Post on 04-Jul-2020
Upscaling DFT Capabilitiesfor the Many Thousand
Atoms Regime
Laura E. Ratcliff
30.10.2017
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Outline
Linear-Scaling DFT
QM of large systems
0
10
20
30
40
50
5000 10000 15000 20000 25000
Wallt
ime (m
in.)
WalltimeLinear extrap. from 10725 atoms
Number of atoms
BigDFT
www.bigdft.org
ONETEP
www.onetep.org
Fragment Approach
exploiting repetition
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Simulating OLEDs
excitations in an environment
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Outline
1 O (N ) DFT
2 Fragment Approach
3 Simulating OLEDs
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Beyond the Cubic-Scaling Limit
Size Limits
thanks to supercomputers wecan treat up ∼ 1000 atoms withDFT, but O(N 3) scaling limitssystem sizes 0
10
20
30
40
50
60
0 1000 2000
Tim
e / i
tera
tion
(s)
Number of atoms
Nearsightedness
• the behaviour of large systems is short-ranged, or“nearsighted”
• the density matrix decays exponentially in systems with a gap
⇒ how can we exploit nearsightedness to treat large systems?
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Key Quantities
Support Functions (SFs)
write KS orbitals as linearcombinations of SFs φα(r):
Ψi(r) =∑
α
cαi φα(r)
• localized (user-defined radius)
• atom-centred
• expanded in systematic basis
Density Kernel
define the density matrixρ(r, r′) and kernel Kαβ:
ρ(r, r′) =∑
i
fi∣
∣Ψi(r)〉〈Ψi(r′)∣
∣
=∑
α,β
∣
∣
∣
φα(r)〉Kαβ〈φβ(r
′)∣
∣
∣
Total Energy
Hαβ = 〈φα|H|φβ〉; Sαβ = 〈φα|φβ〉
E = Tr (KH) ; N = Tr (KS)
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DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
The Algorithm
optimize SFs
atomicorbitals
optimize K
energy& forces
Accurate Minimal Basis
• energy is minimized with respect to bothSFs and kernel
• SFs adapt to the environment
• different options for kernel optimization:Fermi Operator Expansion (FOE), penaltyfunctional, purification, LNV. . .
⇒ minimal, localized basis with the samehigh accuracy as underlying systematic basis
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Basis Sets – Psincs and WaveletsCommon Features
• localized • orthogonal • systematic • use of PSPs
Wavelet Features
• flexible boundary conditions
• analytic operators
• multiresolution grid: 1 grid, 2resolution levels
-1.5
-1
-0.5
0
0.5
1
1.5
-6 -4 -2 0 2 4 6
LEAST ASYMMETRIC DAUBECHIES-16
scaling functionwavelet
Psinc Features
• periodic boundary conditions
• equivalence with plane waves
• regular grid: 1 psinc functioncentred at each grid point
0.0
0.5
1.0
-1.0 -0.5 0.0 0.5 1.0
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Support Functions
Common Features
• strict localization (∼ 6 – 8 bohr)
• minimal number: e.g. 1 SF per H, 4 per C/N/O etc.
BigDFT
• quasi-orthogonal SFs
• use of a confining potential
ONETEP
• Non-orthogonal GeneralizedWannier Functions (NGWFs)
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
From Sparsity to Linear Scaling
Sparse Matrices
• strict localization leads to sparse matrices
• sparsity depends on size anddimensionality
• make use of sparse matrix algebra
• sparsity impacts crossover point
0
200
400
600
800
1000
0 200 400 600 800 1000
Hamiltonian, alkane with 512 atoms
1e-12
1e-10
1e-08
1e-06
0.0001
0.01
1
0
100
200
300
400
500
600
700
800
0 100 200 300 400 500 600 700 800
Hamiltonian, Si cluster with 291 atoms
1e-12
1e-10
1e-08
1e-06
0.0001
0.01
1
0
10
20
30
40
50
5000 10000 15000 20000 25000
Wa
lltim
e (
min
.)Number of atoms
O (N ) DFT
• can treat 1000s of atoms using DFT at a high accuracy
• many functionalities and features available
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Outline
1 O (N ) DFT
2 Fragment Approach
3 Simulating OLEDs
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Exploiting Repetition
Calculation Bottleneck
• SF optimization takes the majority of compute time
• what happens in similar chemical environments?
