DOI: 10.1002/cphc.201100997 Force Fields for Studying the Structure and Dynamics of Ionic Liquids: A Critical Review of Recent Developments Florian Dommert,*[a] Katharina Wendler,[c] Robert Berger,[d] Luigi Delle Site,*[b] and Christian Holm*[a] 1. Introduction In the last decade, the interest in room-temperature ionic liq- uids (ILs) has increased steadily. This is mainly due to their wide range of applications in chemistry and industry.[1–3] Simple chemical modifications of the anions or cations or var- iation of the anion–cation combinations result in different melting points, viscosities, or conductivities of the ILs. Many computational studies have been undertaken to understand the mechanisms responsible for the specific behavior of ionic liquids in order to pave the way towards a rational design of ILs with tunable properties. A valuable tool to study the thermodynamics, structure and dynamics of an ionic liquid on an atomistic level is the molecu- lar dynamics (MD) simulation method based on classical force fields. It typically allows one to investigate system sizes con- taining thousands of ions from which, in principle, all static and dynamic observables can be extracted reasonably well. However, the basis for every MD simulation is the existence of a force field that should reproduce such properties accurately enough over a wide range of state points and for various fluid compositions. Reliable parametrization for biomolecular simu- lations have been achieved during the last thirty years, see for example OPLS-AA[4] or AMBER,[5] which are transferable within a certain temperature range and a large class of molecules. However, for ionic liquid compounds, no force-field parameters were present initially, as parameters for similar compounds had been derived under completely different conditions. For this reason suitable new models had to be derived. While the first idea was obviously to apply the same strategy as for the established force fields, it has been shown that a parametrization of a single ion in the gas phase is, for example, not sufficient to extract partial charges[6] for use in non-polaris- able models. For this reason, more elaborated computational schemes for the parametrization of a force field were pro- posed, in which electronic density functional theory (DFT) re- sults are an inevitable contribution to the parametrization pro- cess since they allow one to study the spatial and electronic structure of large clusters or even bulk systems of ionic liquids. It has been shown[6,8,9] that a reasonable mapping of atomic partial charges to the DFT electron density results naturally in a Classical molecular dynamics simulations are a valuable tool to study the mechanisms that dominate the properties of ionic liquids (ILs) on the atomistic and molecular level. However, the basis for any molecular dynamics simulation is an accurate force field describing the effective interactions between all atoms in the IL. Normally this is done by empirical potentials which can be partially derived from quantum mechanical cal- culations on simple subunits or have been fitted to experimen- tal data. Unfortunately, the number of accurate classical non- polarizable models for ILs that allow a reasonable description of both dynamical and statical properties is still low. However, the strongly increasing computational power allows one to apply computationally more expensive methods, and even po- larizable-force-field-based models on time and length scales long enough to ensure a proper sampling of the phase space. This review attempts to summarize recent achievements and methods in the development of classical force fields for ionic liquids. As this class of salts covers a large number of com- pounds, we focus our review on imidazolium-based ionic liq- uids, but show that the main conclusions are valid for non-imi- dazolium salts, too. Insight obtained from recent electronic density functional results into the parametrization of partial charges and on the influence of polarization effects in bulk ILs is highlighted. An overview is given of different available force fields, ranging from the atomistic to the coarse-grained level, covering implicit as well as explicit modeling of polarization. We show that the recently popular usage of the ion charge as fit parameter can looked upon as treating polarization effects in a mean-field matter. [a] F. Dommert, Prof. Dr. C. Holm Institute for Computational Physics University Stuttgart, Pfaffenwaldring 27 70569 Stuttgart (Germany) E-mail: holm@icp.uni-stuttgart.de dommert@icp.uni-stuttgart.de [b] Dr. L. Delle Site Institute for Mathematics FU Berlin, Arnimallee 6, 14195 Berlin (Germany) E-mail: luigi.dellesite@fu-berlin.de [c] K. Wendler Max Planck Institute for Polymer Research Ackermannweg 10, 55128 Mainz (Germany) [d] Prof. Dr. R. Berger Clemens Schçpf Institute for Organic Chemistry and Biochemistry TU Darmstadt, Petersenstraße 22, 64287 Darmstadt (Germany) ChemPhysChem 0000, 00, 1 – 14 # 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &1& These are not the final page numbers! ÞÞ

charge of the ions that is less than the electronic unit charge. Although this charge reduction had been used before to fit force field parameters a posteriori to experimental data, it could be shown to have a solid basis coming a priori from ab initio data. In fact, it can be viewed as the result from elec- tronic dielectric screening and average polarization effects as well as charge transfer processes. Since the number of ionic liquids is rather large, we concen- trate our review on the development of classical force fields to the ionic liquid family with an imidazolium-based cation. In the first part, the contributions of DFT and ab initio MD are sum- marized and discussed to show their importance for an effi- cient development of classical force fields for ionic liquids. In the second part, we review the construction and performance of various force fields known to us. In the last part, we discuss the issue of charge reduction and polarization for classical force fields and close the article with the conclusions. 