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
  1000s 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

• DFT simulations as a function of pressure and
  temperature
• SIESTA code GGA functional
• Dissociation and exotic behavior in shock waves

• Hot molecular liquid --- 58 Gpa 7600 K
• Nitrogen molecules dissociate and reform

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 in low
  temperature simulations

Molecular N2 N6
Energy/atom
Previously predictedCubic 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
Nitrogen New structures predicted

• New low energy crystal structures found from
  simulations at low temperature GGA functional

Top view
Side view
Fermi Surface of Hexagonal packedzig-zag chains
- Two types of bands
6
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
Quantum Monte Carlo (QMC) simulations of
energetic materials

• Symbiosis between QMC DFT-quantum chemistry
  approaches
• QMC gives benchmark quality results for systems
  of 1000s of valence electrons can describe
  condensed matter
• QMC denotes several stochastic methods
• Variational Monte Carlo ( T0)
• Projector Monte Carlo - diffusion MC
• Path Integral Monte Carlo ( Tgt0)
• 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 lt 1 kcal/mol
• More work needed on minimizing fixed-node error

12
Long standing problem forces in QMC

• Hellman-Feynman forces have 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 distancescomparison 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
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
Hydrogen Phase Diagram
We find a stable solid melting about 100K.
17
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.

18
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.