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Randolph Q. Hood

Performance Measures x.x, x.x, and x.x. Quantum Monte Carlo studies of metals and materials with properties determined by weak dispersive interactions. Randolph Q. Hood. Weak dispersive interaction. + + - - + + - - ++ - - - +. ++ - + + - - + - + - - + -.

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Randolph Q. Hood

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  1. Performance Measures x.x, x.x, and x.x Quantum Monte Carlo studies of metals and materials with properties determined by weak dispersive interactions Randolph Q. Hood Physical Sciences

  2. Weak dispersive interaction + + - - + + - - ++ - - - + ++ - + + - - + - + - - + - Quantum mechanically induced dipoles type of van der Waals interaction Important in life processes such as genetic replication and proteins, and for several types of proposed H2 storage Physical Sciences

  3. Weak dispersive interaction neglected in mean field DFT DFT typically predicts accurate structures, but • van der Waals not included in mean field DFT • LDA & GGA qualitatively disagree on binding • Need “beyond DFT” approaches Quantum Monte Carlo gives correct description of van der Waals interactions Physical Sciences

  4. Overview • Describe quantum Monte Carlo – DMC • Argon – dimers, trimers, and FCC solid phase • Applications for H2 storage. H2 on carbon absorbents - benzene, coronene, and graphene • Applications in metals, FCC aluminum Physical Sciences

  5. QMC solves… Ground state of full many-body Schrödinger equation Electron correlations treated directly, non-perturbative approach Physical Sciences

  6. Variational Monte Carlo (VMC) Slater-Jastrow trial wavefunction Single particle orbitals from DFT and parameters in are determined using variance minimization Physical Sciences

  7. DFT inputs for “production” runs • PWSCF • LDA & GGA exchange-correlation functionals • Plane wave basis sets (150 - 400 Rydberg cutoff) • Norm-conserving, Troullier-Martins pseudopotentials (Casula scheme to maintain variational principle) • Experimental structures (no optimization) Physical Sciences

  8. Improvements to CASINO ver. 2.2.* for large systems Fe with 1024 electrons, timings using blips in seconds Old (ver. 2.1) New (ver. 2.2.*) WFDET in new version is 8-9 times faster WFDET only 8% of total computing time (Jastrow 39%) Physical Sciences

  9. φ1(r) φ1(r) φ2(r) φ2(r) φ3(r) φ3(r) φ4(r) φ4(r) Distributing storage of blips in CASINO ver. 2.2.* Blips in large systems can require large amounts of memory Share blip orbitals among a set of CPUs CPU 1 WFDET CPU 2 r r r share r (r,r) (r,r) evaluate orbitals {φ3(r), φ4(r), φ3(r), φ4(r)} {φ1(r), φ2(r), φ1(r), φ2(r)} Time {φ1(r), φ2(r)} swap orbitals {φ3(r), φ4(r)} Swaps (using MPI) can be done at different points in code Physical Sciences

  10. Overhead of sharing blips in CASINO ver. 2.2.* Fe with 1024 electrons, timings using blips in seconds on 64 CPUs Physical Sciences

  11. FCC argon bound by weak dispersion interactions • Argon (closed electronic shell) very inert • Noble atom solid, argon melts at 84 K • Well characterized experimentally FCC argon Physical Sciences

  12. Ar Ar d Argon dimer- compare DMC and CCSD(T) • Simple system to study the weak dispersive interaction • DMC and highly converged CCSD(T) agree at all separations Physical Sciences

  13. Argon dimer- compare DMC and CCSD(T) DMC fixed-node error independent of separation d Two-body potential from K. Patkowski, et. al., Mol. Phys., 103, 2031 (2005) Physical Sciences

  14. For Å Lennard-Jones potential agrees with DMC Argon dimer- compare DMC and CCSD(T) Lennard-Jones potential Physical Sciences

  15. Including only two-body contributions to FCC argon †R.A. Aziz, J. Chem. Phys. 99, 4518 (1993) Physical Sciences

  16. x Ar d0 Ar Ar Argon trimer – probing 3-body term 3-body term- 8% of cohesive energy in FCC argon Physical Sciences

  17. FCC argon- high precision DMC FCC Ne : N.D. Drummond and R.J. Needs, Phys. Rev. B 73, 024107 (2006) Our statistical error bars are 5 times smaller and time-step 4 times smaller Probed volumes 10 times larger Eliminate finite-size bias Physical Sciences

  18. FCC argon - DMC and DFT LDA severely overbinds while GGA is significantly underbound DMC results not sensitive to nodes Vinet EOS gave best fit to DMC Physical Sciences

  19. FCC argon – comparison with experiment error of 10 meV/atom = 0.2 kcal/mole sub-chemical accuracy error 2.0 kcal/mole Variational principle – get better cancellation of fixed-node error by computing EOS Physical Sciences

