Received: 2 June 2018
Revised: 23 July 2018
Accepted: 8 August 2018
DOI: 10.1002/qua.25795
REVIEW
Ab initio simulations of liquid electrolytes for energy conversion and storage Tuan Anh Pham Quantum Simulations Group, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California, 94551, USA
Abstract Understanding physicochemical properties of liquid electrolytes is essential for predicting and optimizing device performance for a wide variety of emerging energy technologies, including
Correspondence Tuan Anh Pham, Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, CA 94551. Email:
[email protected]
photoelectrochemical water splitting, supercapacitors, and batteries. In this work, we review
Funding information U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office; The Scientific Discovery through Advanced Computing (SciDAC); LLNL Laboratory Directed Research and Development Program, Grant/Award Number: 18-LW-064; U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences; U.S. Department of Energy by Lawrence Livermore National Laboratory, Grant/Award Number: DE-AC52-07NA27344
our understanding of a number of liquids, including aqueous solutions, organic electrolytes and
recent progress and open challenges in predicting structural, dynamical, and electronic properties of the liquids using first-principles approaches. We briefly summarize the basic concepts of first-principles molecular dynamics (FPMD), and we discuss how FPMD methods have enriched ionic liquids. We also discuss technical challenges in extending FPMD simulations to the study of liquid electrolytes in more complex environments, including the interface between electrolytes and electrodes, which is a key component in many energy storage and conversion systems. KEYWORDS
energy conversion and storage, first-principles simulations, liquid electrolytes
1 | I N T RO D UC T I O N Liquid electrolytes are essential components in a wide variety of emerging energy and environmental technologies, including hydrogen production through solar-water-splitting,[1,2] supercapacitors,[3–5] ion batteries,[6–8] and ion-selective membranes.[9–11] Within these devices, a large number of liquids have been explored, ranging from aqueous solutions and ionic liquids to organic, redox-type, and solid-state electrolytes. At the same time, continuing progress has been made during the past several decades in the development of novel liquids. For example, recent studies show that the use of highly concentrated aqueous electrolytes could open new opportunities for the design of high-voltage aqueous lithium-ion batteries while also significantly improving battery safety.[12,13] For several energy storage and conversion systems, the understanding of structure, dynamics, and electronic properties of liquid electrolytes is essential for predicting and optimizing device performance. For example, desolvation of ions in sub-nanometer carbon electrodes is known to lead to improved capacitive performance.[14–16] Controlling transport of the lithium ion in organic electrolytes and at the interface with the graphite anode is key to the development of next-generation lithium ion batteries.[17–20] Tailoring the electronic structures of aqueous solutions for facilitated charge transfer at semiconductor/water interfaces in photoelectrochemical cells is critical for improving the efficiency of water-splitting reactions for hydrogen production.[21,22] Last but not least, understanding the electronic properties of liquid electrolytes is one of the prerequisites for manipulating the electrochemical stability of electrode–electrolyte interfaces in ion batteries and supercapacitors.[5,23] Structural, dynamical, and electronic properties of liquid electrolytes are often intertwined. For example, it is now widely accepted that the solvation structure of ions in liquid water is largely governed by the ions polarizability.[24–26] Similarly, the concept of “structure maker” and “structure breaker” has been utilized to relate the solvation strength of ions with their dynamical properties, such as self-diffusion in liquid water.[27,28] This complex interplay leads to a multiproperty problem for optimizing and manipulating liquid electrolytes, which is difficult to solve experimentally. This is further complicated by the fact that many key processes in energy storage and conversion systems occur at the interface rather than in the bulk liquid,[8,18,23,29] which are challenging to probe by experimental measurements, especially for devices under working conditions. Int J Quantum Chem. 2018;e25795. https://doi.org/10.1002/qua.25795
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In this regard, theoretical models and predictive simulations offer powerful tools for probing properties of electrolytes and complement experimental results. In particular, recent advances in high-performance computing and electronic structure theories have enabled the application of FPMD simulations to a wide variety of electrolytes with increasingly complexity.[30–32] Besides providing a reliable microscopic description of the systems, FPMD simulations can be used to predict and interpret experimental measurements, such as vibrational and X-ray absorption spectroscopies.[33–41] In this context, a close integration between FPMD simulations and in situ experimental characterization techniques promises to probe liquid electrolytes at an unprecedented atomistic level of resolution.[42] The aim of this article is to review recent progress in the simulation of complex electrolytes for energy applications. In particular, we focus on the structure, dynamics and electronic properties of the liquids. We begin with a brief introduction to the basic concepts of first-principles molecular dynamics methodologies. We then discuss the progress that has been made in the simulation of aqueous solutions. Section 3 and 4 discuss the application of FPMD simulations to more complicated electrolytes, including organic electrolytes and ionic liquids, respectively. Finally, open theoretical challenges present in the simulation of liquid electrolytes in complex environments are summarized together with our conclusions.
