Paul G. Hipes

Three-dimensional quantum mechanical reactive scattering using symmetrized hyperspherical coordinates

We report here the first three-dimensional (3D) reactive scattering calculations using symmetrized hyper-spherical coordinates (SHC). They show that the 3D local hyper-spherical surface function basis set leads to a very efficient computational scheme which should permit accurate reactive scattering calculations to be performed for a significantly large number of systems than has heretofore been possible.

Lifetime analysis of high-energy resonances in three-dimensional reactive scattering

Abstract Accurate quantum mechanical three-dimensional reactive scattering calculations for the J = 0 partial wave of the H + H2 system for total energies up to 1.6 eV have been performed using symmetrized hyperspherical coordinates. Six resonances were found having collision lifetimes which, interestingly, increase with the amount of stretching excitation and decrease with that of bending excitation.

Symmetry analysis of accurate H+H2 resonances for low partial waves

Abstract We have performed accurate quantum mechanical three-dimensional reactive scattering calculations for both parities of the J = 1 partial wave of the H + H2 system up to total energies of 1.75 eV. The collision lifetime resonance spectra for both J = 0 and J = 1 are discussed in terms of the characteristics of the systems potential energy surface and of a simple physical model involving its symmetry properties.

Hyper-spherical coordinate reactive scattering using variational surface functions

Abstract An efficient numerical method of calculating surface functions for accurate quantum mechanical three-dimensional reactive scattering using symmetrized hyper-spherical coordinates has been developed. This method is at least 20 times faster than the finite-element method used previously and its accuracy is demonstrated for the H + H 2 system.

Studies of electron collisions with polyatomic molecules using distributed‐memory parallel computers

Elastic electron scattering cross sections from 5–30 eV are reported for the molecules C2H4, C2H6, C3H8, Si2H6, and GeH4, obtained using an implementation of the Schwinger multichannel method for distributed‐memory parallel computer architectures. These results, obtained within the static‐exchange approximation, are in generally good agreement with the available experimental data. These calculations demonstrate the potential of highly parallel computation in the study of collisions between low‐energy electrons and polyatomic gases. The computational methodology discussed is also directly applicable to the calculation of elastic cross sections at higher levels of approximation (target polarization) and of electronic excitation cross sections.

Quantum mechanical reactive scattering using a high-performance distributed-memory parallel computer

Abstract We have performed accurate three-dimensional quantum mechanical reactive scattering calculations for the H + H 2 system on the Caltech/JPL Mark IIIfp 64 processor hypercube, using the method of symmetrized hyperspherical coordinates and local hyperspherical surface functions. The results and timing obtained demonstrate that such distributed memory parallel architectures are competitive with the CRAY X-MP, CRAY 2 and CRAY Y-MP supercomputers and should allow the study of larger, more complicated chemical systems. In addition, we show that a selection rule for scattering resonances developed previously and tested for J = 0, 1 resonances is also satisfied by the J = 2 resonances obtained in the present calculations.

Benchmarking advanced architecture computers

Recently, a number of advanced architecture machines have become commercially available. These new machines promise better cost performance than traditional computers, and some of them have the potential of competing with current supercomputers, such as the CRAY X-MP, in terms of maximum performance. This paper describes the methodology and results of a pilot study of the performance of a broad range of advanced architecture computers using a number of complete scientific application programs. The computers evaluated include: 1shared-memory bus architecture machines such as the Alliant FX/8, the Encore Multimax, and the Sequent Balance and Symmetry 2shared-memory network-connected machines such as the Butterfly 3distributed-memory machines such as the NCUBE, Intel and Jet Propulsion Laboratory (JPL)/Caltech hypercubes 4very long instruction word machines such as the Cydrome Cydra-5 5SIMD machines such as the Connection Machine 6‘traditional’ supercomputers such as the CRAY X-MP, CRAY-2 and SCS-40. Seven application codes from a number of scientific disciplines have been used in the study, although not all the codes were run on every machine. The methodology and guidelines for establishing a standard set of benchmark programs for advanced architecture computers are discussed. The CRAYs offer the best performance on the benchmark suite; the shared memory multiprocessor machines generally permitted some parallelism, and when coupled with substantial floating point capabilities (as in the Alliant FX/8 and Sequent Symmetry), provided an order of magnitude less speed than the CRAYs. Likewise, the early generation hypercubes studied here generally ran slower than the CRAYs, but permitted substantial parallelism from each of the application codes.

Test of variational transition state theory against accurate quantal results for a reaction with very large reaction‐path curvature and a low barrier

We present three sets of calculations for the thermal rate constants of the collinear reaction I+HI-->IH+I: accurate quantum mechanics, conventional transition state theory (TST), and variational transition state theory (VTST). This reaction differs from previous test cases in that it has very large reaction-path curvature but hardly any tunneling. TST overestimates the accurate results by factors of 2×10^10, 2×10^4, 57, and 19 at 40, 100, 300, and 1000 K, respectively. At these same four temperatures the ratios of the VTST results to the accurate quantal ones are 0.3, 0.8, 1.1, and 1.4, respectively. We conclude that the variational transition states are meaningful, even though they are computed from a reaction-path Hamiltonian with large curvature, which is the most questionable case.

Quantum chemical reaction dynamics on a highly parallel supercomputer

SummaryIn this paper we describe the solution of the quantum mechanical equation for the scattering of an atom by a diatomic molecule on a high-performance distributed-memory parallel supercomputer, using the method of symmetrized hyperspherical coordinates and local hyperspherical surface functions. We first cast the problem in a format whose inherent parallelism can be exploited effectively. We next discuss the practical implementation of the parallel programs that were used to solve the problem. The benchmark results and timing obtained from the Caltech/JPL Mark IIIfp hypercube are competitive with the CRAY X-MP, CRAY 2 and CRAY Y-MP supercomputers. These results demonstrate that such highly parallel architectures permit quantum scattering calculations with high efficiency in parallel fashion and should allow us to study larger, more complicated chemical systems. Future extensions to this approach are discussed.

Gauss-Jordan inversion with pivoting on the Caltech Mark II hypercube

The performance of a parallel Gauss-Jordan matrix inversion<supscrpt>1,2</supscrpt> algorithm on the Mark II hypercube<supscrpt>3</supscrpt> at Caltech is discussed. We will show that parallel Gauss-Jordan inversion is superior to parallel Gaussian elimination <italic>for inversion</italic>, and discuss the reasons for this. Empirical and theoretical efficiencies for parallel Gauss-Jordan inversion as a function of matrix dimension for different numbers and configurations of processors are presented. The theoretical efficiencies are in <italic>quantitative</italic> agreement with the empirical efficiencies.