  20. Fixed-node error in DMC Binding energies in semiconductors (eV/atom) Binding energies in molecules 55 molecules (G1 basis set) DMC error =130 meV/atom = 2.9 kcal/mole J.C. Grossman, J. Chem. Phys. 117, 1434 (2002) Computing binding energies using EOS approach would likely give sub-chemical accuracy Physical Sciences

  21. Many-body terms in FCC argon Argon many-body effects reduce the binding energy and the bulk modulus of FCC argon Physical Sciences

  22. Hydrogen economy requires effective hydrogen storage • Ideal storage is at room temperature • High density requires non-hydrogen elements (1liter gasoline has 64% more H than 1liter of liquid H) • Range of H2 binding energies suitable: 0.1 - 0.5 eV/(H2 molecule) BMW Hydrogen 7 Physical Sciences

  23. Understanding physisorption of H2 on carbon substrates Focus :: H2 adsorbed on Benzene Coronene Graphene LDA and GGA unable to correctly describe H2 binding in these systems Physical Sciences

  24. H2 on benzene Single H2 binding energy is ~52 ± 8 meV Physical Sciences

  25. H2 on coronene Single H2 binding energy is ~200 ± 12 meV Physical Sciences

  26. H2 on planar Graphene (1/3 filling ) 128 atom super cell Methods to treat van der Waals interactions accurately within DFT is an active area of research Physical Sciences

  27. vdW potentials are transferable vdWCCSD(T)LDAGGA (a) C2H2 dimer, (b & c) C2H2-H2, (d) C02 dimer, (e) C6H6-H2, (f) C6H6-H20, (g & h) C6H6 dimer 140 structures of DNA base pairs vdW errors of 0.5 kcal/mole Physical Sciences

  28. In progress / future directions • Carbon based materials offer many possibilities for tuning binding energetics of H2 • curvature, damage, doping, decorating, charging • Metal-organic frameworks (MOFs) • have shown promise for H2 storage Physical Sciences

  29. Applying DMC to metals First important application of DMC to electronic systems was homogeneous electron gas at LLNL (D.M Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980)) • Third most cited Physical Review Letters • Results form basis of LDA and GGA approaches There have been few calculations of the EOS of inhomogeneous metals • Li†,Al* – VMC †(G. Yao, et. al., Phys. Rev. B 54, 8393 (1996)), *(R. Gaudoin, et. al., J. Phys.: Condens. Matter 14, 8787 (2002)) • Mg – DMC (M. Pozzo and D. Alfé, Phys. Rev. B 77, 104103 (2008)) Physical Sciences

  30. Challenges for DMC - inhomogeneous metals Numerous semiconductors and insulators have been studied using QMC over the past 20 years • Inhomogeneous metals have a Fermi surface requiring larger supercells containing more electrons • Partial occupation of orbitals at Fermi level cannot be directly translated into a real used in DMC. Have an “open shell” which breaks symmetries Physical Sciences

  31. DMC of FCC Al FCC Al with 256 atoms, 768 electrons Statistical error bars 20 times smaller than previous VMC Physical Sciences

  32. DMC of FCC Al using single determinant Discontinuity in EOS caused by band crossing which changes symmetry of nodes at a=3.97 Å when using a single determinant trial wavefunction Physical Sciences

  33. DMC of FCC Al using multiple determinants optimized using variance minization Obtain smooth EOS but not the lowest energy at all “a” despite having greater variational freedom Physical Sciences

  34. DMC of FCC Al using mulitiple determinants optimized using energy minimization* *M.P. Nightingale and V. Melik-Alaverdian, Phys. Rev. Lett. 87, 043401 (2001) C.J. Umrigar, et. al., Phys. Rev. Lett. 98, 110201 (2007) J. Toulouse and C.J. Umrigar, J. Chem. Phys. 126, 084102 (2007) Physical Sciences Obtain lowest energy smooth EOS

  35. DMC EOS of FCC Al • B0 depended sensitively on the fit • Size of error in Ecoh consistent with fixed-node error • Our value for A0 is close to previous VMC calculation • Understanding errors in A0 is a WIP Physical Sciences

  36. Conclusions • DMC is only feasible approach capable of directly treating the weak dispersive interaction for systems with more than a few atoms • DMC calculated EOS of FCC argon agrees closely with experiment, while DFT fails • Van der Waals interactions play a key role in H2 absorption in planer hydrocarbon absorbents • Computed EOS of FCC aluminum Physical Sciences

  37. Acknowledgments Shengbai Zhang (RPI) Yiyang Sun (RPI) Yong Hyun Kim (NREL) Jonathan Dubois (LLNL) Norm Tubman (Northwestern) Sebastien Hamel (LLNL) Eric Schwegler (LLNL) Physical Sciences

  38. Comparison of first-principles methods *With 6-311G* basis W.M.C. Foulkes, et. al., Rev. Mod. Phys. 73, 33 (2001) Physical Sciences

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