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![Page 1: Quantum Monte Carlo for “Difficult” Systems in Materials Chemistry Ainsley A. Gibson Howard University Washington, DC 20059.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649f1c5503460f94c32f71/html5/thumbnails/1.jpg)
Quantum Monte Carlo for “Difficult” Systems in Materials
Chemistry
Ainsley A. GibsonHoward UniversityWashington, DC 20059
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Black Box Computing
• 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
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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
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“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.
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MethodElectron Correlation,
in Principle
Electron Correlation,
in Practice
Density Functional Theory
Characteristic density and exact density functional
recover system’s properties
Exact functional unknown, functionals generated by fit
to experiment or theory
Traditional ab initio post-HF methods
Infinite excitations from reference state(s) provide approximation from one-
electron basis
Truncated number of excitation types; selected reference state(s) used
Quantum Monte Carlo (QMC)
Random sampling of wavefunction-based probability in real 3-dimensional space
Explicit inter-particle interaction added to
independent-particle trial functions
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Method Pros Cons
Density Functional Theory
Inexpensive, and functionals exist that are
well-tuned to specific chemistries
No hierarchy of functionals, low to medium accuracy
Traditional ab initio post-HF methods
High to very high accuracy; has a hierarchy of methods
Moderately expensive to extremely expensive, may
fail regardless
Quantum Monte Carlo (QMC)
Massively parallel, very high accuracy, simple error
estimation, and simple excited state energies
Expensive to very expensive, small energy differences challenging
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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.
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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.
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Applications
• Atomic Excited States
• Beryllium Dimer
• Nanoscale Ternary Compounds (HU-CREST)
• Transition Metal Energetics (AHPCRC)
• Atmospherically Interesting
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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
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Atomic Excited StatesDeviation from experiment, eV
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Li 2P Be 3P Be 1P B 4P C 1D C 1S N 2D N 2P O 1D O 1S F 4P
B3LYP MP2 CCSD CCSD(T) DMC
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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.
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Dissociation Energies, in cm-1
Method De, cm-1
MRSDCI1 1049
R12MRCI, MRACPF2 898(8)
estimated FCI/cc-pV5Z3 803.61 - 822.71
“extensive” ab initio3 944(25)
VMC/CASSCF(4,8) 90% -867(71)
VMC/CASSCF(4,8) 95% -7422(152)
DMC/CASSCF(4,8) 90% 1293(52)
DMC/CASSCF(4,8) 95% 829(64)
Experiment4 839(10)
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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.
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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.
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Nitrogen Excited States
CISD/cc-pVTZ
VMC DMC Exp’t
2D 2.9227 2.50(3) 2.43(4) 2.3835
2P 3.1458 3.34(4) 3.45(4) 3.5756
4P (2s2p4) 10.6570 10.95(6) 10.84(4) 10.9239
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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
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X-alpha, LSDA, and PL density functionals
IP Deviation, X-alpha, LSDA, PL
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Sc Ti V Cr Mn Fe Co Ni Cu Zn
X-alpha LSDA PL
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B- functionals: B971, BLYP and BPW91
IP Deviation, B Functionals, eV
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Sc Ti V Cr Mn Fe Co Ni Cu Zn
B971 BLYP BPW91
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B1- functionals: B1B95 and B1LYP
IP Deviation, B1 Functionals
-3.50
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
Sc Ti V Cr Mn Fe Co Ni Cu Zn
B1B95 B1LYP
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B3- functionals: B3P86, B3PW91, B3LYP
IP Deviation of B3 Functionals, eV
-4.00
-3.50
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
Sc Ti V Cr Mn Fe Co Ni Cu Zn
B3P86 B3PW91 B3LYP
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Selected post-HF Ionization Potentials
IP Deviation, eV
-6.0
-4.0
-2.0
0.0
2.0
Sc Ti V Cr Mn Fe Co Ni Cu Zn
ROHF MP2 CCSD CCSD(T)
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QMC/HF Ionization Potentials
IP Deviation, QMC/HF Orbitals
-6.0000
-4.0000
-2.0000
0.0000
2.0000
4.0000
6.0000
8.0000
Sc Ti V Cr Mn Fe Co Ni Cu
Devia
tion
, eV
VMC DMC
2.67,VMC
1.52,DMC
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QMC/NO Ionization Potentials
IP Deviation, QMC/Natural Orbitals
-3.5000
-2.5000
-1.5000
-0.5000
0.5000
1.5000
2.5000
3.5000
Sc Ti V Cr Mn Fe Co Ni Cu
VMC DMC
1.71,VMC
1.57,DMC
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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.
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Results to Date, in eV
MRCI 0.943
MRCI+Q 1.049
VMC 0.70(4)
DMC 1.06(16)
Exp. 1.0625(4)
Exp. 1.132(1)
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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
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AHPCRC Current Work:Transition Metals
• Electron Affinity• Proton Affinity
• Small Clusters, Mx, x = 2,…,10
• Surfaces and solids• Silver nanoparticle stability (collaborative with
CREST)
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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
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Acknowlegements
• 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