Quantum Simulations of Materials Under Extreme Conditions

1. Quantum Simulations of Materials Under Extreme Conditions David M. Ceperley Richard M. Martin Simone Chiesa Ed Bukhman William D. Mattson* Xinlu Cheng Department of PhysicsUniversity of Illinois at Urbana-Champaign Not supported by the MURI grant *Thesis at University of Illinois, 2003 now at Army research Lab

2. Simulations of energetic materialsfrom the fundamental equations • Simulation techniques are essential to “solve” many-body problems: e.g. classical simulations of atoms & molecules, reactions, thermal motion • Combine Quantum Monte Carlo, DFT and Quantum Chemistry methods • Density Functional Theory (DFT) • Most widely used approach for large scale simulations of nuclei and electrons • In principle exact, but, in practice, limited by the approximate functionals • Quantum Monte Carlo (QMC) • Most accurate method for large, many-electron systems • A wavefunction-based approach • Provides benchmark quality results for systems of 1000’s of valence electrons • Can describe matter from plasmas to molecules to condensed matter • Provides improved functionals for DFT • DFT provides input for QMC trial functions • Development of new methods --- Applications to energetic materials

3. Nitrogen under extreme conditions • Hot molecular liquid --- 58 Gpa 7600 K • Nitrogen molecules dissociate and reform • DFT simulations as a function of pressure and temperature • SIESTA code – GGA functional • Dissociation and exotic behavior in shock waves Squeezed & Cooled • Connected structures – non-molecular • Two-fold (chain-like) and three-fold (cubic gauche-like) – Large energy barriers • Glassy behavior and meta-stability at low temperature • Prediction of new structures at low temperature

4. Nitrogen under extreme conditions New low energy structures found inlow temperature simulations • Molecular N2 – N6 Energy/atom • Previously predicted“Cubic Gauche” • Hexagonal packedzig-zag chains • Known e phase Volume/atom • W. D. Mattson, D. Sanchez-Portal, S. Chiesa, R. M. Martin, Phys. Rev. Lett. (2004)

5. Hexagonal packedzig-zag chains • Molecular N2 – N6structure • Known e phase Nitrogen: New structures predicted • Top view New low energy crystal structures found from simulations at low temperature GGA functional • Side view • Fermi Surface of • Hexagonal packedzig-zag chains - Two types of bands

6. Energy per atom - eV • Magnetic Transition • Volume per atom - A3 Oxygen: Prediction of energies of atomic phases at high pressure • Collaboration with Brenner to make improved potentials for O • Calculations for simple metallic structures using same method as used for nitrogen – SIESTA with GGA Simple cubic is most stable

7. Nitromethane: CH3-NO2 • Preliminary molecular calculations to study dissociation pathways • Goal: full simulations in condensed phase at high temperature and pressure • Calculations using SIESTA with GGA • Related to work in recent papers • Kabadi and Rice, J. Phys. Chem. A 108, 532 (2004) • Manna, Reed, Fried, Galli, and Gygi, J. Chem. Phys. 120, 10146 ( 2004)

8. QuantumMonte Carlo (QMC) simulations of energetic materials • Symbiosis between QMC & DFT-quantum chemistry approaches • QMC gives benchmark quality results for systems of 1000’s of valence electrons – can describe condensed matter • QMC denotes several stochastic methods: • Variational Monte Carlo ( T=0) • Projector Monte Carlo - diffusion MC • Path Integral Monte Carlo ( T>0) • Coupled electron-ion Monte Carlo (separating energy scales) • What is “niche” for QMC in understanding energetic materials? • Systems with strong correlation such as • Rearrangements of electrons during reactions • Nearly degenerate structures • Disordered systems such as liquids • Significant electronic excitations or temperature effects • New advances this year

9. New method for correcting size effects • Able to treat anisotropic structures, metals, insulators,.. • Potential energy correction from low k-limit of charge-charge response function, S(k). • Kinetic energy corrections from Brillouin zone integration within DFT. Much smaller size dependence Hence, more accurate extrapolation to thermodynamic limit

10. Results for Nitrogen structures: QMC (with extrapolation) compared to DFT • QMC supports our main result using PBE-GGA • Energy of chain very close to cubic gauche; curves very similar • QMC finds shifts in the total energy relative to the N2 molecule

11. Bond dissociation energiesof nitro and amino molecules • QMC studies of energetic molecules in kcal/mol. • Reasonable numbers even for largest molecules. • Statistical error < 1 kcal/mol • More work needed on minimizing fixed-node error

12. Long standing problem: forces in QMC • Hellman-Feynman forceshave infinite variance. • Our approach: • inside core: fit p-wave electronic QMC density using a polynomial basis. • outside core: compute force directly with HF equation • Exact if electronic density is exact. Need to use forward walking or reptation to get the density. • Method is local, very simple to program, and fast. • Is it accurate?

13. Accuracy of bond distances:comparison with other methods Relative error wrt experiment • All other bond distances taken from the NIST website • QMC predicts bond lengths to 0.4% • As accurate as other approaches • Slower convergence for large Z • Goal: applications to structures of energetic materials Chiesa, Ceperley, Zhang, Sept. 04, physics/0409087

14. accuracy Coupled Ionic-Electronic Simulations • Much progress in recent years with “ab initio” molecular dynamics simulations. • However density functional theory is not always accurate enough. • Use power of current commodity processors to enhance accuracy of simulations • Empirical potentials (e.g. Lennard-Jones) • Local density functional theory or other mean field methods (Car-Parrinello or ab initio MD) • Quantum Monte Carlo: CEIMC method Method demonstrated on molecular and metallic hydrogen at extreme pressures and temperatures. Fast code!

15. CEIMC calculations on dense H Temperature dependence in CPMD-LDA is off by 100%. e-p distribution function At the same temperature LDA scaled by 2

16. Progress this year • Calculation of energy of new solid nitrogen structures • New method for QMC finite size corrections • Comparison of QMC and DFT • Paper published in PRL • Calculation of high pressure oxygen • Survey of nitro amines bond dissociation energies with QMC. • Direct coupling of QMC with DFT calculations • New method for computing forces within QMC • Combines simplicity with accuracy. • Paper submitted • Major effort to produce next generation QMC codes. • CEIMC calculations of dense hydrogen showing major problems with DFT temperature scale.

17. Plans for next year • Develop new CEIMC/PIMC code able to treat systems beyond hydrogen. • Appropriate pseudopotentials • Appropriate trial functions • Able to use Teraflop resources effectively. • Apply to energetic materials • DFT simulations of energetic materials at high temperature and pressure • Search for dissociation mechanisms and pathways • Molecules and condensed systems, e.g., nitromethane • Initiate studies of more complex systems, e.g., RDX • Benchmark studies for chemical reactions using QMC molecular forces. • Feasibility study for full simulations of energetic liquids in detonation conditions.