Supplementary Information:
Ab initio molecular dynamic simulation of ionic liquids
Mohammad Hadi Ghatee*, and Younes Ansari
(Department of chemistry, Shiraz University, Shiraz, 71454, Iran)
E-mail: ghatee@sun01.susc.ac.ir
Fax: +98 711 2286008
1. Simulation details
All the simulations are performed with CPMD program version 3.9.11, which combines
the method of density functional theory for the calculation of forces acting between
particles with the molecular dynamic simulation method2, and the possibility of using the
wide range of plane wave pseudopotentials (pps).3 For the ([bmim]I) system, the electronic
structure of valence electrons is described by DFT using Local Density Approximation
(LDA) functional4 at the cut-off energy for the plane wave expansion of 60 Ryd. For core
electrons of C, H, N, and I atoms the pps's developed by Geodecker3,5 are used. The
exchange and correlation functional are applied through Pade approximation. The cut-off
energy of 60 Ryd. satisfies the norm conserving Geodecker pps generation, though cut-off
energy of 70 Ryd. has been often used for old-Geodecker's. The initial configuration for
CPMD run is taken from an NVT ensemble of 10 ([bmim]I) ion pairs, first agitated at an
elevated temperature to distribute the molecules evenly for 5 ps, and next equilibrated
using geometry optimization by classical MD simulation.
For a CPMD run, an ensemble containing 10 ion pairs ([bmim]I) is simulated in
 at 300 K, corresponding to macroscopic density
periodic cubic box of side length 14.54 A
of 1.45 (g/cm3).6 The Nose-Hoover thermostat is used at 300 K to simulate a NVT ensemble
 3 . The diffusion plot shows that equilibrium is attained in the
of total volume 3442.95 A
system after 29000 steps, equivalent to 3.50 ps (see Figure 1). The fictitious electron mass
associated with the plane wave coefficient at 600 au is used to allow a time step of 0.121
ps. The system is allowed to evolve dynamically in the total time of 4.72 ps. We believe
that this small time step is responsible for the detailed dynamic presented in the Letter.
The choice of pseudopotential, the size of the simulation box, the step size, the cutoff
distance and energy in addition to the functional for approximating exchange and
correlation are important for perfect results. We run CPMD program in the parallel mode
on a cluster computing system.7 Primarily, we have verified the stability of the algorithm
(in parallel mode computing) and the role of exchange and correlation functional. To
achieve this, we have used CPMD program and simulated 8 ion pairs of 1,3-dimethyl
imidazolium chloride ([dmim]Cl) with LDA functional at the 60 Ryd. cut off energy of the
plane wave expansion of the wavefunction, and compared the results with the results of the
same simulation reported in the literature with 8 ion pairs (using CPMD and IESTA
programs), in which case the General Gradient Approximation (GGA) functional has been
used8. It has been known that the GGA functional has accomplished quite accurately in a
number of situations including gas and condensed phases. The resulted equilibrium interionic distance of 4.28 Å for Cl -  Cl - , obtained by LDA, is in agreement with the distance
of 4.31 Å obtained by GGA. Hence, using simple LDA functional instead of GGA does not
influence the results of simulation appreciably. The goal is to use the simplest scheme that
gives accurate results.
To our knowledge this is the first ab initio molecular dynamic simulation given here.
The ([bmim]I) salt has been synthesized among other 1-aklyl 3-methyl imidazolium
halides. However, contrary to other halide salts, its thermodynamic and structural
properties have not been studied widely. The structure of the ion pair is most important to
many applications including the feature property of ionic liquids as solvents. The
electrostatic interaction of anion with the cation ring of the ionic liquid has the major role
of governing the physical properties. For most practical purposes, a side chain of certain
length is used in the architecture of the molecule to tailor a solvent with desire salvation
capabilities. The side chain could be responsible for the appropriate solubility. In this work
it is shown that the electron donating alkyl group polarizes the imidazolium cation and
redistributes the over the cation ring, which in turn facilitate the peculiar out-of plane
bending of the ring.
2. Anion and the ring cation structure
The plots of g(r)'s of I  N1 and I  N3 are shown in Figure 2. The same plots for
_
I  C4 and I   C5 are shown in figures 3; details of dynamics and structure based on
these plots are given in the Letter. The features of the dynamics and structures of
I   H8 , I  H9 , and I  H10 , are explored in the following (see Figure 4 for the
corresponding g(r) plots).
The average equilibrium distances of I   H8 , I  H9 , and I  H10 are rather short.
