New algorithms for electronic structure calculations on large molecules.

Abstract

Algorithms for treating large molecules are developed and implemented within the DeFT density functional package. In order to realistically model large molecules by quantum molecular methods, new algorithms whose computational costs increase linearly with system size must be developed. Moreover, to efficiently exploit the vast computing power provided by massively parallel computer architectures, we would like our new linear scaling algorithms to be scalable on such architectures. When developing these new algorithms, we strive to lose as little accuracy as possible. Many of our new approaches are inspired by Yang's divide and conquer (DAC) philosophy. An approximate electronic density is developed exploiting the fact that a molecule's electronic density can be accurately fit in a DAC fashion. It is constructed by using true subsystem densities to calculate contributions from nearby subsystems (in the vicinity of the region of interest) and using fitted subsystem densities to calculate contributions from faraway subsystems. This approximate density can ease the computational burden associated with various calculations. Its application to the calculation of the molecular electrostatic potential is illustrated. An efficient algorithm for carrying out a DAC method on massively parallel computers is developed. This algorithm combines the principles of both coarse and fine parallelism and allows for an uneven distribution of processors among subsystem calculations. The precise approach employed depends on the number of processors available and the number of subsystems to be treated. The processor to subsystem ratio is crucial and can be adjusted to achieve optimal performance. Since each subsystem can be efficiently run on a cluster of processors, our algorithm should be scalable up to hundreds, if not thousands, of processors when treating very large molecules. The exchange and correlation (XC) terms within a Kohn-Sham density functional method can also be fit by a DAC approach. This new DAC XC fitting procedure is outlined. The results and timings of benchmark calculations on extended glycine polypeptides are presented. The benefits of using fitted XC terms versus direct numerical integration of the XC terms are discussed. Other modifications made to achieve linear scaling for every XC procedure are also discussed. New grids containing more radial and angular points have also been created to achieve better precision in the final results. A scheme using fewer points for the fitting procedures and more points for the final numerical integration of the energy and energy gradients is presented. Benchmark calculations on a series of glycine polypeptides are performed to fully analyze the errors introduced by a DAC approach to constructing the electronic density. Various buffer space cutoffs are tested. The errors introduced by dropping various basis functions beyond these cutoffs from subsystem calculations are investigated. The possibility of partially truncating the basis sets beyond the cutoff is tested. Different types of basis functions are found to contribute differently to the DAC errors. This fact is exploited to define a multiple buffer space cutoff approach that will improve the efficiency of DAC calculations.