Quantum Chemistry and Reaction Dynamics

1. Quantum Chemistry and Reaction Dynamics Jeff Nichols, Deputy Director WR Wiley Environmental Molecular Sciences Laboratory Pacific Northwest National Laboratory Richland, WA 99352 Dr. Robert J. Harrison, Pacific Northwest National Laboratory Dr. Martin Head-Gordon, Lawrence Berkeley National Laboratory Dr. Mark S. Gordon, Ames Laboratory Professor Piotr Piecuch, Michigan State University Professor Peter R. Taylor, University of California, San Diego Professor Henry Frederick Schaefer III, University of Georgia Professor Gustavo E. Scuseria, Rice University Professor Russ Pitzer, The Ohio State University Dr. Walter C. Ermler, Program Director for Research, EHR/REC Dr. Albert F. Wagner, Argonne National Laboratory Professor Donald L. Thompson, Oklahoma State University QC RD Basic Energy Sciences

2. Some Collaborations Have Already Been Established Colaboratory Pilot (CMCS) PNNL, LBNL, UGA, UCSD ANL SNL Ames, MSU OkSU UMd OSU, U of Mem Rice ISICs Basic Energy Sciences

3. Collaborators GI Fann, E Apra, PNNL G Beylkin, U Colorado HF Schaefer, III, UGA PR Taylor, UCSD/U Warwick M Head-Gordon, LBNL Advanced Methods for Electronic StructureRobert J. Harrison and Jeff Nichols, PI • One of three complementary projects: • Sandia National Laboratory, “A Computational Facility for Reacting Flow Science,” and • Argonne National Laboratory, “Advanced Software for the Calculation of Thermochemistry, Kinetics, and Dynamics.” • to address electronic structure, chemical kinetics, and fluid mechanics issues necessary to create a software revolution in the simulation of chemically reacting turbulent flows. To the degree that funding allows, our intention is to initiate a collaboration that will grow over time into a coordinated software development program. Basic Energy Sciences

4. A Multiresolution Approach to Quantum Chemistry in Multiwavelet Bases Robert J. Harrison and G.I. Fann Gregory BeylkinPacific Northwest National Laboratory University of Colorado • Complete elimination of the basis error • One-electron models (HF, DFT), pair models (e.g., MP2, CCSD) • Correct scaling of cost with system size • General approach – readily accessible by students, small computer code • Potential impact similar to the FFT on physics • Realizable numerical algebraic regularization • Faster algorithms with separable representation of kernels for integro-differential equations • Applications to other domains including atmospheric dynamics and materials Basic Energy Sciences

5. A Multiresolution Approach to Quantum Chemistry in Multiwavelet BasesHarrison, Fann and Beylkin • Distinguishing features • Multiresolution analysis in multiwavelet bases • Disjoint intervals efficiently adapt to singularities • Non-standard representation of functions / operators • Integral operators scaling as O(Nk4) or better • Density Functional Theory • Integral formulation – nominally no derivatives • Initial applications • Benchmark calculations on polyatomic systems • Connections to ISICs • MRA in 3-D and 6-D; visualization of 3-D and 6-D numerical functions; NUMA programming tools; sparse matrix BLAS and linear algebra, CCA and performance analysis and tuning Basic Energy Sciences

6. A Multiresolution Approach to Quantum Chemistry in Multiwavelet BasesHarrison, Fann and Beylkin • Grid used to represent the nuclear potential for H2 using k=7 to a precision of 10-5. • Automatically adapts – it does not know a priori where the nuclei are. • Nuclei at dyadic points on level 5 – refinement stops at level 8 • If were at non-dyadic points refinement continues (to level ~12) but the precision is still guaranteed. • In future will dyadically refine with various lengths to force nuclei to box corners. Basic Energy Sciences

7. Accurate Properties for Open-Shell States of Large MoleculesPeter R. Taylor, UCSD/ U. Warwick Objectives • Extend the applicability of accurate, reliable chemical predictions for closed-shell molecules to radicals, excited states, and situations in which chemical bonds are broken • Develop response methods for calculating properties for these systems • Improve convergence of results by exploiting two-particle basis functions • Extend this approach to systems with dozens of open-shell electrons Basic Energy Sciences

