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

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*** 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. ***