quantum simulations of materials under extreme conditions
DESCRIPTION
Quantum Simulations of Materials Under Extreme Conditions. David M. Ceperley Richard M. Martin Simone Chiesa Ed Bukhman William D. Mattson* Xinlu Cheng Department of Physics University of Illinois at Urbana-Champaign. Not supported by the MURI grant - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/1.jpg)
Quantum Simulations of Materials Under Extreme Conditions
David M. CeperleyRichard 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
![Page 2: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/2.jpg)
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
![Page 3: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/3.jpg)
Nitrogen under extreme conditions• DFT simulations as a function of pressure and temperature• SIESTA code – GGA functional• Dissociation and exotic behavior in shock waves
Squeezed&
Cooled
•Hot molecular liquid --- 58 Gpa 7600 K•Nitrogen molecules dissociate and reform
– 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
![Page 4: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/4.jpg)
Nitrogen under extreme conditions
Molecular N2 – N6
Hexagonal packedzig-zag chains
Volume/atom
Ene
rgy/
atom
Known phase
W. D. Mattson, D. Sanchez-Portal, S. Chiesa, R. M. Martin, Phys. Rev. Lett. (2004)
New low energy structures found in low temperature simulations
Previously predicted“Cubic Gauche”
![Page 5: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/5.jpg)
Nitrogen: New structures predictedNew low energy crystal structures found from simulations at low temperature
GGA functional
Known phase
Hexagonal packedzig-zag chains
Molecular N2 – N6 structure
Top view
Side view
Fermi Surface of
Hexagonal packedzig-zag chains - Two types of bands
![Page 6: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/6.jpg)
Oxygen: Prediction of energies of atomic phases at high pressure
• Calculations for simple metallic structures using same method as used for nitrogen – SIESTA with GGA
En
ergy
per
ato
m -
eV
-433
-432
-431
-430
-429
-428
-427
-426
-425
0 10 20 30 40 50
Simple cubic
BCC
Volume per atom - A3
Magnetic Transition
• Collaboration with Brenner to make improved potentials for O
Simple cubic is most stable
![Page 7: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/7.jpg)
• Preliminary molecular calculations to study dissociation pathways
• Goal: full simulations in condensed phase at high temperature and pressure
Nitromethane: CH3-NO2
• 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)
![Page 8: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/8.jpg)
Quantum Monte 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
![Page 9: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/9.jpg)
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
![Page 10: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/10.jpg)
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
![Page 11: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/11.jpg)
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
molecule DMC Other theory Exp.Methylamine CH3-NH2 86.6 81.5 DFT 85.7
Nitroamine NH2-NO2 62.3 53.6 G2
Nitromethane CH3-NO2 64.2 54.6 DFT 60.8-63.7
DMN (CH3)2N-NO2 52.5 39.6-43.8
RDX C3H6N5O4-NO2 72.1 41.6 DFT
![Page 12: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/12.jpg)
Long standing problem: forces in QMC
3
i j i j
ji ij
e e r rF
r
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?
![Page 13: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/13.jpg)
Accuracy of bond distances:comparison with other methods
• 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
Relative error wrt experiment
![Page 14: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/14.jpg)
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!
![Page 15: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/15.jpg)
CEIMC calculations on dense HTemperature dependence in CPMD-LDA is off by 100%.
e-p distribution function
At the same temperature LDA scaled by 2
![Page 16: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/16.jpg)
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.
![Page 17: Quantum Simulations of Materials Under Extreme Conditions](https://reader036.vdocuments.net/reader036/viewer/2022062322/56814621550346895db32a9f/html5/thumbnails/17.jpg)
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.