New Developments in Quantum Chemistry

Richard P. Muller¹, Bob Ward², and William A. Goddard, III¹

¹ Materials and Process Simulation Center, Beckman Institute, Caltech
² Department of Computer Science, University of Tennessee, Knoxville, Tennessee

The slides for the full talk are available here.

Abstract:

Over the last decade, it has become routine to carry out Quantum chemistry calculations that would have been impossible just 10 years ago. Part of this improvement is in the Hardware, but an equally important factor has been the improvement in the methods. Thus ten years ago the cost of a Hartree-Fock calculation scaled as the fourth power of the size of the system, O(N⁴) while a Density Functional Theory (DFT) calculation scaled as O(N³). Today, (due in part to work at the MSC) these computations scale as the second power of the system size, O(N²).

Modern supercomputers gain much of their speed advantage from parallelization of the computations over a large number of processors. This has been difficult with quantum chemistry calculations because of the large amount of intermediate data required. None the less, there has been significant progress toward good parallelization over a few (1-10) processors.

Our quest in QC is to develop ways to improve the methods to allow linear scaling, O(N) while improving the parallelization to run efficiently over a large number of processors. Divide and Conquer techniques have the potential to solve both of these problems, because they divide a large molecule into a set of smaller fragments, which can then be solved on a variety of processors. Divide and Conquer techniques work well for simple systems, but increasingly large fragments are required when the molecule contains conjugation or metallic bonding.

We present results of simple Divide and Conquer schemes. At the simplest level, divide and conquer offers no coupling between the various fragments. As one would expect, it exhibits excellent scaling behavior and poor reproduction of the full Hamiltonian results. Typically, one includes "buffer zones" which offer a better coupling between the regions, at a correspondingly higher price. The timings and errors for simple and buffered divide and conquer computations are shown below:

We also discuss new techniques for coupling the fragments in divide and conquer schemes that will be less expensive and will potentially allow reproduction of the full Hamiltonian results.

This work is supported by DOE-ASCI and NSF-NPACI.

The slides for the full talk are available here.