Advanced Software for the Calculation of Thermochemistry, Kinetics, and Dynamics
R. Shepard, S. K. Gray, A. F. Wagner, D. Medvedev, and M. Minkoff
The Born-Oppenheimer separation of the Schrodinger equation allows the electronic and nuclear motions to be solved in three steps. 1) The solution of the electronic wave function at a discrete set of molecular conformations; 2) the fitting of this discrete set of energy values in order to construct an analytical approximation to the potential energy surface (PES) at all molecular conformations; 3) the use of this analytical PES to solve for the nuclear motion using either time-dependent or time-independent formulations to compute molecular energy values, chemical reaction rates, and cumulative reaction probabilities. This project involves the development of technology to address all three of these steps.
During the development of the Subspace Projected Approximate Matrix (SPAM) diagonalization method (described last year), it was necessary to compute bounds of approximate eigenvalues and eigenvectors. This work resulted in the development of a general computational procedure to compute rigorous eigenvalue bounds for general subspace eigenvalue methods. This method consists of the recursive application of a combination of the Ritz Bound, the Residual Norm Bound, the Gap Bound, and the Spread Bound. In addition to application within the SPAM method, this method may also be applied to the Davidson method as used in molecular electronic structure calculations and to the Lanczos method as used in the computation of molecular vibrational eigenvalues.
In collaboration with Theoretical Chemical Dynamics Studies of Elementary Combustion Reactions (Thompson, Univ. of Missouri) we are developing accurate PESs for ab initio calculations involving large polyatomic molecules and radicals. We are using interpolating moving least-squares methods and singular value decomposition (SVD) to obtain a black-box package for addressing higher dimensional PES including features such as automatic point selection and selection of basis sets. As an example, for the full 6-D HOOH PES, we were able to fit an energy range of 100 kcal/mol to an accuracy of 1 kcal/mol with approximately 1350 points.
Iterative quantum mechanics methods are often used to determine either bound state information or chemical reaction dynamics information (e.g. wave packed based reaction probability calculations) for large-scale quantum mechanical problems. We developed an approach to parallel iterative four-atom quantum mechanics calculations based on a combination of OpenMP and MPI. The approach may be applied in a computing environment of distributed nodes, each node consisting of two or more processors sharing a common local memory. In such calculations, the matrix-vector product of a large Hamiltonian matrix is the computational bottleneck. Our parallel implementation was tested on a realistic chemical reaction dynamics problem with runs involving up to 1024 processors at the NERSC computing facility. It was shown to scale very well up to 512 processors, working at nearly 20% of theoretical peak performance. The best floating point rate was 0.16 Tflops with 768 processrs. The code can also run on more common linux clusters involving 2 processor nodes. The main ideas should also be applicable to systems involving more than four atoms.
Based upon methods developed by Miller and coworkers, we are using iterative eigenvalue methods and iterative solutions of linear equations to solve large-scale time-independent cumulative reaction probability calculations. We use the PETSc toolkit which is a component of the SciDAC TOPS ISIC to obtain a GMRES solution of the linear systems (Greens functions in the probability operator). We have recently replaced our Lanczos eigensolver with the SLEPc interface from PETSc to a wide collection of quality software of eigenvalue calculation (e.g. ARPACK). Since the key computational kernel of our CRP software is the matrix-vector product calculation in GMRES, we are exploring the use of tensor product representations of the Hamiltonian and achieving more than 50% of peak processor performance in the associated matrix-vector products.