2 | AB INITIO MOLECULAR DYNAMICS Since the pioneering work of Stillinger and Rahman on liquid argon and water,[43–45] molecular dynamics has been widely used to investigate properties of molecules, solids, and liquids. In these original papers, the interatomic interactions are described by a set of analytical functions socalled force fields, and the theoretical framework is referred to as classical molecular dynamics. These analytical functions are often fixed during the simulation, and hence enable classical simulations to explore events associated with relatively large length and time scales at an affordable computational cost. However, the main drawback of this approach lies in the transferability of the force fields to more complex chemical systems. For example, most standard force-fields are not suitable for studying chemical reactions, which are associated with significant changes in the electronic structures. Conversely, FPMD simulations do not require empirical or fitted interatomic potentials, as these interactions are directly computed from the electronic structures of the systems.[46–49] Accordingly, FPMD methods have a distinct advantage over classical simulations in that they are able to provide a more accurate description of chemically active species in realistic environments. For instance, charge transfer and polarization effects are directly taken into account during FPMD simulations, allowing for the description of bond-breaking and bond-forming processes. The accuracy of FPMD simulations, however, depends on the level of the quantum mechanical approach utilized for the description of the electronic structures of the systems. In practice, the most common approach is density functional theory (DFT),[50,51] whose practical applications rely on the approximation of the exchange-correlation potential (V
xc).
For condensed systems, the generalized gradient approximation (GGA) is
currently one of the most popular forms of the V xc, as it offers a good compromise between the accuracy and computational efficiency.[52] In particular, GGA-based FPMD simulations have been employed to investigate structure and dynamics of a wide variety of liquid electrolytes, including aqueous solutions, organic electrolytes and ionic liquids.[53–55] The same methodology has also been applied to study electrolyte interfaces, primarily for simple aqueous solutions at the interface with solids.[31] Despite the great success of the FPMD method, a number of limitations remain to be overcome to establish an efficient and predictive theoretical framework for the simulation of liquid electrolytes. In particular, further development of novel algorithms and codes is essential to enable FPMD simulations to explore events at larger length and time scales.[56,57] Another major difficulty in advancing the accuracy of the FPMD method lies in the limitation of the GGAs.[58] In particular, it is well-known that these approximations suffer from the self-interaction error and the lack of van der Walls (vdW) interactions, which may lead to an inaccurate description of hydrogen bonds and charged species.[59–63] In recent years, a number of approaches have been proposed to alleviate these errors in GGA functionals, including the development of vdW-corrected functionals,[64–67] as well as novel meta-GGA[68–70] and hybrid exchange-correlation functionals.[71,72] Finally, DFT is inherently a ground-state theory, and thus it is not expected to provide an accurate description of excited-state properties. In particular, it is well-known that DFT with GGA functionals underestimates band gaps and band edges of semiconductors and insulators. Similar errors are expected to present in the description of the electronic structure of insulating electrolytes, which may ultimately lead to an inaccurate description of several properties, such as redox reactions of the liquids.[73–75] In these instances, more accurate determination of the electronic properties can be achieved using hybrid density functionals, and methods based on many-body perturbation theory (MBPT) within the so-called GW approximation.[76] Among these approaches, the GW method offers a promising way to access electronic properties of not only bulk electrolytes but also electrode/electrolyte interfaces,[77,78] due to its ability to treat the electronic structure of semiconductors and liquids on the same footing.[79–82]
3 | A Q U E O U S SO L U T I O N S In this section, we discuss recent progress in the study of structure, dynamics, and electronic properties of liquid water and aqueous solutions using first-principles methods. This is of particular interest as water is involved in nearly all physical and chemical processes, including those in
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energy storage and conversion systems, such as photoelectrochemical solar-water-splitting for hydrogen production. In addition, studies of these liquids can serve as a baseline for the investigation of more complex electrolytes.
