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创新的替代方法来评估大分子中的库仑相互作用。近年来，密度泛函理论（DFT）作为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，它相对便宜。对于最大的分子系统，其研究是可行的，目前的DFT程序（几百个原子），库仑相互作用的治疗，其二次成本是系统的大小，是计算占主导地位。为了能够在真正的大分子上进行计算，需要在库仑贡献的标度方面取得突破。在这一领域，存在着超越现有技术的重大进步机会。最近的研究在有限总体抽样理论已经产生了一个突破性的方法，QCKR算法，它产生的解决方案，某些组合问题非常有效地相对于标准技术，往往提供几个数量级的改进。有趣的是，它是可能的表达库仑问题的形式是密切相关的这些组合问题。在第一阶段的努力，QCKR方法将被扩展到解决库仑问题，并促进DFT计算非常大的分子系统的方法的潜力将进行评估。

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.