2. Electronic Density Functional Theory The electronic structure study of the bulk phase of molecular liquids plays an important role as it can describe with good ac- curacy those cooperative effects that characterize liquid-phase behavior. This is true in particular for ionic liquids for which in- formation gained at quantum level is extremely useful to de- velop reliable classical force fields in turn needed urgently. As a technique for electronic structure calculations, the density functional theory (DFT) approach often represents a suitable compromise between accuracy and efficiency, at least for ionic liquid systems in the liquid phase. This is in contrast to more accurate, but also more demanding, post-Hartree–Fock meth- ods as for example, second-order Møller–Plesset perturbation theory (MP2) whose use is typically restricted to small systems only. In general, DFT was shown to capture the decisive as- pects of complex molecular liquids and solutions. For instance in salt solutions, the water–water interaction was found to dominate the polarization process of water, explaining unex- pected experimental findings.[10–12] In ionic liquids, the com- plexity is even higher than that of simple molecular liquids since the molecular electrostatic properties in the bulk phase are linked to non-trivial conformational cooperative effects. As a result, the mean dipole moment in the liquid phase was found to be different from that of isolated ions (increased by 0.7 D),[13] the net ion charge was reduced in the bulk phase compared to single ion pairs[6,8] and the correct NMR shifts were only found in the bulk phase.[14] Thus, cooperative effects such as polarization have a strong impact on the properties of the bulk phase and reliable force fields must be able to prop- erly describe these aspects. Here, an approach such as DFT is a precious tool to this aim. However, an intrinsic limitation of the DFT approach is the empiricity in choosing functionals for the exchange and correlation energy. These functionals lead to one of the basic practical limitations of standard DFT, that is, the lack of accuracy in describing dispersion interactions. In the following, we describe how one may circumvent this prob- lem in practice and introduce somehow the effects of disper- sion in the DFT calculations and, thus, provide reliable data for the parametrization of classical force fields. To gauge the accuracy of the DFT approach, the results were often compared to post-Hartree–Fock methods such as MP2 and usually a reasonable agreement was found.[7,15–24] MP2 is a common computational compromise for including electron correlations and, as a consequence, dispersion interactions, while standard functionals in DFT do not capture dispersion in- teractions properly, but usually add them in an empirical way based on results of the post-Hartree–Fock studies. Despite the fact that MP2 is not the most accurate approach, the corre- sponding results were found to be close to the highly accurate coupled-cluster approach with single, double, and perturbative triple excitations CCSD(T) benchmark data[6,8,17,25,26] and, thus, appear trustworthy. Hence, the evaluation of DFT studies com- pared to MP2 results suggested being a robust path to check- ing the accuracy of the DFT setup. In general, this was made by comparing the results of DFT and MP2 regarding ion pair binding energies, relative total energies or equilibrium distan- ces of isolated ion pairs. Regarding the computational setup of the DFT calculations, the standard Becke three-parameter Lee– Yang–Parr functional[27] (B3LYP) was employed[15–23] and shown to not perform well for ionic liquids[16,17,22,25,28,29] as it gave the wrong energetic order of ion pair conformations compared to MP2.[16,22,28] Furthermore, B3LYP was found to have larger devi- ations from MP2 than other functionals as for instance the Perdew–Burke–Ernzerhof functional[30] (PBE).[25,29] As a conclu- sion, the B3LYP functional (in principle suitable for the situa- tions treated) seemed not to be appropriate this time. In gen- eral, more accurate hybrid functionals as PBE0 or B3LYP did not perform much better than generalized gradient-corrected functionals (GGA) as PBE.[29] They were affected by the same limitation of semi-locality in the context of reproducing disper- sion interactions.[31] Indeed, in systematic comparison of semi- local and hybrid functionals as well as functionals with disper- sion corrections to MP2, the Becke Lee Yang Parr[32,27] function- al with Grimme dispersion correction[33–35] (BLYP-D) was recom- mended as a reliable choice.[25,29] It has been argued that only the inclusion of a dispersion correction enables a reliable DFT description of ion pairs in the gas phase.[25,29] For instance, the equilibrium interionic distan- ces between ions in an ion pair or between ion pairs were shifted significantly below the electrostatic equilibrium dis- tance by induction and dispersion.[36,37] Furthermore, the dis- persion component of the ion pair binding energy correlated well with conductivity and viscosity of several ionic liquids.[38] In general, BLYP-D and also the Becke–Perdew functional[32,39] with DCACP pseudopotentials[40,41] (DCACP-PB86) setups were identified as reliable, giving the correct energetic order of ion pair conformations. In BLYP-D with the Grimme dispersion cor- rection,[33–35] the dispersive energy is described by damped in- teratomic potentials of the form C6R 6. As a consequence, the electron density is not changed by this correction while the energies and forces are. The dispersion-corrected atom-center potentials DCACP[42] consist of optimized non-local higher an- gular-momentum-dependent terms. Hence, DCACP increase the computational cost more than the Grimme dispersion cor- &2& www.chemphyschem.org # 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 0000, 00, 1 – 14 ÝÝ These are not the final page numbers! F. Dommert, L. Delle Site, C. Holm et al.