Multi-scaleModelingusingtheAdaptive...
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Multi-scale Modeling using the Adaptive
Resolution Scheme
Christoph Junghans
Los Alamos National LaboratoryNM, USA
Oct. 9, 2012
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Coworkers
A lot of people have contributed to AdResS:
Cecilia Clementi (Rice University, Texas)
Luigi Delle Site (MPI-P → FU Berlin)
Sebastian Fritsch (MPI-P)
Kurt Kremer (MPI-P)
Brad Lambeth (Rice University, Texas)
Debashish Mukherji (MPI-P)
Patrick Kiley (University of Cambridge)
Simon Poblete (MPI-P → FZ Julich)
Adolfo Poma (MPI-P → Sapienza University of Rome)
Matej Praprotnik (MPI-P → National Institute of Chemistry,Slovenia)
Stac Bevc (National Institute of Chemistry, Slovenia)
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
IntroductionThe Adaptive Resolution Scheme (AdResS)
The big idea1
Coupling of two resolutions (AA and CG) by a forceinterpolation:
~Fαβ = wαwβ~FAAαβ + [1− wαwβ] ~F
CGαβ ,
where α and β are molecules
1M. Praprotnik, L. Delle Site, and K. Kremer, JCP 123, 224106 (2005).UNCLASSIFED(LA-UR 12-25129) 3
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
IntroductionIllustration
Magnifier: Free motion:
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
IntroductionMotivation
Inherited from coarse-graining
Accessibility of bigger time- and length-scales
Avoids sampling of unimportant degrees of freedom
Better sampling through smoother energy landscape
Computational speed-up
As an analysis tool
Study influence of coarse-graining
Replace surrounding environment
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
IntroductionWhat kind of systems can be coupled?
Atomistic and coarse-grained representation of the samesystem
Atomistic and very simplified (LJ) system
Quantum and atomistic systems
Coupling conditions2
ρat = ρcg, T at = T cg, (pat = pcg)
2M. Praprotnik, L. Delle Site and K. Kremer; Annu. Rev. Phys. Chem. 59,545 (2008).
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Methodic DetailsThe Weighting Function I
Atomistic Hybrid Coarse-grained
1
a0
x
w(x
)
b
w(x) =
1 : atomistic/explicit region0 < w < 1 : hybrid region
0 : coarse-grained region
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Methodic DetailsThe Weighting Function II
Atomistic Hybrid Coarse-grained
1
a0
x
w(x
)
b
Boundary conditions
Monotonic → No artificial barriers
w ′(dex) = 0 = w ′(dex + dhy) → smooth free energy transition
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Methodic DetailsThe Weighting Function III
Atomistic Hybrid Coarse-grained
1
a0
x
w(x
)
b
w(x) =
0 : x> dex + dhy
cos2(
π2dhy
(x − dex))
: dex + dhy >x> dex
1 : dex >x
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
AdResS at a First GlanceRadial Distribution Function (Tetrahedral Liquid)
r [σ]
g(r)
[1]
5.04.03.02.01.0
2.42.01.61.20.80.40.0
Explicit simulationAdResS AdResS as a
“magnifier” fora certain region
RDF matches andaccuracy dependsmore on the accuracyof the coarse-grainingthan on AdResS
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
AdResS at a First GlanceParticle Fluctuations
ATHYCG
x∗
N
35302520151050
50
40
30
20
10
0
t∗
= 0t∗
= 100t∗
= 200
ATHYCG
x∗
N
35302520151050
50
40
30
20
10
0
t∗
= 0t∗
= 100t∗
= 200
Particles can freely diffuse through the hybrid region
Profile is slightly asymmetric
Coarse-grained dynamics is slightly faster
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
AdResS at a First GlanceDensity Artifacts in the Hybrid Region
There is no free lunch!