8. Accurate Properties for Open-Shell States of Large MoleculesPeter R. Taylor, UCSD/ U. Warwick Approach • Implement scalable CASPT2 energies and response properties (new software) • Integrate existing work on CASPT2 using two-particle basis functions (existing software) • Develop and implement group function approach for weakly coupled open-shell sites such as polynuclear transition-metal complexes or ferredoxins (new equations, new algorithms, new software) Basic Energy Sciences

9. Development of Next-Generation, Explicitly-Correlated Electronic Structure Methods for Sub-Chemical AccuracyFritz Schaefer, University of Georgia • New closed-shell, integral-direct MPn-R12 and CCn-R12 codes are being created to take advantage of our recently developed integrals package CINTS. Our MP2-R12 work has already provided the scientific community explicitly-correlated methodologies for workstation computations with as many as 1500 basis functions and essentially no angular momentum limits, at least through k functions. • The full promise of R12 methods is being pursued by further development of evaluation methods for many-electron integrals. Through demanding computations with enormous basis sets, deficiencies in the standard approximations of R12 theory are being identified and understood. Improvements, such as dual basis set schemes, are being investigated for better completeness insertions, particularly ones with improved consistency over broad regions of potential energy hypersurfaces. • For combustion and atmospheric chemistry applications, we plan critical development and implementation of explicitly-correlated (R12) open-shell perturbation and coupled-cluster theories, both within less complicated unrestricted (UHF) formalisms and more difficult spin-adapted (ROHF) approaches. Basic Energy Sciences

10. Local CorrelationMartin Head-Gordon, LBNL • Coupled cluster (CC) methods are the most accurate quantum chemistry methods in wide use. • They are accurate for reaction barriers where simpler density functional theory (DFT) methods often fail. • But CC methods are restricted to small molecules, and are very computationally expensive compared to DFT. • Application to large molecules is blocked because cost rises with the 6th and 7th powers of molecular size. • Thus immediate development of parallel algorithms is not going to permit application to larger molecules. • Goal: develop alternative formulations of CC theory which reduce the cost scaling to quadratic or linear with molecular size, without destroying accuracy. Basic Energy Sciences

11. Local Correlation - Overview of Planned Work Martin Head-Gordon, LBNL • Our reduced scaling CC methods must permit: • Continuous potential surfaces. • Viability with large basis sets. • Both energies and forces must be available. • We’ve defined a new ansatz that reduces the number of CC variables to quadratic, and satisfies the above criteria. • The accuracy of this ansatz must be established • We’ll avoid the difficulty of very large basis sets by combining our CC methods with a density functional style correlation functional. • The performance of this hybrid approach must be tested. • Serial code will be developed for testing and refinement. • When results justify it, parallel algorithms will be pursued in collaboration with the NWChem team. Basic Energy Sciences

12. Participants: Mark Gordon Mike Schmidt Klaus Ruedenberg James Evans Collaborators: Piotr Piecuch (Michigan State) Don Truhlar (Minnesota) Scalable Computing Lab: Ames Lab PNNL Computational ChemistryMark Gordon, Ames Laboratory Basic Energy Sciences

13. Computational Chemistry – Objectives for Highly Accurate Quantum Chemistry Codes 1Mark Gordon, Ames Laboratory • Full Configuration Interaction (Full CI) • Exact wavefunction for a given atomic basis • Serves as benchmark for approximate correlated methods: • Currently limited to modest basis sets, atoms, very small molecules • Need scalable code to apply Full CI more broadly • Replicated data algorithm: limited molecular size • Distributed data algorithm: communication issues • Programming Models interface: Data compression (Kendall) • Scalable General CI • Full CI limited in scope • Most truncated CI based on “full space” ansatz • Extend scope of CI by eliminating “deadwood”: only include important configurations Basic Energy Sciences

14. Computational Chemistry – Objectives for Highly Accurate Quantum Chemistry Codes 2Mark Gordon, Ames Laboratory • Scalable MCSCF • Frequently require orbitals optimized in CI space • More demanding than CI • Most common MCSCF implementation: FORS/CAS • Expand Accessible MCSCF Active Space • MCSCF based on General CI: eliminating deadwood • Q-CAS based on localized orbitals • Efficient Scalable Coupled Cluster Methods: Piecuch • Open Shell Perturbation Theory Gradients Basic Energy Sciences

