regions with high grid density. Evaluating the Coulomb and XC terms are the most time-consuming steps in a DFT calculation, and therefore the improvements in this project will substantially reduce execution time and enhance the productivity of researchers. These improvements will bring DFT much closer to our goal of being able to replace the less accurate but computationally less demanding models currently used today in molecular dynamics or Monte Carlo simulations of proteins and other large molecular systems.