This is because of the small size of the H atom and also because of the fact that when the
ring is being posed dynamically for another anion, the configuration of the closest approach
is less hindered at the moment that the anion is (dynamically) in the plane of the ring,
indicating that the anion approaches to H's in the plane of the ring. However, at the first
maxima, values of g(r) of H's are rather smaller than those of C's and N's. This indicates
that approach and interaction of an anion with H's are mainly in the same plane of
imidazolium plane in a transient manner. Meanwhile, the first maximum of g(r) of the
anion-H8 is higher because its interaction is less hindered than that of I--H9 and I--H10
interactions.
Comparison of the g(r)’s of ([emim]PF6) with ([bmim]PF6) has shown that no
appreciable shift in the mean distance of PF6  C 2 is take placed when the ethyl group is
replaced by a butyl group.9 However, when PF6 is replaced by I , the position of mean
_
 (for I  C ) in
 in ([emim]PF6) to 3.23A
distance of PF6  C 2 shifts from 4.2A
2
([bmim]I). Therefore the alkyl chain length does not play a significant role in the mean
distance of anion-C2 and only the size of anions is the main factor for determining the mean
distance of the anions to the imidazolium ring cation.
From the trajectories, it is noticed that the facial positioning of the ring is a response
to the position as well as the atmosphere of the anion. The sluggish dynamics of N1 and N3
facilitates the ring to bend over the axis passing through the two nitrogen atoms. The ring
bends and oscillates rather systematically between a flat and a bend configuration. When
the ring plane starts turning away from one anion and recognizes itself for another one, it
passes over a barrier with flat position (see Figure 2.d of the Letter). On the other hand,
when the ring starts facing towards the anion, it vibrates and distorts, and the triangle plane
N1-C2-N3 bends over the trapezoid plane N1-N3-C4-C5. Because the ring is floppy and the
anion has a high inertia, the bending oscillates much faster than the anion motion. The time
duration of complete flatness (being perpendicular to an anion residing far from the
position of the nearest neighbor) is short indicating that most of the time the plan of the
ring is taking the position almost perpendicular to the anion (see Figure 5).
4. Hartee-Fock static energy calculation
Tables 1 to 3 are the continuation of the data earlier presented in the Table 2 of the Letter.
These calculations are directed to show the effect of anion type ( I  and Cl ), the alkyl
chain length (methyl and butyl) in both gas and liquid environment on the electronic
polarization and geometrical polarization of the imidazolium ring cation. The net
polarization is presented by the bending angle , calculated by using CPMD output
trajectories of all atoms in the ensemble. The full discussion on the results also can be
found in the Letter.
Average bond lengths in ([bmim]I) are shown I Table 4 and that of ([dmim]I) in Tables 5.
These are derived based on the corresponding pair correlation functions are given here in
support of the materials given in the Letter.
3. Comparison with experiment: the IL lattice instability
The fact that ionic liquids are salts in liquid state at ordinary temperature has been
subjected to many investigations for a logical modeling of this peculiarity. Based on
structure factor determined by the experimental X-ray diffraction data, a zigzag structure
has been used to model the structure of the ([bmim]I).10 This attempt has actually led to a
model structure for the anion. The fact that the experimental pair correlation function
 has suggested a unit cell containing
shows peaks and shoulders at 4.5, 5.5, 8.5 and 9.2 A
four iodide atoms. By arranging these four iodide anions at the apices of a trapezoid on a
plane, a possible model consistence with the distribution function has been proposed. In the
 and to the peak at 9.2
model, the two parallel edges are assigned to shoulder at 5.5-5.6 A
 . In same way, the two non-parallel edges are assigned to the peak at 4.5 A
 and the two
A
 . As a result, the distance at 4.5 A
 corresponds to those
diagonal lines to shoulder at 8.5 A
of the first nearest neighbors in the zigzag chain of the crystal. In the same way the
 have been assigned to the distance between the chains. In this way
distances 5.5 and 9.2 A
the interior of the trapezoid contains a single (or possibly more) cation. It has been assumed
logical that this structure is rigid enough to be observed in X-ray scattering by the liquid. In
present study, where g(r) of the I  I in liquid environment of ([bmim]I) is simulated by
using all the CPMD trajectories of anions in the ensemble, the position of the first, second,
… peak must be the average of the position of the anion in the typical first closest, typical
second closest… shells, respectively. Figure (6) demonstrates the I  I pair correlation
function in ([bmim]I) liquid environment.
