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Motivation Force Field Tuning [MMIM][Cl] Conclusion
Modeling Room Temperature Ionic Liquidsby Classical Molecular Dynamics Simulations
Florian Dommert
ICP - Institute for Computational PhysicsUniversity Stuttgart
NSASM 2010
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Outline
1 Motivation
2 Force Field Tuning
3 Dimethylimidazolium chloride [MMIM][Cl]
4 Conclusion
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Outline
1 Motivation
2 Force Field Tuning
3 Dimethylimidazolium chloride [MMIM][Cl]
4 Conclusion
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Room Temperature Ionic Liquids
Class of salts that are liquid at room temperature
“Green” solventsnon-flammablenon-volatileenvironmental friendly
“Designer” solvents
variation of side chainsexchange of anions
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Computational techniques
1 quantum chemical→ high accuracy but restricted in system size
2 DFT and ab–initio MD→ “bulk-like” systems but very time limited
3 classical all-atom MD→ systems up to millions of atoms and hundreds ofnanoseconds of simulation time but dependent on aconsistent force field
⇒ Multiscale approach to refine or setup a force field
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Force Field
Modeling the molecular interactionsby simple mathematical terms
Nonbonded interactions
Coulombic interaction of point charges: ∼ 1r
dispersive terms, Pauli repulsion, . . . : ∼ ar12 − b
r6
Bonded interactions
bond potentials: 12kb (r − r0)2
angle potentials: 12ka (α− α0)2
dihedral potentials:∑5
i=0 Ci [cos (Ψi)]i
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
The CLaP force field [Lopes et al. JPC B 104 (2004)]
wide range of ILs coveredtransferablecompatible with OPLS-AAand AMBER frameworkgood representation ofstaticspoor description ofdynamics
Dommert et al., JCP 129 (2008)
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80
MS
D / n
m2
time / ns
EMIM+
BF4-
0.0010.01
0.11
10100
0.0001 0.01 0.1 1 10
MS
D /
nm
2
time / ns
D+ D− σ
10−10 m2s−1 Sm−1
CLaP 1.39 0.65 3.5exp. 4.40 3.94 8.3
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Outline
1 Motivation
2 Force Field Tuning
3 Dimethylimidazolium chloride [MMIM][Cl]
4 Conclusion
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Nonbonded Interactions
Electrostatic interaction
Different techniques available to assign partial charges
Basic idea1 calculation of the electron density2 mapping of the electron density to point charges
TechniquesRESP, CHELPG→ isolated moleculesBlöchl method→ periodic systems→ bulk properties
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Nonbonded Interactions
The Blöchl method [JCP 103, 7422 (1995)]Idea: Multipole expansion of the charge density
QL =
∫V
rLYL(r)nV (r) dV
Model charge density nV (r) composed of Gaussians gi :
nV (r) =∑
i
qigi(r), with gi(r) =1(√πrc,i
)3 exp
(−(
r − Ri
rc,i
)2)
Method of Lagrangian multipliers to obtain nV (r) in rec. spacewith w = 4π(G2 −G2
c)/(GcG)2, for |G| < Gc , and 0 elsewhere:
F (qi , λ) =V2
∑G 6=0
w(G)
∣∣∣∣∣n(G)−∑
i
qigi(G)
∣∣∣∣∣2
− λ
[n(0)V −
∑i
qigi(0)V
]
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Nonbonded Interactions
Short range interactions
most time consuming part of force fieldparametrization
dependent on charge distributiondihedral parametrization affected by short rangeinteractions“simple” technique not available
iterative methods to incorporate missing interactions
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Short range interactions
Iterative adaption of force field parameters by MD
Target properties
experimental density at different temperaturesradial distribution given by “ab–initio” MD simulations
Adaption procedure1 sampling of a small part of the parameter space2 determination of a target error function ε3 minimization of ε→ new starting point for step 1
Tuning of the force field up to a certain accuracy
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Short range interactions
Sampling of the parameter space
Simulations of varying parameters around a reference point
Simulation protocolenergy minimizationequilibrationproduction
Simulation detailsLeap frog algorithmvelocity rescale thermostatBerendsen barostatoptimized smooth PME
Wang, Dommert, and Holm, JCP 133 (2010)F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Bonded interactions
stretching and bending modes from QM calculations on anisolated moleculedihedral interactions
1 scan of the dihedral energies by QM techniques2 correction of the QM potential due to 1-4 interactions
0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8Rotation angle / rad
200
0
200
400
600
800
1000
1200
Ener
gy d
iffer
ence
/ kJ
mol−
1
to fitref.
