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How to make coarse grain force fields
from atomistic simulations.
Vale Molinero
Materials and Process Simulation Center,
Caltech
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outline
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What is a coarse grain model
Developing a model from atomistic
What to be reproduced by the cg
Scales in cg / time in cg
Parameterization vs numerical functions
Possible targets to reproduce
Optimization
Transferability of cg parameters
Can we use the same parameters always?
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What’s a coarse grain model?
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Polymers and many materials show a hierarchy of
length scales and associated time scales.
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Coarsening is limiting the number of degrees of
freedom and the frequency of their motion.
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What are the links between scales?
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No clear definition of CG, but is a scale in which
particles represent atoms in the order of a
monomer of polymer chain (5-50 atoms, approx).
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Preserve connectivity.
Terminology:
Coarse grain simulations

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Difference between generic (toy) models and
coarse grain is that cg are derived to represent a
specific material.
Multiscale simulations
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QMAtomistic
Comparing
&
Atomistic 
averages over degrees of
freedom (electronic) that are
usually well separated from the
one retained (nuclear)
  1/c
For  = 1800 cm-1,  = 55 fs
To integrate MD equations of
motions, the time step
shouldn’t be longer than
~  /10 = 5.5 fs
CG
the degrees of freedom in the
atomistic model not always are
well separated.
How much is retained is a
measure of the coarseness of
the model.
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QMAtomistic
Comparing
&
Atomistic 
the atomistic interaction sites
are usually located on the nuclei
of the QM atoms.
Symmetry of the molecule is
preserved while averaging
electronic degrees of freedom.
CG
the particles should be
positioned to describe the
lowest frequency modes of the
molecule & to represent the
excluded volume interaction
(shape).
Low frequency modes of a
molecule are usually not
localized… so, trimming the
number of particles usually
change significantly the shape
of the power spectrum.
the CG model and the atomistic
one do not have the same
symmetry.
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Atomistic 
CG
The steps of the coarse graining machinery
0) Define your goals
1) Degree of coarsening
2) Mapping atomistic into coarse grain
3) Interaction between the coarse grain particles
4) Atomistic target functions to be reproduced by the CG model
5) Parameter/function optimization
6) Enjoy! (but check first…)
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Atomistic 
Decisions to make:
CG
1) Degree of coarsening (how many particles per monomer/molecule): this is
application driven.  What are the minimal features of the atomistic model
that should be retained to reproduce the desired properties?
Examples of features that may be sought to be preserved:
interaction energies,
shape of the molecule or total volume (density),
flexibility
connectivity in a polymer chain
ability to form a given phase (crystalline or amorphous)
handedness or asymmetry in the chains
This defines the number of beads (superatoms/coarse-grain particles)
Examples:
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PEO polymer modeling: -(CH2-CH2-O)nwe wanted to represent the helicity of the overall chain, the flexibility, and
the excluded volume. We choose one coarse grain particle per monomer.
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Glucose monomer and oligomer: we wanted to represent the helicity of the chain, its segmental motion, shape, and
to retain the exceptional glass forming abilities of glucose: we choose 3 particles per monomer.
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Atomistic 
CG
2) Mapping of the atomistic into the coarse grain.
Where are the beads?
This is crucial in defining the shape of the molecule.
In a polymer chain is relevant for the connectivity and branching.
This defines the position of beads (superatoms/coarse-grain particles) and
affects the parameterization of the cg force field.
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Graphical Examples
Bisphenol-A polycarbonate
a-glucose molecule
1 bead per
monomer
2 beads per
monomer
Kremer et al.
1 bead per monomer
polymer
1 bead per monomer in different positions
R4=C4 C1
E6=C6C6
3 beads per
monomer
R1=C1
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Atomistic 
CG
3) How the coarse grain particles interact?
two posibilities: 1) analytical functions (like LJ, harmonic potentials, etc)
2) numerical functions of the bead coordinates.
analytical f. are easier to handle in standard molecular simulation software
are less versatile
have analytical derivatives!
need to be parameterized
numerical f. can represent “whatever” but sometimes at the cost of introducing
back high frequencies. The derivatives should be obtained and listed
numerically (interpolation). (I think MC is better suited for numerical than MD).
