Modeling Room Temperature Ionic Liquids by Classical ...nsasm10/dommert.pdf · macroscopic properties of ionic liquids suitableforce ﬁeld required!force ﬁeld tuning for Blöchl

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


Outline

1 Motivation

2 Force Field Tuning

3 Dimethylimidazolium chloride [MMIM][Cl]

4 Conclusion



Outline

1 Motivation



4 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



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



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



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



Outline

1 Motivation



4 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




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

]




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




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




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


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.



Outline

1 Motivation



4 Conclusion



Partial charges

An isolated ion pair

q = -0.67

q = -0.63

q = -0.80

q = -0.73



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



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



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(∆

)



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.



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



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



Force field tuning

Final force field

partial charges from Blöchlbonded interactions from CLaPadapted dihedral potentials to chargestuned short-range parameters

→ Validation of tuned parameters



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



Outline

1 Motivation



4 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



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


Documents

Modeling Room Temperature Ionic Liquids by Classical ...nsasm10/dommert.pdf · macroscopic properties of ionic liquids suitableforce ﬁeld required!force ﬁeld tuning for Blöchl