Transcript ccstut 9737

Topics relevant to program
Kieron Burke
UC Irvine Chemistry and Physics
with
Lots of other folks
Many papers available at
http://dft.uci.edu
March 15, 2011
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Outline
• Kieron’s conjecture
– Rise of empiricism in DFT
– Changing Z, keeping N=Z.
– Orbital-free theory
• Embedding:
– atoms in molecules
– O(N) methods
– QM/MM
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Rise of empiricism
CECAM workshop: How to Speed Up Progress
and Reduce Empiricism in Density Functional
Theory
Location : ACAM, Dublin, Ireland
June 20, 2011 - June 24, 2011
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Things users despise about DFT
No simple rule for reliability
No systematic route to improvement
If your property turns out to be inaccurate,
must wait several decades for solution
Complete disconnect from other methods
Full of arcane insider jargon
Too many functionals to choose from
Can only be learned from a DFT guru
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Things developers love about DFT
No need to be reliable
No route to systematic improvement
If a property turns out to be inaccurate, can
spend several decades looking for solution
No need to connect other methods
Lots of lovely arcane insider jargon
Oh so many functionals to choose from
Everyone needs their own DFT guru
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Alphabet soup
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Semiclassical derivations
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Kieron’s conjecture
All success of DFT approximations
stems from exactness of local
approximations as N=Z→∞
March 1, 2011
CalTech
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Results so far
• Can show LDA is leading term in semiclassical
expansion in terms of either potential or
density
• Expansion is asymptotic
• Leading corrections are universal as
functionals of the potential, not the density
• Derived parameter in B88.
• New conditions on kinetic energy functional.
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Structural and Elastic Properties of solids
Errors in LDA/GGA(PBE)-DFT computed lattice constants and
bulk modulus with respect to experiment
→ Fully converged results
(basis set, k-sampling,
supercell size)
→ Error solely due to
xc-functional
→ GGA does not outperform
LDA
→ characteristic errors of
<3% in lat. const.
< 30% in elastic const.
→ LDA and GGA provide
bounds to exp. data
→ provide “ab initio
error bars”
Blazej Grabowski, Dusseldorf
 Inspection of several xc-functionals is critical to estimate
March
predictive
15, 2011
power and error bars!
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I along first row
p-group
s-group
Ne
Li
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Noble gases
alkalis
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I along first and second rows
p-group
s-group
Ar
Na
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Noble gases
alkalis
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Extrapolation of Z→∞ by column
Lucian
Constantin
Using code of
Eberhard Engel
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I along last row
p-group
s-group
First row
Second row
Infinith row
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Noble gases
alkalis
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I along last row
p-group
s-group
HF
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Noble gases
alkalis
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I along last row
p-group
s-group
HF
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Noble gases
alkalis
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I along last row
p-group
s-group
XC
HF
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Noble gases
alkalis
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I along last row
p-group
s-group
XC
HF
ETF
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Noble gases
alkalis
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Z→∞ limit of ionization potential
• Shows even energy
differences can be found
• Looks like LDA exact for
EX as Z→∞.
• Looks like finite EC
corrections
• Looks like extended TF
(treated as a potential
functional) gives
average.
•
Constantin, Snyder, Perdew, and KB,
J. Chem. Phys. 133, 241103 (2010)
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Orbital-free theory
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Potential functional theory
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Orbital-free potential-functional
for C density (Dongyung Lee)
4pr2n(r)
r
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•I(LSD)=11.67eV
• I(PFT)=11.43 eV
•I(expt)=11.26eV
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Things we hope to fix about DFT
approximations
Give rules for reliability
Systematic route to improvement
If your property turns out to be inaccurate,
try a different resumming of asymptotic
series
Semiclassical connection with other methods
Semiclassical explanation of DFT effects
Limited non-empirical set of functionals
Does not require explanation from DFT guru
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Road to partition
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Atoms in molecules
O(N)
QM/MM
Effective charges
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Basic partition theory
• Consider fragments as isolated and minimize
their energies, but requiring sum of densities
equal molecular density:
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Basics: Partition potential
• How to find minimum? Use Lagrange
multipliers:
• Lagrange multiplier is called partition
potential, vp(r), a global property of the
molecule
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Example: Partition potential
• Each fragment
density is the
ground-state
density in
effective
fragment
potential,
va(r)+vp(r)
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12-atom chain
• Construct chain of Eckhardt potentials
• Peter Elliott solved 12 single-atom fragment
problems.
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Fragment densities for the A-atom when ZA = 1.005 and: solid lines: ZB = 0.995, and
R = 1.65; dotted lines: ZB = 0.895, and R = 1.80. These have been shifted and
renormalized to test shape transferability (see text).
Published in: Yu Zhang; Adam Wasserman; J. Chem. Theory Comput. 2010, 6, 3312-3318.
March
15, 2011
DOI: 10.1021/ct100247q
Copyright © 2010 American Chemical Society
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Basic statements
• Can perform your KS calculation as sum of atomic
calculations, each atom in an effective field.
• This can be done exactly, but costs more than
molecular/solid calculation.
• Should be possible to make simple
‘neighborhood’ approximation to get linear
scaling
• Directly calculate the dissociation energy, without
total energies.
• We’ve done it for model systems
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Embedding exact calc
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Aside: First ever KS calculation with exact
EXC[n]
• Used DMRG
(density-matrix
renormalization
density
group)
• 1d H atom chain
• Miles
Stoudenmire,
Lucas Wagner,
Steve White
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Summary
• Conjecture
– New way to think about DFT approximations
– What about going down columns?
– What about large Z: everything is continuous
• Partition
– Formalism for answering many questions
– Allows embedding of accurate calculation within
KS-DFT calculation
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