Quantum Monte Carlo for “Difficult” Systems in Materials Chemistry

1. Quantum Monte Carlo for “Difficult” Systems in Materials Chemistry Ainsley A. Gibson Howard University Washington, DC 20059

2. Pros: Widespread adoption of techniques Relative ease of use Always gets a number as output Cons: Often promotes misconceptions Usually no error estimation Always gets a number as output Black Box Computing

3. State-of-the-Art Computing • Pros: • End results are well-analyzed • Results are frequently great! • Near-complete explanation • Cons: • Expensive (human, not CPU) cost • Not for everyone • Potentially highly selective

4. “Golden Box” Computing • Lies somewhere between black box and state of the art. • Use of high level techniques in a generalized form. • Tradeoff between high accuracy/high expertise and variable accuracy/low expertise.

7. This Work… • There is a significant degree of “art” in QMC calculations, due to the lack of strict restriction on trial function form. • We wish to determine the degree of necessary “art” in trial function form. • We also wish to retain the ability to accurately describe “difficult” systems.

8. Difficult? This isn’t rocket science… • Typical “difficult” systems have: • Ionized or excited states • Radical or metallic character • Significant delocalization or resonance • More broadly, “difficult” systems require use of an atypical variant of the technique that need not be used for 95% of chemical systems.

9. Applications • Atomic Excited States • Beryllium Dimer • Nanoscale Ternary Compounds (HU-CREST) • Transition Metal Energetics (AHPCRC) • Atmospherically Interesting

10. Atomic Excited States • Simple test of ability to describe electronic structure • Some reactions require accurate description of excited states • “Proof of capability” study for future applications to molecular systems

11. Atomic Excited States

12. Beryllium Dimer • Poorly described by simpler traditional basis set ab initio techniques. • Multi-reference character due to 2s-2p near degeneracy. • Motivated by prior success with atomic excited states. • A few-electron system amenable to all-electron fixed-node DMC.

13. Dissociation Energies, in cm-1

14. Nanoscale Ternary Compounds • Formation of novel compounds at the nanoscale have been proposed. • The reactions use carbon and oxygen in the presence of a nitrogen plasma. • We propose to predict some basic properties of proposed reactions and compounds using QMC techniques.

15. Higher Excited States • Reactions proposed may proceed through excited and/or ionized states. • QMC offers the allure of unprecedented accuracy for ionized and excited species. • QMC is generalized for any electronic state. • The higher states of nitrogen are first in a series of excited state calculations.

16. Nitrogen Excited States

17. Transition Metals • When carefully chosen, there are methods able to describe selected metallic systems. • Satisfaction with price, performance and general applicability is elusive. • QMC shows promise for metallic systems, and has three features in its favor: • System-independent methodology • Consistent error estimates • Ideal for HPC environments

18. X-alpha, LSDA, and PL density functionals

19. B- functionals: B971, BLYP and BPW91

20. B1- functionals: B1B95 and B1LYP

21. B3- functionals: B3P86, B3PW91, B3LYP

22. Selected post-HF Ionization Potentials

23. 2.67, VMC 1.52, DMC QMC/HF Ionization Potentials

24. 1.71, VMC 1.57, DMC QMC/NO Ionization Potentials

25. Ozone Dissociation Energy • Traditional ab initio has difficulties: • Resonance character of ozone • Low-lying excited state contributions • Estimates of the dissociation limit are relatively small (1.02 – 1.13 eV). • Various excited states lie above and below the dissociation limit.

26. Results to Date, in eV

27. HU-CREST Current Work: Novel Nanoscale Compounds • Characterization of excited states: • CN, CO, NO, N2, C2, O2 • ONC, OCN • Energetic profile of proposed reactions • Large-scale network compounds

28. AHPCRC Current Work:Transition Metals • Electron Affinity • Proton Affinity • Small Clusters, Mx, x = 2,…,10 • Surfaces and solids • Silver nanoparticle stability (collaborative with CREST)

29. Future/Current Work:Atmospherically Interesting • Ozone dissociation and excited state characterization • S4 inter-conversion energetics • Excited and ionized states of binary (O, N, C) compounds as atmospheric species

30. John A. W. Harkless* William Lester, Jr. James Mitchell William Hercules Floyd Fayton Gordon Taylor José González Mike Towler NSF CREST Center for Nanomaterials Characterization and Design Army High Performance Computing Research Center Computer Learning and Design Center TTI Acknowlegements