The first peak is quite sharp at the rising edge of the closest approach; however, it is
quite wide at the falling edge of long range and likely contains embedded peaks and or
shoulder(s). Although the simulation box in the present work does not permit studying the
 (achieved in the experimentally X-ray study10), still we
structure at long distance as 9.2 A
believe that our findings are consistence with this zigzag model.10 The position of the first
 , which is exactly the average of
peak of g(r) of I  I calculated by CPMD is at 5.01 A
 ) distance and the non-parallel edge (4.5 A
 ) distance of the
the short parallel edge (5.5 A
trapezoid in the zigzag model. This is consistent with the dynamic of the ring as it is
revealed by studying the bending angle of the ring in the gas phase and in the liquid phase
(The imidazolium face turns from one anion to another one constantly). It can be proposed
that the dynamic of the ring is influenced by the thermal fluctuation of the ensemble and
drifting towards the minimum energy as dictated by the presence of the two types of anions
located at distances of short parallel and the non-parallel edges. It has been claimed that the
zigzag model explains why an ionic liquid is liquid instead of forming a rigid solid matrix.
We believe that the particular dynamics of the ring explored in this study (presented in the
Letter) including the geometrical polarization (e.g., the out-of-plane bending of the
imidazolium ring cation), electronic polarization induced and enhanced by the electron
donation butyl group, and the peculiar anion-anion structure (given in this supplementary)
can be regarded as independent evidences for the instability of the ion pair matrix, hence
the low melting point of imdazolium based ionic liquids. A primary observation of the
pyridinium's simulations16 has indicated a geometrical and electronic polarization
enhancement, and quite reasonably pyridinium based ionic liquid lattice may be instable by
the above line of evidences.
4. Transport properties
Molecular dynamic simulation provides the possibility of calculating the mean
displacement of the particles in the ensemble, and thus to simulate the transport properties
of a fluid. The diffusion factor of the ([bmim]I) liquid at 300K is found to be
2.22  1012 (m2 / s) , using the output mean displacement (of the CPMD run). To our
knowledge no experimental or theoretical value of diffusion coefficient for ([bmim]I) are
available. However, the calculated diffusion coefficient for ([bmim]PF6) by the method of
classical molecular dynamics has been reported 1.431011 (m2 / s) .11 Understandably the
diffusion of ([bmim]I) must be smaller. Using the diffusion coefficient, we can calculated
the viscosity  , of ([bmim]I) by using the Stocks-Einstein relation:12
  kT f Da
(1)
where k is the Boltzman constant, D is the diffusion coefficient, T is the absolute
temperature, a is the radius of the penetrating particle, and f is a constant parameter
characteristics of the nature of the particle and is determined empirically. The value f is
normally 3 to 6. In the case of ([bmim]I) the value of f equals to 5, and the a is determined
according to the literature procedure.13,14 The viscosity calculated for ([bmim]I) at 300K is
about 1080 cp, which is within 2.7% of the experimental value (1110 cp15).
References:
1
CPMD, Copyright IBM Corp 1990-2001, Copyright MPI fÄur FestkÄorperforschung
Stuttgart 1997-2001.
2
R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
3
S. Geodecker, J. Hutter, and M. Teter, Phys. Rev. B 54, 1703 (1996).
4
P. Geerlings, F. D. Proft, and W. Langenaeker (eds.), Density Functional Theory,
Proceedings of a two day international symposium organized under the auspices
of the FWO-Flanders scientific network: "Quantum Chemistry: Fundamental and
Applied Aspects of Density Functional Theory" Free University of Brussels, May 1415, 1998.
5
http://www.pwscf.org/pseudo.htm; http://www.nest.sns.it/giannozz/software.html
http://www.tddft.org/programs/octopus/pseudo.php;http://www.fhi
berlin.mpg.de/th/fhi98md/fhi98PP/; http://www.physics.rutgers.edu/dhv/uspp/
http://www.cpmd.org/
6
K. Kim, B. Shin, and H. Lee, Korean J. Chem. Eng. 21, 1010 (2004).
7
W. Andreoni and A. Curioni, Parallel Computing 26, 819 (2000).
8
M. G. Del Po´polo, R. M. Lynden-Bell, and Jorge Kohanoff, J. Phys.
9
Chem. B 109, 5895 (2005).
A. Alavi and D. L. Thompson, J. Chem. Phys. 122, 154704(2005).
10
H. Katanayagi, S. Hayashi, H. Hamaguchi, and K. Nishikawa, Chem. Phys. Lett. 392,
460 (2004).
11
C.J. Margulis, H.A. Stern, and B.J. Berne, J. Phys. Chem. B 106, 12017 (2002).
12
M.F Refojo, Invest. Ophthalmol. Vis. Sci. 22, 129 (1982).
13
M. H. Chen and D. J. Turubull, J. Chem. Phys. 31, 1164 (1959).
14
M. F. Helmke, W. W. Simpkins, and R. Horton, Vadose Zone Journal 3, 1050 (2004).
15
J. G. Huddleston, A. E. Visser, W. M. Reichert, H. D. Willauer, G. A. Broker, and R. D.
Rogers, Green Chem. 3, 156 (2001).
