Theoretical investigation of intermolecular forces in ionic liquids:
Dynamics and structure
Institut für Physikalische und Theoretische Chemie, Universität Leipzig,
Linnestr. 2, D-04103 Leipzig, bkirchner@uni-leipzig.de
Barbara Kirchner
Introduction
Static consideration
Topic: Theoretical investigation of intermolecular forces in ionic liquids: Dynamics and structure of ionic liquids and interaction with other chemicals with
respect to reaction and solvent properties.
A. Protonated betaine bis(trifluoromethylsulfonyl)imide, [Hbet][Tf2 N] in collaboration with Koen Binnemans
To gain insight into the location of electron pairs, the electron localization function
(ELF) for the anion was calculated. Large
spheres are observed at the nitrogen typical
for two lone pairs. Doughnut-shaped spheres
are found around the oxygen atoms. Where0.8
as the oxygen atoms are open for an electrophilic attack or coordination from each side,
the basin of the central nitrogen atom is only extended at the open side of the S-N-S
angle, which means that the electron density is largely localized on this side of the nitrogen atom. Therefore, priorily the oxygen
Fig: ELF for isosurface values atoms are involved in hydrogen bonding. At
0.85 (above) and 0.8 (below) the fluorine atoms, the electron pairs are less
probable than around the
oxygen atoms. As a result, the preferred hydrogen-bonding acceptor will again
be one of the oxygen atoms instead of one of the fluorine atoms, although
fluorine is the more electronegative element. The lone pairs at the nitrogen
atom enforce the bending of the anions, but the bending is not as large as in
the water molecule; the S-N-S angle is between 123◦ and 126◦ in the [Tf2N]anion, whereas the H-O-H angle is 109◦ in water. The larger angle of the anion
is due to the fact that the electron pairs repel each other at the two oxygen
atoms opposite the nitrogen atom.
The following pairs were considered (EI in kJ/mol, distances in pm and angles
in degrees):
0.85
Methods
There are two major tools in theoretical chemistry, namely static quantum
chemical methods and dynamical methods. Car–Parrinello molecular dynamics
simulations (CPMD) is the combination of both, i.e., the combination of traditional molecular dynamics simulations with electronic structure calculations at
every instance in time.1 With the Car–Parrinello method the efficient fictitious
dynamics of the electronic degrees of freedom is introduced by an extended
Lagrangian technique.2 The advantages over traditional molecular dynamics
simulations are that in the course of the simulations spontaneous events can occur, because the electronic structure problem is solved on the fly. Polarization
effects are explicitely included and the pairwise additivity as used in almost
all force field simulations is circumvented. Therefore many-body or cooperative effects are properly treated.3 However, disadvantages of such first-principle
calculations are the short simulation time only possible due to high computational costs and the (related to this latter problem) simple electronic structure
methods. Therefore, traditional molecular dynamics simulations based on empirical and desirably polarizable force fields as well as (correlated) static quantum chemical calculations are likewise important and necessary. Traditional
molecular dynamics simulations of ionic liquids employing pair potentials were
pioneered by the Lynden-Bell group.4–6 Polarizable force fields have also been
tested for molecular dynamics simulations of ionic liquids.7 So far, only a few
first-principle simulations have appeared in literature, these have mostly examined the 1,3-dimethylimidazolium chloride ([C1 C1 im]Cl) ionic liquid.8–10 In
Ref.8 Car–Parrinello molecular dynamics simulations with 25 pairs and 41 pairs
of [C1 C1 im]Cl, both with an energy cutoff of 60 Ryd were undertaken. Ref.9
presents a simulation with 8 pairs (39 ps) and one with 24 pairs (3.5 ps) of the
[C1 C1 im]Cl system. A 32 ion pairs Car-Parrinello simulation at 425 K run for
almost 10 ps was undertaken by Bhargava and Balasubramanian.10 A study on
the ([C2 C1 im]+ ) chloroaluminates system was published recently by our group.11
References
[1] Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471.
[2] Thar, J.; Reckien, W.; Kirchner, B. Top Curr Chem 2006, 268, 1.
[3] a) Kirchner, B. J. Chem. Phys. 2005, 123, 204116. b) Kossmann, S.;
Thar, J.; Kirchner, B.; Hunt, P. A.; Welton, T. J. Chem. Phys. 2006,
124, 174506.
[4] Hanke, C. G.; Price, S. L.; Lynden-Bell, R. M. Mol. Phys. 2001, 99, 801.