15. Computational Chemistry – Objectives for Spanning Multiple Time and Length ScalesMark Gordon, Ames Laboratory • Scalable Kinetic Monte Carlo Codes with Focus on Surface Phenomena • Develop New Integrated Atomistic & Mesoscale Descriptions of Surface Phenomena • Pattern formation in catalytic surface reactions • Nanostructure evolution during surface processes • Chemical vapor deposition (CVD) • Etching of semiconductor surfaces • Heterogeneous catalysis • Interface with continuum mesoscale modeling Basic Energy Sciences

16. Examples of applications: dynamics of reactive collisions highly excited and metastable ro-vibrational states of molecules rate constant calculations collisional quenching of electronically excited molecular species New Coupled-Cluster Methods For Molecular Potential Energy SurfacesPiotr Piecuch, Michigan State University The “holy grail” of the ab initio electronic structure theory: The development ofsimple,black-box, andaffordablemethods that can providehighly accurate(~spectroscopic) description of ground- and excited-state potential energy surfaces • Motivation: • elementary processes that occur in combustion (e.g., reactions involving OH and NxOy) • collisional quenching of the OH and other radical species Basic Energy Sciences

17. New Coupled-Cluster Methods For Molecular Potential Energy Surfaces - Specific GoalsPiotr Piecuch, Michigan State University • New CC methods for ground-state potential energy surfaces: • method of moments of CC equations • renormalized CC approaches • New CC methods for excited-state potential energy surfaces: • method of moments of CC equations • active-space EOMCC approaches MBPT(2)-like choices of  lead to the renormalized and completely renormalized CCSD(T), CCSD(TQ), CCSDT(Q), etc. approaches Basic Energy Sciences

18. New Coupled-Cluster Methods For Molecular Potential Energy Surfaces – Future WorkPiotr Piecuch, Michigan State University • Methods and algorithms - ground-state problem • Incorporation of the renormalized CCSD(T), CCSD(TQ), and CCSDT(Q) methods in GAMESS • Development of the MMCC schemes with the non-perturbative choices of  • Extensions of the MMCC and renormalized CC methods to open-shell states and reference configurations of the ROHF type • Work with Professor Mark S. Gordon and coworkers on parallelizing the MMCC and renormalized CC methods within GAMESS • Methods and algorithms - excited-state problem • Extension of the MMCC theory to the MMCC(2,4) case and extension of the active-space EOMCC theory to the EOMCCSDtq case • Development of efficient computer codes for the MMCC and active-space EOMCC methods and incorporation of these codes in GAMESS • Development of the MMCC and active-space EOMCC methods for non-singlet states and formulation of the EA and IP extensions of the active-space EOMCC approaches • Extension of the active-space EOMCC approaches to properties other than energy • Development of the MMCC schemes with the perturbative choices of  (renormalized EOMCCSD(T) method ?) • Work with Professor Mark S. Gordon and coworkers on parallelizing the excited-state MMCC codes within GAMESS Basic Energy Sciences

19. Quantum Chemistry for Periodic SystemsGustavo E. Scuseria, Rice University • Objectives • To develop methods and computational programs for the accurate prediction of electronic and optical properties of polymers, surfaces, and solids with large unit cells • Applications to polymers and catalysis • Approach • Use Gaussian orbitals for across the Periodic Table reliability • Use Fast-Multipole Methods for achieving linear scaling in the Coulomb problem • Fast quadratures and alternatives to diagonalization for O(N) performance • Develop better DFT functionals for increased accuracy • Payoffs • Increase capabilities for modeling materials and processes • Big impact on areas where quantum molecular modeling is routinely used: chemical, pharmaceutical, and defense industries • Incorporation to Gaussian package Order (N) tools for Periodic Systems Basic Energy Sciences

20. Relativistic Multireference Quantum ChemistryR. M. Pitzer, B. E. Bursten, I. Shavitt Ohio State University • Strengths • Includes relativistic effects • Describes complicated electron coupling • Includes electron correlation • Needs • Extensive testing and tuning of recent parallel version • More flexible core potentials (W. C. Ermler) • Parallel versions of ancillary programs • Refinement of diagonalization algorithm • Applications • Actinide complexes in solution and on surfaces • Lanthanide intensities in crystals Basic Energy Sciences

