New Numerical Solutions for Density Functional Theory

描述（由申请人提供）：第一原理（从头算）量子化学方法广泛用于生物学、化学和材料科学中的计算研究。在各种量子化学模型中，密度泛函理论（DFT）在计算成本和准确性之间提供了良好的平衡，因此在许多科学领域（包括生物研究）中使用最广泛的方法。在这个项目中，我们建议开发和实施两个新的计划，这将显着降低DFT计算的计算成本，可能是3倍或更多。首先，我们将实现傅里叶变换库仑（FTC）方法来评估库仑DFT的贡献。FTC已被证明能够加速计算库仑相互作用的一到两个数量级，并通过将其与其他有效的库仑方法已经在Q-Chem，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方案，以提高计算效率的交换相关（XC）的DFT的贡献。这种新方法称为多分辨率XC（mrXC），它认识到基集中的高斯函数具有不同的分辨率，并且那些分辨率较低（在空间中缓慢变化）的函数可以在较粗糙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，因此该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型分子系统的蒙特卡罗模拟中使用的不太准确但计算要求不高的模型。

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.