[5] Hanke, C. G.; Atamas, N.; Lynden-Bell, R. M. Green Chem. 2002, 4,
107.
[6] Lynden-Bell, R. M. Mol. Phys. 2003, 101, 2625.
[7] Yan, T.; Burham, C. J.; Del Pópolo, M. G.; Voth, G. A. J. Phys. Chem.
B 2004, 108, 11877.
[8] Bühl, M.; Chaumont, A.; Schurhammer, R.; Wipff, G. J. Phys. Chem.
B 2005, 109, 18591.
[9] Del Pópolo, M. G.; Lynden-Bell, R. M.; Kohanoff, J. J. Phys. Chem. B
2005, 109, 5895.
[10] Bhargava, B. L.; Balasubramanian, S. Chem. Phys. Lett. 2006, 417, 486.
[11] Kirchner, B.; Seitsonen, A. P. Inorg. Chem. 2007, 47, 2751.
Workplan
We plan to carry out four steps according to different methods:
I. Intermolecular forces:
Firstly, we will test quantum chemical methods including expensive correlated
methods in order to understand how reasonable the electronic structure will
be described Then we carry out a systematic study of test cases with varying
side chains, cations, anions. If for some properties the relation between static
electronic structure analysis and the experimental data works, combinations of
new ions studied ions will be used in order to predict the properties of the novel
ionic liquids.
II. Traditional molecular dynamics simulations:
Care has to be taken when classical simulations will be undertaken, since potential parameters for ionic liquids can not easily be developed. We want to test
polarizable force fields within commercial programs and methods implemented
in our own simulation package. The cluster method should be facilitated. Here
snapshots along the trajectories are analyzed with regard to quantum chemical
properties such as the electric field gradient.
III. First-principle simulations:
First principle simulations will be employed in order to study 1.) spontanous
events in ionic liquids. 2.) Ionic liquids dissolved in molecular liquids will also
be within the scope of FPMD. 3.) After testing the polarizable force fields reactions in ionic liquids shall be carried out with the help of a QM/MM code.
Results obtained so far are discussed in the following.
IV. Alternative methods:
A complementary method (quantum cluster equilibrium method) that determines populations of different sized clusters in order to calculate thermodynamic
properties was recently refined and implemented in our postprocessing code.
This method should also be applied in order to determine the thermodynamic
properties of ionic liquids. Since it is not clear from previous studies what the
dominant or important structural motifs are in ionic liquids, this statistical model should be applied to the ionic liquids. It should be emphasized that this
method provides a link between quantum chemistry (see work package I.) and
molecular dynamics simulations (see work package II.). This statistical method
is an alternative to first-principle simulations.
Fig: Structures of investigated
pairs. 1 and 2 are observed experimentally.
It is difficult to determine structures of pairs from gas phase geometry optimizations.
A. 1-ethyl-3-methylimidazolium ([C2 C1 im]+ ) chloroaluminates based ionic liquids
We are interested in 1-ethyl-3-methylimidazolium ([C2 C1 im]+ ) chloroaluminates
based ionic liquids as discovered by Wilkes and coworkers.1 Depending on the
mole fraction of AlCl3 in the mixture the Lewis acidity-basicity can be altered.
Compositions containing an excess of Cl− (i.e., x(AlCl3 ) < 0.5) are called basic
and those where x(AlCl3 ) > 0.5 are called acidic.2–5 It is the general belief that
such acidic liquids contain anionic species that are larger than AlCl−
4 such as
− 2–5
Al2 Cl−
While sometimes it is discussed that only the Al2 Cl−
7 or Al3 Cl10 .
7 anion
is present, the larger trimeric anion could be shown to play a role for example
by Raman IR-spectroscopy studies.6–8 Nevertheless, it is still a matter of debate
how large the anionic species are and at which composition of AlCl3 they occur.
One decade ago Oye and coworkers brought up the interesting question of an
9
even larger species, namely the Al4 Cl−
13 unit. In a thorough investigation of the
vapor pressure and by derivation of a thermodynamic model the presence of a
tetrameric species could be established together with neutral Al2 Cl6 dimers at
high mole fractions of AlCl3 , i.e, in highly Lewis acidic mixtures.9 The different
mole fractions of AlCl3 in ionic liquids which are genuinely very complex are
accompanied by numerous anions in equilibrium with each other.