EXHYCG
x [σ]
ρ/ρ
0[1
]
3020100
1.41.21.00.80.6
System is inhomogeneous inthe hybrid region
Linear interpolation is toosimple
Can be corrected, but is notnecessary in all cases
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Theory of the Thermodynamic ForceIdea
w
µex
1.00.80.60.40.20.0
20
19
18
17
16
15
14
Chemical potential in thehybrid region is different
Add an external field3
~fthermo = −∇(µAA − µ(w))
to the linear interpolation torepair the densityinhomogeneity
Correction is not alwaysnecessary
Allows to couple systems ofdifferent pressures
3S. Poblete, M. Praprotnik, K. Kremer and L. Delle Site, JCP 132, 114101(2010)
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Theory of the Thermodynamic ForcePressure View
Chemical potential is tedious to measure
Assumption of constant weight
To obtain a flat density profile one needs to compensate forthe different pressures in the hybrid region4
~fthermo = −1
ρ0∇(pAA − p(w))
Local pressure depends on the local density
~fthermo = −1
ρ20κ∇(ρ(w))
Easier, because ρ(w) can be measured on the fly
Iterative correction is possible4S. Poblete, S. Fritsch, C. Junghans, G. Ciccotti, K. Kremer and L. Delle
Site, PRL 108, 170602 (2012)UNCLASSIFED(LA-UR 12-25129) 14
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsOverview I
The problem is the hybrid region!
Question
How to reintroduce the atomistic details?
How to initialize the atomistic velocities?
How to introduced the correct bond distribution?
How to map the molecular force interpolation to the atoms inthe atomistic region?
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsOverview II
Consumed Computer Times in MD
70% Force calculation
15% Communication
8% Neighbor search
5% Position update
2% IO
Position update is cheap → do NOT remove atomistic particles,but do not treat them force-wise and integrate them everywhere.
Double representation trick5 ( everywhere)
5C. Junghans and S. Poblete, Comp. Phys. Comm. 181, 1449 (2010).UNCLASSIFED(LA-UR 12-25129) 16
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsVirtual Sites
How to implement the double representation?
Virtual sites: Dummy particles, which are movedaccording to a geometrical rule rather than byNewton’s equation of motion.
Force distribution
Force on an atom in an molecule with a virtual site:
~F atomi = −
∂(V + V cg)
∂~ri= ~F ex
i + ~F cg∂~rcg
∂~ri
COM= ~F ex
i +mi
∑
i∈αmi
~F cg
Can be easily added to the integrator!
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsIntegrator
Velocity Verlet Integrator (with AdResS and virtual sites)
1. v(t +∆t/2) = v(t) + ∆t/2 f (t)/m
2. p(t +∆t) = p(t) + ∆t v(t +∆t/2)
2b. Update the positions, velocities and weighting functions w(~R)of the virtual sites
3. Calculate f (t +∆t) from p(t +∆t), v(t +∆t/2) (andthermostat)
3b. Distribute the force of the virtual sites to the real particles
4. v(t +∆t) = v(t +∆t/2) + ∆t/2 f (t +∆t)
Virtual sites increase the amount of communication (O(N2/3VS )).
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsThermostat
A thermostat is needed for a smooth transition.
Langevin Thermostat
Thermostat force acting on the atoms
~f thermoi = ~f Di + ~f Ri = ξi~vi + σi~ηi .
One can show that
∑
i∈α
~f thermoi = ~FD
α + ~FRα
is also a Langevin thermostat with a commonfluctuation-dissipation theorem (σ2 = kBT ξ) if the frictionconstants ξi have been scaled with the masses, ξi = miξ.
DPD thermostat can also be used, but more theory is involved.UNCLASSIFED(LA-UR 12-25129) 19
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsReinitialization
Possiblities for Velocity and Bond Reinitialization
Initialization from Maxwell/bond distribution
Freeze and unfreeze them
Keep on integrating them
Reminder: We have hybrid molecules everywhereBonded interactions are cheap→ keep on integrating them is the easiest solution
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsCut-Offs
AdResS needs a molecule-based cut-off due to the forceinterpolation.