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Atomistic 
CG
4) Obtain the atomistic target function to be reproduced with the CG model.
Two general possibilities:
1) use minimized structures, T=0 properties.
2) use thermalized systems at the T that the CG is going to be used.
(1)
Is easier because does not require running MD for the atomistic target, nor for the CG to check the
data.
(2)
Is more correct, cause the coarse grain parameterizations are state dependent
Targets: radial distribution function (T>0)
potential of mean force (T>0)
density, cell parameters, RMS displacements (T=0)
cohesive energies, compressibility (T>0 or T=0)
dynamics, power spectrum (T>0)
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All the important decisions
are made here (and once!)
The only iterative part
is here… in the
optimization of the CG
parameters or
functions that
reproduce the
atomistic
Transferability
of parameters should be
checked
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Illustration of CG development from
atomistic simulations
M3B: a coarse grain model for the simulation
of malto-oligosaccharides and their water
mixtures.
V. Molinero; W.A. Goddard III,
J. Phys. Chem. B 2004, 108, 1414-1427.
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Atomistic 
CG
The steps of the coarse graining machinery
0) Define your goals
1) Degree of coarsening
2) Mapping atomistic into coarse grain
3) Interaction between the coarse grain particles
4) Atomistic target functions to be reproduced by the CG model
5) Parameter/function optimization
6) Enjoy! (but check first…)
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The goal: to model polydisperse mixtures of
Motivation
oligosaccharides, and glucose glasses
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Molecule size: 3 to 1000 atoms.
Minimum formulation 104-105 atoms.
1 Degree of polymerization
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Broad distribution of length and timescale:
Dilute solutions of amylose, experimental:
DP38
* segmental dynamics  ~ ns (NMR)
DP4
DP1
water
* persistence length ~ 1.5 -3 nm (ho)
(helical structures)
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Unsolved questions that we could not answer through atomistic
simulations and we aimed to study with the CG model.
Motivation
Structure
-Conformation of chains in the mixture:
Coil?
Helix?
Hybrid?
(persistence length)
- Water distribution in the structure:
Pockets?
Channels?
Scattered?
Dynamics
-Diffusion in supercooled mixtures (hopping?)
-How water diffuses in glasses of carbohydrates
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Atomistic 
CG
The steps of the coarse graining machinery
0) Define your goals
1) Degree of coarsening
2) Mapping atomistic into coarse grain
3) Interaction between the coarse grain particles
4) Atomistic target functions to be reproduced by the CG model
5) Parameter/function optimization
6) Enjoy! (but check first…)
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M3B model:
Water molecule  1 bead
monomer  3 beads
a-glucose residue:
monomer unit
B4=C4
B6=C6
B1=C1
Molecular shape is well captured
24 atoms  3 beads
B1-B4’
glycosidic bond
Can represent the chain conformation
around glycosidic bonds
Bonus!
Reconstruction: M3B 
atomistic
the 3 beads completely define the
orientation of the glucose monomer.
