Advanced Software for the Calculation of Thermochemistry, Kinetics, and Dynamics and Theoretical Chemical Dynamics Studies for Elementary Combustion Reactions

Albert Wagner, Stephen Gray, Ron Shepard, Michael Minkoff, Argonne National Laboratory
Donald Thompson, Oklahoma State University
ISIC PIs: Barry Smith [TOPS / ANL], Dave Bernholdt, [CCTTSS / ORNL]

Summary

Our two integrated projects are developing both scalable kinetics/dynamics software and infrastructure software. The infrastructure focus is on preconditioners and on potential energy surface fitting schemes that reduce the number of electronic structure calculations necessary for accurate kinetics and dynamics. The infrastructure software has benefited from Integrated Software Infrastructure Centers (ISIC) support.

KINETICS/DYNAMICS:

The calculation of reaction rate constants is fundamental to the accurate simulation of many chemical phenomena. Rate constants are typically calculated by approximate but practical methods. Exact calculations via quantum dynamics are so computationally intensive that approximate theories are not as calibrated as they could be. Exact rate constants can be calculated with Cumulative Reaction Probability (CRP) approaches in both time-independent and time-dependent forms. We are pursuing both approaches.

• Time Independent CRP : A time independent CRP calculation can be formulated as an iterative solution to the eigenvalues of the reaction probability operator. Each iteration requires the resolution of two separate Green's functions via the iterative solution of associated linear equations. A parallelized code has been developed using the PETSc library (in collaboration with the TOPS ISIC) in which the GMRES method resolves the Green's functions while an orthogonalized Lanczos approach resolves the eigenvalues. Using an analytic model problem that has the property of being expandable to any number of reacting atoms (with associated internal degrees of freedom [DOF]), the code has been shown to be scalable to over a hundred or more processors. Times to solution at NERSC are measured at less than ten minutes per eigenvalue for a 7 DOF calculation. While the current code uses only diagonal preconditioning for Green's function resolution, future work will examine more global preconditioners including the Subspace Projected Approximated Matrix approach (see below) and optimal block orthogonal preconditioning (in collaboration with W. Poirier under DOE/MICS support). Strategies to collapse the two Green's function resolutions into one grand iterative linear solve are being pursued.

• Time Dependent CRP and Quantum Dynamics : A mixed MPI/OpenMP parallel wave packet code for the calculation of reaction probabilities and the CRP of arbitrary four-atom systems is in development. The OpenMP component of the code has been extensively tested on the computationally challenging four-atom OH+CO reaction. The scalability of the MPI component is now being tested. In the future, a parallel wave packet code based on Cartesian coordinates will be developed.

INFRASTRUCTURE:

All kinetics/dynamics studies compute how molecules move over a potential energy surface (PES) that is a function of internal DOFs. Electronic structure calculations provide the “altitude” of each point on the surface. The terascale application of electronic structure calculations is the subject of most of the BES SciDAC projects. We are developing ways to produce PESs that reduce the number of electronic structure calculations needed for accurate kinetics/dynamics. In addition, we are developing preconditioner approaches for the numerics of kinetics/dynamics applications but with implications for electronic structure applications. These efforts are described below.

• Interpolative Moving Least Squares (IMLS) PES fitting methods : Reducing discrete ab initio electronic structure calculations into a continuous PES is a major fitting problem. An ANL/OSU collaboration is exploring higher order IMLS solutions to this problem. The IMLS approach involves solving a weighted linear least squares problem every time a PES value is required. Special weights confer non-linear flexibility to the fit. The goal of the program is to develop automatic PES generation or on-the-fly PES computation with parallel electronic structure codes. In the past year, 1, 3, and 6 dimensional realistic and model PES higher order fits have been generated, in some cases generated automatically. These tests have involved direct fits and fits to differences between the real and a model PES. A generalized IMLS code for value and derivative has been developed for any number of DOF and for any IMLS order with user-supplied basis sets and weights. Schemes using weight sizes to limit explicit consideration of only nearby points ab initio points are being developed. On-the-fly tests of IMLS techniques for trajectory problems are also in progress. IMLS technology can be useful in many other applications that involve fitted surfaces.

• Subspace Projected Approximate Matrix (SPAM) method : The SPAM method is a multigrid-like preconditioner for large-scale iterative eigensolvers and linear solvers where matrix-vector products dominate the solution. Projection operators allow the use of a sequence of approximating user-specified preconditioners incorporating user generated mathematical or physical insight. The sequence acts to accelerate the iterative convergence. Fortran95 “black box” code for symmetric, Hermitian, or real generalized symmetric eigenvalue problems have been developed (see ftp.tcg.anl.gov). Parallel extensions are being developed based on distributed-memory message passing (e.g. MPI), on the global array library (GA_lib), and on the PETSc environment. This work is in conjunction with the TOPS ISIC. SPAM applications to problems in vibrational spectroscopy, CRP kinetics (see above), and electronic structure methods (e.g., COLUMBUS Program System) are in progress.

For further information on this subject contact:
Dr. Albert Wagner,
Chemistry Division,
Argonne National Laboratory,
wagner@tcg.anl.gov

Prof. Donald Thompson,
Department of Chemistry,
Oklahoma State University,
dlt@osuunx.okstate.edu

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