Kieron Burke UC Irvine Chemistry and Physics with Lots of other folks March 15 2011 IPAM 1 Many papers available at httpdftuciedu Outline Kierons conjecture Rise of empiricism in DFT ID: 213110
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Slide1
Topics relevant to program
Kieron Burke UC Irvine Chemistry and Physicswith Lots of other folks
March 15, 2011
IPAM
1
Many papers available at http://dft.uci.eduSlide2
Outline
Kieron’s conjectureRise of empiricism in DFTChanging Z, keeping N=Z.Orbital-free theoryEmbedding:atoms in
moleculesO(N) methodsQM/MM
March 15, 2011
IPAM
2Slide3
Rise of empiricism
March 15, 2011IPAM3
CECAM workshop:
How to Speed Up Progress and Reduce Empiricism in Density Functional TheoryLocation : ACAM, Dublin, Ireland
June 20, 2011 - June 24, 2011Slide4
Things users despise about DFT
No simple rule for reliabilityNo systematic route to improvementIf your property turns out to be inaccurate, must wait several decades for solutionComplete disconnect from other methods
Full of arcane insider jargonToo many functionals
to choose fromCan only be learned from a DFT guru
March 15, 2011
IPAM
4Slide5
Things developers love about DFT
No need to be reliableNo route to systematic improvementIf a property turns out to be inaccurate, can spend several decades looking for solutionNo need to connect other methods
Lots of lovely arcane insider jargonOh so many functionals
to choose fromEveryone needs their own DFT guru
March 15, 2011
IPAM
5Slide6
Alphabet soup
March 15, 2011
IPAM
6Slide7
Semiclassical derivations
March 15, 2011IPAM
7Slide8
Kieron’s conjecture
All success of DFT approximations stems from exactness of local approximations as N=Z→∞March 1, 2011
CalTech
8Slide9
Results so far
Can show LDA is leading term in semiclassical expansion in terms of either potential or densityExpansion is asymptoticLeading corrections are universal as functionals of the potential, not the densityDerived parameter in B88.New conditions on kinetic energy functional.
March 15, 2011
IPAM
9Slide10
Improvements of PBEsol
Structural and Elastic Properties of solids
Errors in
LDA/GGA(PBE)-DFT computed lattice constants and
bulk modulus with respect to experiment
Inspection of several
xc-functionals
is critical to estimate
predictive power and error bars!
→
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
March 15, 2011
10
IPAMSlide11
I along first row
March 15, 2011IPAM11
alkalis
Noble gases
s-group
p-group
Li
N
eSlide12
I along first and second rows
March 15, 2011IPAM
12
alkalis
Noble gases
s-group
p-group
Na
ArSlide13
Extrapolation of Z→∞ by column
March 15, 2011IPAM
13
Lucian
Constantin
Using code of
Eberhard
EngelSlide14
I along last row
March 15, 2011IPAM
14
alkalis
Noble gases
s-group
p-group
First row
Second row
Infinith
rowSlide15
I along last row
March 15, 2011IPAM
15
alkalis
Noble gases
s-group
p-group
HFSlide16
I along last row
March 15, 2011IPAM
16
alkalis
Noble gases
s-group
p-group
HFSlide17
I along last row
March 15, 2011IPAM
17
alkalis
Noble gases
s-group
p-group
XC
HFSlide18
I along last row
March 15, 2011IPAM
18
alkalis
Noble gases
s-group
p-group
XC
HF
ETFSlide19
Z→∞ limit of ionization potential
Shows even energy differences can be foundLooks like LDA exact for EX as Z→∞.Looks like finite E
C correctionsLooks like extended TF (treated as a potential functional) gives average
.Constantin, Snyder,
Perdew, and KB, J. Chem. Phys. 133
,
241103
(2010
)
March 15, 2011
IPAM
19Slide20
Orbital-free theory
March 15, 2011IPAM
20Slide21
Potential functional theory
March 15, 2011IPAM
21Slide22
Orbital-free potential-functional for C density (Dongyung Lee)
March 15, 2011IPAM
22
4p
r2n(r)
r
I(LSD)=11.67eV
I(PFT)=11.43 eV
I(
expt
)=11.26eVSlide23
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 effectsLimited non-empirical set of
functionalsDoes not require explanation from DFT guru
March 15, 2011
IPAM
23Slide24
Road to partition
Atoms in moleculesO(N)QM/MMEffective chargesMarch 15, 2011
IPAM
24Slide25
Basic partition theory
Consider fragments as isolated and minimize their energies, but requiring sum of densities equal molecular density:March 15, 2011IPAM
25Slide26
Basics: Partition potential
How to find minimum? Use Lagrange multipliers:Lagrange multiplier is called partition potential, vp(r), a global property of the molecule
March 15, 2011
IPAM
26Slide27
Example: Partition potential
Each fragment density is the ground-state density in effective fragment potential, va(r)+vp(r
)
March 15, 2011
IPAM
27Slide28
12-atom chain
Construct chain of
Eckhardt
potentialsPeter Elliott solved 12 single-atom fragment problems.
March 15, 2011
IPAM
28Slide29
Fragment densities for the A-atom when
Z
A = 1.005 and:
solid lines
:
Z
B = 0.995, and
R
= 1.65;
dotted lines
:
Z
B = 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.
DOI: 10.1021/ct100247q
Copyright © 2010 American Chemical Society
March 15, 2011
29
IPAM
Adams
partitionsSlide30
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 scalingDirectly calculate the dissociation energy, without total energies.We’ve done it for model systems
March 15, 2011
IPAM
30Slide31
Embedding exact calc
March 15, 2011IPAM
31Slide32
Aside: First ever KS calculation with exact
EXC[n]Used DMRG (density-matrix renormalization group)1d H atom chainMiles Stoudenmire
, Lucas Wagner, Steve White
March 15, 2011
IPAM
32
x
densitySlide33
Summary
ConjectureNew way to think about DFT approximationsWhat about going down columns?What about large Z: everything is continuousPartitionFormalism for answering many questionsAllows embedding of accurate calculation within KS-DFT calculation
March 15, 2011
IPAM
33