21. Reliable Electronic Structure Calculations for Heavy Element Chemistry: Molecules Containing Actinides, Lanthanides, and Transition Metals W. C. Ermler and M. M. Marino, Department of Chemistry, The University of Memphis Relativistic Pseudopotentionals (RPPs) • RPPs are based on extending the usual two-space representation of atomic electrons (core and valence) to three spaces (core/outer core/valence). • The RPP has embedded within it the standard small-core RECP that relegates the outer core electrons to the valence space. • The RPP is ultimately calculated in its entirety at runtime and is specific to the molecular geometry and electronic state. • Only the smallest numbers of molecular valence electrons need to be treated explicitly. • The RPP can be used in any treatment of the electronic structure [DFT, CI, CCSD(T), etc.] Small-core RECPs embedded within very-large-core RPPs, in conjunction with advanced computing platforms, permit the highly accurate ab initio treatment (including correlation, outer-core/valence polarization, and spin-orbit coupling) of systems possessing orders of magnitude more electrons than are tractable using current codes and platforms. Basic Energy Sciences

22. Advanced Software for the Calculation of Thermochemistry, Kinetics and Dynamics - Parallelization of Cumulative Reaction Probabilities (CRP)Al Wagner, ANL • computationally intensive core of reaction rate constants • mathematical kernel (all matrices are sparse with some structure): - method 1: - iterative eigensolve (imbedded iterative linearsolves) - clever preconditioning important - portability based on ANL PETSc library of kernels - method 2: - Chebyschev propagation (=> matrix vector multiplies) - novel finite difference representation (helps parallelize) • programing issues: - parallelization - exploiting data structure (i.e., preconditioning) Basic Energy Sciences

23. Advanced Software for the Calculation of Thermochemistry, Kinetics and Dynamics - Parallel Implementation of Subspace Projection Approximate Matrix (SPAM) methodAl Wagner, ANL • novel iterative method to solve general matrix equations • eigensolve - linear solve - nonlinear solve • applications are widespread • in chemistry: CRP, electronic structure (SCF, MRSDCI,…) • mathematical kernel: • related to Davidson, multigrid, and conjugate gradient methods • subspace reduction (requiring usual matrix vector multiplies) • projection operator decomposition of matrix vector product • substitution of user-supplied approximate matrix in computationally intensive part of decomposition • sequence of approx. matrices => multilevel method • programing issues: • generalization of approach (only done for eigensolve) • incorporation into libraries (connected to TOPS project at ANL) • test of efficacy in realistic applications (e.g., CRP) Basic Energy Sciences

24. 1. Potential Energy Surfaces We are developing methods for direct use of ab initio energies and forces in dynamics simulations based on interpolating moving least-squares. The method can be used to generate global representations for dynamics calculations. It can also be integrated into direct (on-the-fly) dynamics simulations, providing a means of reducing the computation expense by using interpolation. Furthermore, we will attempt to develop methods for "on the fly scaling" of values so that lower-level quantum methods can be used. Note: The interpolating moving least-squares method requires the determination of optimum polynomial expansion coefficients. The extension of this approach to large numbers of atoms will be made practical by the using parallel computing. Theoretical Chemical Dynamics of Elementary Combustion ReactionsDon Thompson, Oklahoma State University Project goal: Development of methods and software for more accurate and efficient simulations and rate calculations for complex chemical reactions involving large polyatomic molecules and radicals. Basic Energy Sciences

25. 2. Molecular Dynamics Simulations and Rate Calculations The treatment of the dynamics of reactions involving polyatomic molecules presents a challenging problem since they often involve quantum effects, yet quantum mechanical methods are not capable of treating more than a few atoms. We are developing quasiclassical and semiclassical methods for practical dynamics simulations of complex reactions in large molecules. We are developing a general computer code that implements these methods and that incorporates various ways of representing the potential, including the direct use of ab initio forces. The size of problems that can be treated can be greatly increased by taking advantage of many processors to compute the large ensembles of trajectories needed to determine rates and other dynamical properties of a system. Theoretical Chemical Dynamics of Elementary Combustion ReactionsDon Thompson, Oklahoma State University Basic Energy Sciences

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