New Numerical Solutions for Density Functional Theory

描述(申请人提供)：第一原理(从头算)量子化学方法被广泛用于生物、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，因此是包括生物研究在内的许多科学领域中应用最广泛的方法。然而，尽管密度泛函理论在过去十年中取得了显著的进展，但其在处理大型生物系统或分子动力学方面的应用仍然受到计算成本的限制。因此，本文提出的研究目标是通过实现新的算法将DFT计算的效率提高几倍。在密度泛函计算中，有两个主要的耗时部分，即库仑和交换相关(XC)贡献的计算。在这个项目的第一阶段，我们实现了傅里叶变换库仑方法来计算库仑贡献，并发展了一种新的算法，称为多分辨XC(MrXC)，用于计算具有局域泛函的XC对DFT能量的贡献。结果表明，与最有效的库仑算法相比，FTC算法的库仑计算速度提高了4.5倍。在该项目的第二阶段，我们将开发和实现用于密度泛函计算中最广泛使用的分量的FTC和mrXC，包括基态和激发态核运动的能量和梯度。还将努力进一步提高效率。公式也将在一般梯度近似的水平上发展，这是最广泛使用的DFT泛函类型。为了证明这里开发的密度泛函算法的实用性，我们将对光诱导细菌视紫红质结构变化的机制进行最先进的计算研究。这些改进会显著增加Q-Chem的用户吗？并极大地扩展了可用密度泛函理论研究的分子系统的复杂性。此外，它将使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。本项目旨在提高密度泛函理论(DFT)的计算效率。离散傅立叶变换是分子模拟的核心，在生物研究和药物开发中得到了广泛的应用。改进后的离散傅里叶变换将显著提高研究人员的工作效率，扩大其应用范围。

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. However, despite the remarkable advances in DFT in the past decade, the application of DFT to treat large biological systems or molecular dynamics is still limited by computational cost. Accordingly, the goal of the research proposed here is to increase the efficiency of DFT calculations by several fold through the implementation of novel algorithms. There are two major time-consuming parts in a DFT calculation, namely computation of the Coulomb and the exchange-correlation (XC) contributions. In the Phase I of this project, we implemented the Fourier Transform Coulomb method for the evaluation of the Coulomb contribution, and developed a new algorithm called multiresolution XC (mrXC), for the evaluation of XC contribution to the DFT energy with local functionals. The results show that FTC accelerates Coulomb calculation by up to a factor of 4.5 over the most efficient Coulomb algorithms. The mrXC method speeds up the calculation of XC contribution by as much as a factor of 5. In the Phase II of the project, we will develop and implement FTC and mrXC for the most widely used components of DFT calculations, including energy and gradients with respect to nuclear motions for both ground and excited states. Efforts will also be made to further improve the efficiency. Formulism will also be developed at the level of general-gradient approximation, the mostly widely used type of DFT functional. In order to demonstrate the utility of DFT algorithms developed here, we will carry out a state-of-the-art computational study of the mechanism of light-induced structural change in bacteriorhodopsin. These improvements will significantly increase Q-Chem users? productivity and greatly extend the complexity of molecular systems that can be studied using DFT. Furthermore, it 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. This project aims to improve the efficiency of the density-functional theory (DFT) calculations. DFT is at the core of molecular modeling and is applied widely in biological research/development and in drug discovery. The improved DFT will significantly increase researchers' productivity and extend its application scope.