DP11
RMS=0.34Å
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Atomistic 
CG
The steps of the coarse graining machinery
0) Define your goals
1) Degree of coarsening
2) Mapping atomistic into coarse grain
3) Interaction between the coarse grain particles
4) Atomistic target functions to be reproduced by the CG model
5) Parameter/function optimization
6) Enjoy! (but check first…)
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M3B energy expression
Harmonic bonds
1
E (d )  kb ( d  d 0 ) 2
2
E=
64
Harmonic angles
Shift dihedral torsions
1
E ( )  k (   0 ) 2
2
1
E ( )   bk (1  cos( nk   k0 )
k 2
+
641’
+
641’6’
Morse nonbond
+
V ( Rij )  Do{( e
0.5a ( Rij / Ro 1) 2
)  2(e
0.5a ( Rij / Ro 1)
)}
(all pairs, except 1,2 & 1,3 bonded)
NV
T
Parameterization scheme
Step 3 - VALENCE
POTENTIAL
THAT MATCH GAS PHASE
DISTRIBUTIONS
NV
T
Step 1- INITIAL GUESS FOR
NONBONDING POTENTIAL
Step 2-NONBONDING
POTENTIAL REFINEMENT
WITH MCSA FOR FIXED
GEOMETRY
Step 4 - VALENCE & NONBOND JOINT OPTIMIZATION
FOR A WIDE RANGE OF STRESSES AND ALLOWING
RELAXATION OF THE M3B STRUCTURES.
Morse parameters of water
chosen to reproduce E, r and D of
liquid water at 300 K.
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Atomistic 
CG
The steps of the coarse graining machinery
0) Define your goals
1) Degree of coarsening
2) Mapping atomistic into coarse grain
3) Interaction between the coarse grain particles
4) Atomistic target functions to be reproduced by the CG model
5) Parameter/function optimization
6) Enjoy! (but check first…)
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Fidelity of the parameterization
Density
Cohesive Energy
Bond distances
Angles
Results for glucose, minimization results.
Different colors correspond to different reference samples.
Equation of state (0 K)
Structural
Glucose shape is very well
represented
Final bond constants are ~2
parameterized by gas phase
simulations.
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Chain conformation
141’4’
L
R
Handedness
141’4’
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Atomistic 
CG
The steps of the coarse graining machinery
0) Define your goals
1) Degree of coarsening
2) Mapping atomistic into coarse grain
3) Interaction between the coarse grain particles
4) Atomistic target functions to be reproduced by the CG model
5) Parameter/function optimization
6) Enjoy! (but check first…)
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Comparison of CPU time
cerius2 in 1 processor sgi origin RS10000
Atomistic model
Coarse Grain Model
• 1 fs time step
• 21-24 particles per
monomer
• ewald for the nonbond
• 10 fs time step
• 3 particles per
monomer
• spline for the nonbond
Timing of MD for the same DP4 bulk system shows that
the bead model is ~7000 times faster
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Water distribution in sugar mixtures
8%w
Water structure is
heterogenous in a lengthscale of a few water
molecular diameters
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Water structure percolates
between 17-20%w/w for all the
atomistic & coarse grain models
studied.
(clustering distance= 4 A)
Water content increases
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16.5%
M3B gives the same water
distribution (percolation, waterwater coordination distribution)
than the atomistic model.
20%w
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Helical structures
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Left-hand single helices
n~5.5-7
h~7-8.3 Å
40 ns simulation 300 K, starting from helix
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L- Double helices
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Parallel & antiparallel have comparable energy
Anti
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Parallel
Vh-amylose structure
M3B cell parameters between 3-6% of Xray data.
Density within 1% of experimental value.
M3B can form a variety of helical structures without having directional
interaction (hydrogen bonds)
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successes of M3B
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It reproduced the atomistic structure of water in sugar mixtures without
using any HB or directional interaction. (packing/shape and right E)
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Was able to form all the helical structures of polysaccharides: left and
right hand single helices, parallel and anti-parallel double helices.
Predicted relative stabilities and structures in agreement with atomistic
simulations and experimental observations. (segmental modes kept/ well
parameterized torsions).
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Predicted glass transition temperatures in excellent agreement with the
experiment. (surprise! Energetics/shape).
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Was used to unravel the mechanism of water and glucose diffusion in
supercooled mixtures, all the predictions in quantitative agreement with
experiments. (shape/energetics)
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Was used to explain how water diffusion continues below the glass
transition temperature in carbohydrate mixtures. (shape/energetics)