Albert F. Wagner, Larry A. Curtiss, Peter Zapol, and Michael Minkoff,
Argonne National Laboratory

Research Objectives

High fidelity simulations of combustion devices will require the application of (1) electronic structure methods to the thermochemistry of hydrocarbons with up to 16 carbon atoms, (2) electronic structure methods to account for local and bulk environmental effects at active molecular sites in catalytic converters, and (3) theoretical kinetics approaches to much larger combustion chemistry problems than are currently examined. Our objective is to carry out scaling studies of code performance using existing or emerging algorithms in both the kinetics and electronic structure areas.

Computational Approach

Most of this work utilizes the NWChem package and PETSc software. The applications codes themselves are written in Fortran.

Accomplishments

In our thermochemistry effort, the most expensive step in the G3(MP2,CCSD) method, namely a single-point CCSD(T) calculation, was carried out on linear alkane hydrocarbons up to C₁₄H₃₀. These results were used in the G3(MP2,CCSD) method to obtain enthalpies of formation that agree well with experiment. It was found that the CCSD CPU time is proportional to the number of Gaussian basis functions to the power of 5.8. The relative times and accuracies for a series of alkanes are shown in the figure. The atomic basis set for the largest molecules, C₁₄H₃₀, had 270 basis functions, giving a CPU time of almost 11 hours using 256 PEs, or 2850 hours of serial time. Besides establishing the scaling dependencies for computer resources, these calculations test G3 theory accuracy for much larger molecules than those included in the usual test sets and provide a solid basis for accurate chemical calculations of large hydrocarbon reaction energetics.

In our catalytic effort, we have used NWChem on the T3E to study with Hartree-Fock theory the effect on reaction energies of including up to 112 tetrahedral atoms of the zeolite framework about the active site. Time-to-solution scales as the 2.1 power of the number of Gaussian basis functions. The largest system completed (58 tetrahedral atoms) takes about 160 PE hours. The environmental effects track with size such that by 112 tetrahedral atoms, we believe for even polarizable reactants the environmental effects will be converged.

In our kinetic effort, we completed a successful port and initial scaling studies of our cumulative reaction probability code with the PETSc linear solver.

Relative total CPU times and deviations with experimental enthalpies of formation for quantum chemical energy calculations on CnH2n+2 linear alkanes containing up to 14 carbons.

Significance

We hope to provide baseline information that will motivate either new method development or define the scale of applications studies that would be required in high fidelity combustion simulations. Besides establishing the scaling dependencies for computer resources, these calculations have the following benefits: (1) for the thermochemistry studies, extending tests of G3 theory accuracy to much larger molecules than those included in the usual test sets, providing a solid basis for accurate calculations of large hydrocarbon reaction energetics; (2) for the catalysis studies, determining the sphere of influence of chemical and electrostatic forces around a catalytic site and thus contributing to more approximate but efficient theoretical methods; (3) for the kinetics studies, shedding light on how many degrees of freedom in a reaction need to be explicitly treated with quantum dynamics and how many are just spectators to the reaction and need be only approximately and implicitly included.

Publications

L. A. Curtiss, K. Raghavachari, P. C. Redfern, A. G. Baboul, and J. A. Pople, "Gaussian-3 theory using coupled cluster energies," Chem. Phys. Lett. 314, 101 (1999).

L. A. Curtiss, S. A. Sygmunt, and L. E. Iton, "Ab initio and density functional studies of hydrocarbon interaction with zeolitic clusters," in Proceedings of the 12th International Zeolite Conference, edited by M. M. J. Treacy, B. K. Marcus, M. E. Bisher, and J. B. Higgins (Materials Research Society, 1999).

L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, and J. A. Pople, "Gaussian-3 (G3) theory for molecules containing first and second-row atoms," J. Chem. Phys. 109, 7764 (1998).