16
M.H. Ghatee, L. Pakdel, and A.R. Zolghader, to be published.
Figure captions
Figure 1. The calculated relative mean displacement for ([bmim]I) at 300 K. The
dashed line is the trend line (doted line) through the CPMD output (solid line).
Figure 2. The I  N1 and I  N3 pair correlation functions in liquid ([bmim]I) at
_
300 K.
Figure 3. The I  C4 and I  C5 pair correlation functions in liquid ([bmim]I) at
300 K.
Figure 4. The I   H8 , I  H9 , and I  H10 pair correlation functions n liquid
([bmim]I) at 300 K.
Figure 5. Plot of the bending angle versus time step for ([bmim]I) in liquid
environment at 300K. The doted line shows the average bending angle.
Figure 6. The I  I pair correlation function of the anion-anion of ([bmim]I) in
liquid bulk at 300 K.
0.030
Mean Displacement
0.025
0.020
0.015
0.010
0.005
0.000
0.00
Ghatee and Ansari
1.00
2.00
3.00
time(ps)
Figure 1
4.00
4.50
N1 and I
N3 and I
4.00
3.50
g(r)
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
r/A
Ghatee and Ansari
Figure 2
3.00
C4 and I
C5 and I
2.50
g(r)
2.00
1.50
1.00
0.50
0.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
r/A
Ghatee and Ansari
Figure 3
2.50
H8 and IH9 and IH10 and I-
2.00
g(r)
1.50
1.00
0.50
0.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
r /A
Ghatee and Ansari
Figure 4
185
[bmim]I
Bending angle/degree
180
175
170
165
160
155
150
29000
Ghatee and Ansari
31500
34000
Number of time step
Figure 5
36500
2.0
I- and I-
g(r)
1.5
1.0
0.5
0.0
0.0
Ghatee and Ansari
1.0
2.0
3.0
4.0
r/A
Figure 6
5.0
6.0
7.0
Table 1. Characterized Bending angles and the corresponding energies of
([bmim]Cl) ion pair
Bending
[bmim]Cl
Small
Average
Large
ion pairs
angle
energya
angle
energya
angle
energya
1
179.94
-88.1123856
176.80
-88.1262471
164.13
-88.0811247
4
179.96
-88.1683556
174.98
-88.3278967
161.93
-88.1384375
a
Hartree-Fock energy (in Hartree unit) obtained by Gaussian 98 at b3lyp/CEP-4G nosym level of theory.
Angles are in degree.
Table 2. Characterized Bending angles and the corresponding energies of
([dmim]Cl) and ([dmim]I) ion pair in gas phase
Bending
Small
Average
Large
angle
energya
angle
energya
angle
energya
[dmim]I
179.98
-64.2571386
176.31
-64.3817877
166.92
-64.3023171
[dmim]Cl
179.96
-67.6612054
176.42
-67.7191732
167.76
-67.70807146
a
Hartree-Fock energy (in Hartree unit) obtained by Gaussian 98 at b3lyp/CEP-4G nosym level of theory.
Angles are in degree.
Liquid environment,
10 ion pairs
Table 3. Characterized Bending angles and the corresponding energies of
([dmim]Cl) and ([dmim]I) ion pair in liquid phase
Bending
Small
Average
Large
a
a
angle
energy
angle
energy
angle
energya
[dmim]I
179.80 -64.3191226 174.61 -64.3218814 162.13
-64.3001619
[dmim]Cl
179.97 -67.7487643 176.11 -67.7731447 163.51
-67.7699915
a
Hartree-Fock energy (in Hartree unit) obtained by Gaussian 98 at b3lyp/CEP-4G nosym level of theory.
Angles are in degree.
Gas environment,
1 ion pair
Table 4. The average bond lengths (in Angstrom) between atoms in ([bmim]I).
Bond
C4-C5
C4-N3
N3-C2
C2-N1
N1-C5
N3-C6
N1-C7
C7-C8
Distance
1.38
1.39
1.36
1.37
1.40
1.51
1.53
1.56
Bond
C8-C9
C9-C10
H8-C2
H9-C4
H10-C5
H-C6
H-C7
_
Distance
1.57
1.57
1.12
1.11
1.11
1.12
1.12
_
Table 5. The average bond lengths (in Angstrom) between atoms in ([dmim]I).
Bond
C4-C5
C4-N3
N3-C2
C2-N1
N1-C5
N3-C6
N1-C7
Distance
1.378
1.365
1.335
1.335
1.366
1.430
1.430
Bond
H8-C2
H9-C4
H10-C5
H-C6
H-C7
Distance
1.11
1.11
1.10
1.10
1.11