Water Droplet
• internal molecularenvironment dominates
• differences between watermolecules are small
• can we use the same SFsfor each molecule?
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
ReformattingRototranslations
how do we account for varying orientations and positions?• scheme to detect rototranslations with respect to reference(“template”) coordinates
• accurate and efficient wavelet interpolation scheme
0.001
0.01
0.1
1
10
180 0 180 0 180 0 180 0 180 0 180 0 1800
E−
Ere
f(m
eV
/ato
m)
θ (°), u
(0,0,1) (0,1,0) (0,1,1) (1,0,0) (1,0,1) (1,1,0) (1,1,1)
cubic eggboxlinear eggbox
template
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Fragment Approach
Calculation Steps
• template calculation: optimize SFs for isolated fragment
• reformatting: replicate and rototranslate template SFs foreach fragment instance
• full calculation: use fragment SFs as a fixed basis, optimizingdensity kernel only
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Fragments in Action
R (Å)
−0.4
−0.3
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
0.5
1 1.5 2 2.5 3 3.5 4 4.5 5
E −
Ere
f(e
V)
R (Å)
cubiclinear
fragment 1,4fragment 2,5fragment 5,8
1.75
1.80
1.85
1.90
1.95
2.00
Req
(Å)
1e−04
1e−03
1e−02
1e−01
1e+00
E −
Ecu
bic
(eV
)
H2O Dimer
• energies affected by basis set superposition error
• but equilibrium bond length less affected
• can increase basis to improve accuracy
• approach is suited to weakly interacting fragments
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Constrained DFT I
Constrained DFT (CDFT)
• wavelet basis is ideal for adding a (constrained) charge
• in CDFT we find the lowest energy state satisfying a given(charge) constraint on the density
• we want to associate a given charge with a particular fragment
• can be used to reduce the self-interaction problem and includeenvironmental effects on site energies
CDFT with SFs
W [n, Vc] = EKS [n] + Vc (2Tr [Kwc]−Nc)
The SF basis lends itself to a Lowdin like approach for theweight function: wc = S
12PS
12
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Constrained DFT II
-0.1
0.0
0.1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Vc
Nc
0.0
1.0
2.0
3.0
4.0
∆E
(eV
)
ZnBC-BC complex
• varying charge separation between two molecules
• can find charge transfer states
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Outline
1 O (N ) DFT
2 Fragment Approach
3 Simulating OLEDs
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
OLED Transport Parameters (a)
Jholeij = 〈ψHOMO
i(mol.)
∣
∣
∣H∣
∣
∣ψHOMO
j(mol.)〉
(b)
Eholeon-site = E+1
tot − E0tot
Fragments in Disordered Host-Guest Material
• extract cluster of nearest neighbours for each molecule
• template calculations for isolated host and guest molecules
• use fragment basis to calculate transfer integrals in clusters (a)
• use CDFT to add charge to central molecule in each cluster
• calculate on site energies using CDFT results (b)
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
OLED Transport Parameters
6.2 6.4 6.6 6.8 7.0 7.2 7.4Energy (eV)
guest
pure host
host
Statistics
• disorder ⇒ dispersionof values for Eon-site
and Jij
Environmental Effects
• shift in average Eon-site (- - -) vs.isolated molecules (—)
• differences between pure host andhost guest materials
Future Challenge for Simulating OLEDs
improve the description of excitations in realistic morphologies
DFT for
1000s of
Atoms
Laura
Ratcliff
O (N )DFT
Fragment
Approach
Simulating
OLEDs
Summary
Linear-Scaling DFT
QM of large systems
0
10
20
30
40
50
5000 10000 15000 20000 25000
Wallt
ime (m
in.)
WalltimeLinear extrap. from 10725 atoms
Number of atoms
BigDFT
www.bigdft.org
ONETEP
www.onetep.org
Fragment Approach
exploiting repetition
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Simulating OLEDs
excitations in an environment
PhD and postdoc position available
Thank you for your attention!