A Fast Hybrid Fourier Real Space Algorithm for Coulomb Energies

这个小企业创新研究第一阶段项目将研究一种评估大分子中库仑相互作用的创新替代方法。近年来，密度泛函理论(DFT)作为一种预测分子物理性质的通用方法受到了越来越多的关注，与传统的相关方法相比，它的成本相对较低。对于目前的DFT程序研究是可行的最大分子系统(数百个原子)，库仑相互作用的处理，其二次代价是系统大小，在计算上占主导地位。为了能够对真正的大分子进行计算，需要在库仑贡献的比例方面取得突破。在这一领域有一个重大的机会，可以在现有技术之外取得长足的进步。最近在有限总体抽样理论的研究中产生了一种突破性的方法，即QCKR算法，该算法相对于标准技术非常高效地给出了某些组合问题的解，通常提供了几个数量级的改进。有趣的是，库仑问题可以用一种与这些组合问题密切相关的形式来表示。在第一阶段的工作中，QCKR方法将被扩展到解决库仑问题，并将评估该方法在促进超大分子体系密度泛函计算方面的潜力。

This Small Business Innovation Research Phase I project will investigate an innovative alternate approach to the evaluation of the Coulomb interactions in large molecules. Recently there has been a rapidly growing interest in Density Functional Theory (DFT) as a general procedure for predicting physical properties of molecules, which is relatively inexpensive compared to traditional correlated methods. For the largest molecular systems whose study is feasible by the current DFT programs (several hundred atoms), the treatment of the Coulomb interactions, with its quadratic cost is system size, is computationally dominant. In order to be able to perform calculations on truly large molecules, a breakthrough in the scaling of the Coulomb contribution is required. There is a significant opportunity for considerable advancement beyond current technology in this area. Recent research in finite-population sampling theory has yielded a breakthrough method, the QCKR algorithm, which yields the solution to certain combinatorial problems extremely efficiently relative to standard techniques, often affording several orders of magnitude improvement. Interestingly, it is possible to express the Coulomb problem in a form which is closely related to these combinatorial problems. During the Phase I effort, the QCKR method will be extended to solve the Coulomb problem, and the potential of the method for facilitating DFT calculations on very large molecular systems will be assessed.