SBIR Phase II: A Fast Hybrid Fourier/Real Space Algorithm for Coulomb Energies

*95-31459约翰逊这个小企业创新研究第二阶段项目将继续开发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及其系统大小的二次方代价，在计算上占主导地位。为了能够对真正的大分子进行计算，需要减小库仑贡献的比例。第一阶段的研究确定了一种突破性的傅里叶/实空间混合方法-Kwik算法的可行性，该算法仅在系统大小的线性工作中解决库仑问题。在一维版本的Kwik的第一阶段中获得的经验将用于开发处理二维和三维系统以及处理电子结构计算中的连续分布所需的扩展。第一阶段的研究工作表明，实现Kwik算法不仅在技术上是可行的，而且Kwik程序模块的内核是简单和可调的。它还表明，Kwik的结构非常容易同时进行矢量化和并行化--这两个因素都是在许多现代计算平台上实现接近峰值性能的关键因素。在第二阶段，第一阶段的结果将被细化并附加到Q-Chem量子化学计划中，并将实施扩展到并行平台。因此，预计这项工作将产生一个用于研究前所未有大小的分子的高效并行程序。这项研究将允许在比目前的技术和程序可能的更大的分子系统上进行高精度的密度泛函计算。这将对大学以及工业和政府机构的计算量子化学和物理研究人员具有相当大的价值。***

*** 95-31459 Johnson This Small Business Innovation Research Phase II project will continue the development of 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 in system size, is computationally dominant. In order to be able to perform calculations on truly large molecules, a reduction in the scaling of the Coulomb contribution is required. The Phase I research established the feasibility of a breakthrough hybrid Fourier/real space method, the KWIK algorithm, which solves the Coulomb problem in only linear work in system size. The experience gained in Phase I with the one-dimensional version of KWIK will be used to develop the extensions that are required to handle two- and three-dimensional systems and to treat the continuous distributions in electronic structure calculations. The Phase I research effort has revealed not only that it is technically feasible to implement the KWIK algorithm, but also that the kernel of a KWIK program module is simple and tunable. It was also shown that the structure of KWIK is quite amenable to simultaneous vectorization and parallelization - ingredients that are both critical to achieving near-peak performance on many modern computing platforms. During Phase II, the Phase I results will be refined and attached to the Q-Chem quantum chemistry program, and the implementation will be extended to parallel platforms. It is therefore anticipated that a highly efficient parallel program for the study of molecules of unprecedented size will result from this work. This research will allow highly accurate d ensity functional calculations to be carried out on much larger molecular systems than is possible with current techniques and programs. This will be of considerable value in computational quantum chemistry and physics researchers at universities as well as industrial and govemment facilities. ***