practical quantum monte carlo calculations: qwalk
DESCRIPTION
Practical quantum Monte Carlo calculations: QWalk. Lucas Wagner. Used by >100 people Open source: http:// www.qwalk.org Solids, liquid, gas phase Scales to >20,000 processor cores. Simple separable architecture . Distributed development. Cohesive energy. Lattice constant. - PowerPoint PPT PresentationTRANSCRIPT
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Practical quantum Monte Carlo calculations: QWalk
Lucas Wagner
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• Used by >100 people• Open source: http://www.qwalk.org
• Solids, liquid, gas phase• Scales to >20,000 processor cores
Distributed development
Simple separable architecture
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Cohesive energy
FN-DMC (eV)
Expe
rimen
t (eV
)Lattice constant
Expe
rimen
t (An
gstr
oms)
FN-DMC (Angstroms)Kolorenc and Mitas Rep. Prog. Phys. 74 (2011) 026502
Petruzielo, Toulouse, and Umrigar J. Chem. Phys. 136, 124116 (2012)
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Information passed from DFT/Hartree-Fock program to QMC code:
• Positions of atoms• Pseudopotentials• The one-particle orbitals and their occupations
QWalk supports reading this information from several DFT/quantum chemistry codes:• GAMESS• Gaussian• NWChem• SIESTA• ABINIT• CRYSTAL
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The GAMESS-QWalk pipeline
Most developed interface for molecules. 5 steps to accurate calculations
1. Choose pseudopotentials and basis sets2. Run GAMESS3. Run gamess2qmc4. Add a Jastrow factor and optimize5. Run diffusion Monte Carlo
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Step 4a: Jastrow factor• General form of wave function
– Slater determinant (Hartree-Fock)
– Two-body Jastrow
– Three-body Jastrow
• We optimize only the c coefficients
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2-body:• Homogeneous systems (silicon,
hydrogen, etc)• Very cheap
3-body:• Strongly inhomogeneous systems• More expensive
Can always check how much it improves the wave function
2-body or 3-body?
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Properties of an exact ground state wave function:• Energy is minimized • Variance of the local energy is zero
Usually the variance decreases by a factor of ~2 between the Slater determinant and the Slater-Jastrow wave function.
How to know if if a wave function is good
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Timestep: you must extrapolate this to zero
The ultimate accuracy of DMC calculations is determined by the nodes, the zeros of your trial wave function.
Step 5: Diffusion Monte Carlo
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The variance (sigma in QWalk) is high(>10). Causes:• Poor basis• Unconverged DFT/HF run• Bad geometry
The kinetic energy should match the DFT/HF kinetic energy.
Conceptual questions:
How does the total energy of QMC relate to:• DFT?• Hartree-Fock?• Coupled-cluster?
How to immediately recognize that your run is messed up:
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All numbers in QWalk are reported with one-sigma stochastic errors. There is a 33% chance that the true average is outside this range.
Errors are reduced as 1/sqrt(T), where T is the computer time.
A discussion on error bars
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Using QWalkEvaluate Slater determinant properties
Optimize a Jastrow factor->filename.wfout
Run diffusion Monte Carlo with optimized Slater-Jastrow trial function
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Dealing with stochastic simulation (VMC/DMC)
• Calculation is divided into blocks of moves• Averaged information for each block is
appended to filename.log • Checkpoint is written every block to
filename.config
To decrease error bars, just rerun the input file, the calculation will continue where it left off.
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Units
• Energy: 1 Hartree=27.216 eV• Distance: 1 Bohr=0.529177 Angstrom
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Discussion points
• When might one want to use QMC? • What questions can it answer?• When is it easy?• When is it hard?
• When might fixed node error be large?
Much of the challenge in QMC calculations is setting up the pseudopotentials, getting DFT converged, etc. Not so much the actual run.
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Lucas K. Wagner, NSE C242 & Phys C203, Spring 2009, U.C. Berkeley
Where does the fixed-node approximation fail?
Most of the time, the approximation is good.
Let’s look at a classic case where it fails: Be atom.
HF trial nodes: ~85% of the correlation energyIncluding the 2p orbitals: ~99% -- almost exact!
1s
2s
2p
Hartree-Fock ground state
Almost the same energy