We undertook dynamical Car–Parrinello simulations of one pair of [C2 C1 im]Cl
(1-methyl-3-ethylimidazolium chloride, emim chloride) in 30 AlCl3 (i. e. modeling the acidic mixture). We calculated two trajectories, one where in the beginning we placed the ions in close proximity (denoted with traj-1 or trajectory1); and one where we started from separated ions (abbreviated with traj-2 or
trajectory-2;)
B. Method evaluation and cooperative effects in ILs
References
3
No
1exp
2exp
1
2
3
4
5
6
5
1 exp
6
2 exp
EI r(OH) a(OHO)
-233.8
188
163
-222.0
188
175
-334.9
171
152
-289.8
141
178
-310.1
220
174
-325.8
189
140
-386.5
171
177
-381.0
167
165
1b
1a
r2
r1
Intermolecular
distances
agree within 5 pm for
the monomers 1a and 1c
comparing DFT and MP2.
In 1d this distance depends
more on the employed
method. 1b is probably the
monomer where dispersion
interactions play a more
r2
r1
r2
important role than in any
r1
1c
1d
other configuration. This
is reflected in the large
Fig: Structures of investigated pairs denoted deviations between MP2
and DFT for all distances.
monomers
fails to obtain accurate intermolecular distances. The intramolecular distances
are all in agreement with each other at all configurations for different methods.
rx denotes the r(C-H) distance. The r3 distances of 1b are for HF=424.5;
BP86=383.8; B3LYP=390.3 and MP2=355.4 pm.
HF BP86 B3LYP
MP2
HF BP86 B3LYP MP2
Complex 1a
Complex 1b
r1
213.5 190.7
196.7 194.2
247.5 259.9
260.6 279.1
r2
257.6 252.8
258.5 250.7
293.6 283.5
287.4 274.0
rx
108.4 115.4
112.7 112.2
105.0 108.1
107.2 107.2
d
14.3
11.7
12.4
12.7
11.3
7.2
8.4
8.5
-433.4 -449.9
-404.6 -372.2
EI
-362.6 427.5
409.3 384.7
Etot
13.3
-0.6
1.8
-9.1
0.0
0.0
0.0
0.0
The dipole moment has the value of 7-18 D, depending on the monomer unit
and method. The following order is observed for all methods 1d>1c>1a>1b.
For both the total and the binding energy the order 1a, 1b,1c and 1d can be
observed. For the binding energy EI we found 1a to be more stable than 1b
for HF and BP86, while 1b is more stable for B3LYP and MP2. In order to
clarify the energetic behavior, we add more accurate calculations. Using a larger
TZVPP basis set in combination with MP2 we find EI values of -366.5 kJ/mol
for 1a and -376.6 kJ/mol for 1b.
r3
r(C−H)
[1] Wilkes, J. S.; Levisky, J. A.; Wilson, R. A.; Hussey, C. L. Inorg. Chem.
1982, 21, 1263.
r1 r2
The behavior of the energy per ions is depicted below
We find from dimer unit on an increasing stability. The monomer
unit is more stable than the dimer
or the trimer, as discussed in the
previous sections. From the tetramer on the complexes are more
stable than the monomer, which
corresponds with the structural
transition observed in the dipole
moment. We also depicted the interaction energy of the most stable ring trimer structure. Only
the nonamer is as stable as the
trimer.
Fig: Binding energie with No units
[2] Cocalia, V. A.; Gutowski, K. E.; Rogers, R. D. Coord. Chem. Rev. 2006,
150, 755-764.
[3] Welton, T. Chem. Rev. 1999, 99, 2071–2083.
[4] Welton, T. Coord. Chem. Rev. 2004, 248, 2459–2477.
[5] Wilkes, J. S. Green Chemistry 2002, 4, 73–80.
[6] Dymek JR, C. J.; Wilkes, J. S.; Einrasrud, M.; Oye, H. A. Polyhedron
1988, 7, 1139–1145.
[7] Dymek JR, C. J.; Hussey, C. L.; Wilkes, J. S.; Oye, H. A. Thermodynamics
of 1-Methyl-3-Ethylimidazolium Chloride-Aluminium Chloride. In Proceedings of the Joint International Symposium on Molten Salts, Vol. 87–7, The
Electrochemical Society, Pennington, NJ, p.93–104; Mamantov, G.; Blander, M.; Hussey, C.; Mamantov, C.; Saboungi, M. L.; Wilkes, J. S., Eds.;
1987.
[8] Gale, R. J.; Gilbert, B.; Osteryoung, R. A. Inorg. Chem. 1978, 17, 2728–
2729.
[9] Oye, H. A.; Jagtoyen, M.; Oksefjell, T.; Wilkes, J. S. Material Science
Forum 1991, 73–75, 183–190.