0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8Rotation angle / rad
5
0
5
10
15
20
25
30
35
Ener
gy d
iffer
ence
/ kJ
mol−
1
to fitref.
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Outline
1 Motivation
2 Force Field Tuning
3 Dimethylimidazolium chloride [MMIM][Cl]
4 Conclusion
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Partial charges
An isolated ion pair
q = -0.67
q = -0.63
q = -0.80
q = -0.73
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Partial charges
Comparison of different charge assignment methods
Structure 1 Structure 2 Structure 3 Structure 4MP2 - C -0.74 -0.71 -0.85 -0.78MP2 - R -0.74 -0.72 -0.85 -0.79MP2 - Ba -0.85 -0.81 -0.91 -0.86BP86 - C -0.70 -0.64 -0.80 -0.73BP86 - R -0.70 -0.65 -0.80 -0.74BP86 - Ba -0.80 -0.73 -0.86 -0.82PBE - C -0.70 -0.64 -0.80 -0.73PBE - R -0.70 -0.65 -0.80 -0.74PBE - Ba -0.80 -0.72 -0.86 -0.81PBE - Bl -0.68 -0.63 -0.80 -0.73
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Partial charges
Blöchl method
Inclusion of bulk properties into partial charges
-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3charge (e)
0
0.02
0.04
0.06
0.08
0.1
0.12
rela
tive
occu
rren
ce
mean charge of the chloride
C1N+
C2 C2
NC3C3
H1
H2H2
H3
H3
H3H3
H3
H3
C1
C1
C2
C2
C3
C3
H1
H1
H2
H2
H3
H3
N
N
Cl
Cl
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
char
ge (
e)
Schmidt et al., JPC B 114 2010Dommert et al, JML 152 2010
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Force field tuning
Relative error of the target properties
∆ =
√∑i
(ysim,i − yref ,i
)2, with yi ∈ {ρ(425K ), ρ(440K ), ρ(465K )}
0 1 2 3 4iteration
0.04
0.1
0.5
Loga
rithm
ic ro
ot m
ean
squa
re e
rror
ln(∆
)
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Force field tuning
Density
420 430 440 450 460 470T / K
1080
1100
1120
1140
1160
1180
1200ρ /
kgm−
3
1. iter, C,N2. iter, C,N3. iter, C,N4. iter, C,Nexp.
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Force field tuning
RDF
0.2 0.3 0.4 0.5 0.6 0.7 0.8Distance / nm
0.0
0.5
1.0
1.5
2.0
2.5
g(r)
H3 -ClCLaPBLFFC,NBTFFCPMD
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Distance / nm
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5H1 -Cl
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Force field tuning
Coordination number
0.2 0.3 0.4 0.5 0.6 0.7 0.8Distance / nm
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Coor
dina
tion
num
ber
H3 -ClCLaPBLFFC,NBTFFCPMD
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Distance / nm
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5H1 -Cl
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Force field tuning
Final force field
partial charges from Blöchlbonded interactions from CLaPadapted dihedral potentials to chargestuned short-range parameters
→ Validation of tuned parameters
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Validation
Conductivity
0 100 200 300 400 500Time / ps
0
1
2
3
4
5
6
7∆
MJ /
6 V
k B T
·10−
9 /
Sm−
1ps
σexp.=10.65 Sm−1
CLaP σ=0.48 Sm−1
BLFF σ=14.19 Sm−1
C,N σ=0.70 Sm−1
BTFF σ=8.64 Sm−1
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Outline
1 Motivation
2 Force Field Tuning
3 Dimethylimidazolium chloride [MMIM][Cl]
4 Conclusion
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Classical MD simulations allow to accessmacroscopic properties of ionic liquids
suitable force field required→ force field tuning for Blöchl charges
adaption to static properties allows description of dynamiconesinformation obtained on different scales allows to setup aforce field for ionic liquids straightforwardly
F. Dommert Classical MD Simulations of Ionic Liquids
Motivation Force Field Tuning [MMIM][Cl] Conclusion
Acknowledgment
DFG SPP 1191 for fundingHöchstleistungsrechenzentrum Stuttgart (HLRS) for thehuge amount of computer timethe members of the Multiscale project (AGs Delle Site,Berger, Holm)the GROMACS developer team for providing a fast, freeand flexible simulation tool
F. Dommert Classical MD Simulations of Ionic Liquids