Molecular Cut-Offs
Avoid that molecules interact half atomistic - halfcoarse-grained
Avoid dipoles at the cut-off
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Numerical DetailsSpeed-up
Simulation of a big system with small atomistic region: 6
Ideal strong speed-up (const. systemsize)
s−1 =
(
tnew
told
)
VAA<<VCG=tnot-forces
ttotal+
tforces
ttotal
1
(atoms per molecule)2
Toluene= 0.26 + 0.74 ·
1
2× 122≈ 3.6−1
6S. Fritsch, C. Junghans and K. Kremer, JCTC 8, 398 (2012).UNCLASSIFED(LA-UR 12-25129) 22
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesTetrahedral Liquid
Toy model for a liquid (methane-like). 7
Explicit (all-atom) Interactions
Non-bonded (even inside the molecules), LJ:
UexLJ(riαjβ) =
{
4ǫ[
(σ/riαjβ)12 − (σ/riαjβ)
6 + 14
]
, riαjβ ≤ 21/6σ
0, riαjβ > 21/6σ
Bonded, FENE:
UexFENE (riαjα) =
{
−12kR
20 ln
[
1− (riαjβ/R0)2]
, riαjβ ≤ R0
∞ riαjβ > R0
Coarse-grained Interactions
Isotropic one-site tabulated potential U(rij) by IBI
7C. Junghans and S. Poblete, Comp. Phys. Comm. 181, 1449 (2010).UNCLASSIFED(LA-UR 12-25129) 23
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesTetrahedral Liquid (Structure)
r [σ]
g(r)
[1]
5.04.54.03.53.02.52.01.51.0
2.01.81.61.41.21.00.80.60.40.20.0
2.01.91.81.7
2.01.81.6
Explicit simulationNo correctionip correctiontf correction
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesTetrahedral Liquid (Density profile)
x [σ]
tfco
rrec
tion
ρ/ρ
0[1
]
35302520151050
1.2
1.0
0.8
0.6
EXHYCG
noco
rrec
tion
ρ/ρ
0[1
]
1.4
1.2
1.0
0.8
0.6
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater
A realistic, but simple system
Electrostatics by Reaction Field
One bead coarse-grained model
Can we couple a not pressure-corrected model, too? 8
8S. Poblete, S. Fritsch, C. Junghans, G. Ciccotti, K. Kremer and L. DelleSite, PRL 108, 170602 (2012)
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Coarse-grained Model)
r [nm]
g(r)
[1]
0.90.80.70.60.50.40.30.2
3.0
2.0
1.0
0.0
U(r)
[kJ/
mol
] 4.0
2.0
0.0
-2.0full atomistic
pcg = pexκcg = κat
pcg = pexκcg = κat
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Perturbation without Thermodynamic Force)
r [nm]
g(r)
[1]
1.81.61.41.21.00.80.60.40.20.0
2.01.81.61.41.21.00.80.60.40.20.0
dex = ∞ (AA)dex = 0.20 nmdex = 0.35 nmdex = 0.55 nmdex = 1.00 nmdex = 0 (CG)
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Density profile)
CGHyAA
x [nm]
ρ/ρ
0[1
]
1615141312111098
1.2
1.1
1.0
0.9
0.8
uncorrected AdResSit 1it 2it 3it 4
One can even bring non-pressure corrected model in equilibrium
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Thermodynamic Force)
CGHyAA
x [nm]
~ Ftf(x)
[kJ/
mol
/nm
]
15141312111098
12
10
8
6
4
2
0
-2
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Diffusion Profile)
CGHyAA
x [nm]
ρ/ρ
0[1
]
1615141312111098
1.0
0.8
0.6
0.4
0.2
0.0
2ps100ps200ps300ps400ps
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Particle Fluctuations in AA zone)
N
p(N
)
650064506400635063006250
0.02
0.01
0.00
AdResSAll-atom
Gaussian approximation
→
Grand-canonical behaviour
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Particle Fluctuations)
CGHyAA
x [nm]
<N
2>
−<
N>
2/<
N>
1615141312111098
0.4
0.3
0.2
0.1
0.0
AdResS pcg = pexAdResS κcg = κat
full atomistic
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Basic ExamplesWater (Thermodynamic Force)
CGHyAA
x [nm]
p[b
ar]
15141312111098
6000
4000
2000
0 local pxxρ0/Mα
∫ xa Fthdx
′
Thermodynamic force compensates the pressure difference.
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Introduction The Method First Glance Thermodyn. Force Implementation Basic Examples Outlook
Outlook
AdResS:
Useful analysis tool
Speed-up simulations
Molecules exchange betweenthe two resolutions
Things to work on:
Electrostatics
Adaptive implementation→ESPResSo ++ X
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The End
Thank you for your attention !
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