Taking a look at the development of the cluster size, we find
two regions in the simulation
trajectory-1
trajectory-1 where both ions are
trajectory-2
closely together, one with cluster
size two (first 16 ps) and one
with cluster size four (last ps)
which is accompanied by fluctuations to a trimer and seldomly to
even larger clusters, see grey lisimulation time [ps]
ne. In trajectory-2, see black line,
we find that larger clusters of up
Fig: Evolution of the cluster size (coun- to nine units are stable for about
ting the number of aluminium atoms 10 ps, and after this a cluster size
in an observed anion) for both trajec- of approximately seven is populated for
tories.
10 ps. In the last time region of trajectory-2 the average size of the cluster is
like for trajectory-1 about four. Thus, the major cluster size of the anion in
−
simulations of this kind is four (Al4 Cl13 ). Experimentally the accepted picture
is that of an Al2 Cl−
7 and since the seminal work of Dymek and coworkers an
Al3 Cl−
10 is proven to play a role at mole fractions of AlCl3 being larger than 0.5.
Although our main cluster species contains four units we also see fluctuations to
other cluster sizes which is in agreement with the requirement that the anions
must be in equilibrium with each other.
12
10
cluster size n
If we aim to understand order, dynamics and structure of ionic liquids, part
of our work package is to systematically study intermolecular forces with the
help of electronic structure calculations. Thereby a relation between the microscopic properties and the macroscopic behavior should be established. Molecular dynamics simulations aid in receiving insight into the degree of ordering, cluster formation and the dynamical behavior of ionic liquids. Interactions
of ionic liquids with dissolved substances are studied with the help of first
principle simulations. The Car–Parrinello ansatz allows us to observe reactions
like proton transfer. Furthermore, model reactions carried out in a molecularmechanics(MM)-solvent and ion pairs dissolved in molecular liquids are within
the scope of this project. Thereby structure-forming effects on molecular liquids
and the interplay between the different components can be investigated. New
structures will be built according to the rationale of the knowledge gained from
investigated systems by simple substitution at the side chains and of ions. Analyzing the calculated properties of these new structures will enable us to predict
their behavior as solvents in comparison to well-known ionic liquids.
For the sake of comparison we added the Cl− and the AlCl−
4 which we obtained
from geometry optimization. ELF is shown for the isosurface value 0.88 (blue
spheres). We immediately recognize that Cl− (V) is a Lewis base and Al2 Cl−
7
(II) as well as Al2 Cl6 (I) are both Lewis acids, because Cl− displays a full sphere, while the dimers exhibit at the terminal chlorine atoms also full doughnut
shaped spheres but at the bridged chlorine atoms half moon-shaped spheres.
It is obvious that due to the half moon shaped spheres electron pairs can be
accepted at these sites as opposed to the doughnut shaped spheres. AlCl−
4 (IV)
fits this picture since the four terminal chlorine atoms also are enclosed by the
full doughnut formed sphere. Note that the anionic dimer is connected via shared corners and the neutral dimer via shared edges; this is displayed in the inlet
of panel I and II of the Figure. Since in the neutral dimer two half moons are
found, i.e. one half moon per monomer unit, and in the anionic dimer there are
0.5 half moons per unit, it is clear that either the neutral dimer and/or larger
anions (for example 0.75 half moons per unit in the tetramer) must play a role.
These species are formed simply to account for the “lack of electrons” present in
the acidic melt. A smaller anion with Lewis base character would immediately
be captured by an neutral Al2 Cl6 according to this picture.
8
6
4
2
0
0
10
20
30
40
The neutral mixture
Dynamical studies with A. Seitsonen
III
I
II
V
IV
Fig: The electron localization
function for different units in blue.
−
I: Al2 Cl6 ; II: Al2 Cl−
7 ; III: Al4 Cl13 ;
−
IV: AlCl−
4 ; V: Cl . Green atoms:
Cl; orange atoms: Al. In order to
shed light on the Lewis acidic properties we calculated the electron localization function (ELF) at anions that were
extracted from the CPMD simulations
and at smaller anions like the Cl− .
Fig: A snapshot from the Car–Parrinello simulation of the “neutral”
ionic liquid [C2 C1 im]AlCl4 . Left panel: The system in atomistic resolution. Blue spheres: nitrogen; cyan: carbon; white: hydrogen; silver:
aluminium; green: chlorine. Right panel: Center of mass of [C2 C1 im]+ ,
white spheres, and AlCl−
4 , green spheres.