3.1 | Structure and dynamics Despite that FPMD simulations of liquid water have been a topic of interest for several decades, an accurate description of the complex interaction present in the liquid remains a significant challenge. For instance, it is well-known that the use of popular GGA exchange-correlation functionals, such as the PBE functional,[83] leads to over-structured water,[84–86] and hence GGA-based simulations of water and other aqueous solutions are often carried out at elevated temperatures to mimic room temperature structure and dynamics of the systems.[87–90] In recent years, significant progress has been made in the FPMD description of liquid water, much of which has been reviewed by Gillan et al.[91] For example, DiStasio et al.[92] assessed the performance of the PBE0 hybrid functional[93] with dispersion corrections to describe water, and they concluded that both exact exchange and dispersion corrections are necessary to reproduce the structure and the dynamical properties of the liquid. In addition, Chen et al.[94] employed SCAN, a meta-GGA functional,[95] to simulate water, reporting results comparable in accuracy to those obtained in Ref. [92]. More recently, Gaiduk et al.[96] carried out FPMD simulations of liquid water using the dielectric-dependent hybrid (DDH) functional,[97,98] showing that the use of a fraction of exact exchange as the inverse of the high-frequency dielectric constant of the liquid leads to an excellent description of not only structural and dynamical properties but also the electronic structure of the system. For example, Figure 1 shows that the pair distribution functions of water obtained with the DDH functional yield an impressive agreement with experimental measurements. Overall, these developments promise to open up opportunities to probe properties of not only liquid water but also of more complex aqueous solutions with high accuracy and fidelity. Compared to liquid water, only a few FPMD simulations beyond the GGA level of theory have been reported for solvated ions. Simulations of the NaCl solutions with the PBE0 functional show that the inclusion of the exact exchange only slightly alters the ion solvation structure with respect to PBE.[101] Specifically, for Na+ ion, PBE0 simulations leave the solvation structure almost unaltered. The effects observed for Cl− are more subtle, that is, the PBE0 hybrid functional extends the first solvation shell of Cl− ion compared to PBE, and slightly increases its coordination number. A similar trend was found in Ref. [102], where the authors concluded that the inclusion of the exact exchange and vdW corrections collectively weakens the interaction between the Cl− ion and water molecules in the first solvation shell, leading to larger ion coordination numbers (Figure 2). As a result, these studies indicate that the solvation structure of the anion is more sensitive to the level of theory employed in FPMD simulations compared to that of the cation. However, it appears that effect of the exact exchange on the ions is less significant compared to water. For instance, it was found that the intensity of the first maximum in the Cl O radial distribution function decreases by 0.15 compared to the corresponding reduction of 0.52 obtained for the O O one, when the PBE0 functional with vdW corrections is used instead of the conventional PBE functional.[92,102]
FIGURE 1 Oxygen–oxygen and oxygen–hydrogen radial distribution functions of liquid water as computed using a dielectric-dependent hybrid (DDH) functional at 311 K, the PBE functional at 400 K, and the SCAN functional at 330 K. The experimental O O radial distribution function, shown by the solid gray shaded area, is from Skinner et al.[99] and the O H distribution function for light water is from Soper[100] Reprinted with permission from Gaiduk et al.,[96] copyright 2018 American Chemical Society
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Probability distributions of the A, Cl O and B, Cl H coordination numbers for Cl− in liquid water, as obtained from different density functionals, with and without vdW corrections. The coordination numbers were calculated by integrating the corresponding radial distribution functions up to their respective first minimum. Reprinted with permission from Bankura et al.,[102] copyright 2015 Taylor & Francis Group
FIGURE 2
Effects of the delocalization error in the description of complex anions and their chemical reactions in liquid water have also been discussed. For sulfuric acid solutions, Wan et al.[103] showed that the concentration of SO24 − was seriously overestimated when the PBE functional is employed. Conversely, simulations with the hybrid functional PBE0 alleviate the delocalization error and provide results in qualitative agreement with experiments. Significant differences between PBE and PBE0 simulations have also been reported by Pan and Galli[104] for aqueous solutions containing carbonate and bicarbonate ions, where the authors found that the PBE functional overestimates the concentration of HCO3− with respect to PBE0. Accordingly, these simulations suggest that the delocalization error present in GGAs could play a significant role in the description of the kinetics of chemical reactions in aqueous solutions. Next, we discuss progress in the FPMD simulation of transport properties of aqueous solutions, and we focus on ion effects on water diffusion. In this context, it is known that water dynamics in salt solutions can significantly deviate from pure liquid water.[27] For example, experimental measurements showed that the self-diffusion of water can be either enhanced or suppressed by the inclusion of CsI and NaCl, respectively. For these solutions, Ding et al.[105] found that, unlike classical force fields, FPMD simulations successfully reproduce the experimental trends (see Figure 3). This conclusion is then further supported by Yao et al.[106] that showed Cl− and I− ions accelerate water translational diffusion, whereas Na+ and K+ ions slow down the water diffusion, in qualitative agreement with experiments. In addition, the authors found that, among the classical force fields, only those that incorporate explicit charge transfer and polarization are able to reproduce the ion-specific behavior. As a result, these studies provide strong evidence that an explicit treatment of the electronic degrees of freedom is essential for an appropriate description of ion effects on water diffusion. Finally, it is important to emphasize that FPMD simulations remain limited to relatively small system sizes and short time scales due to the high computational expense. As a result, conclusions on the accuracy of theories employed in FPMD simulations need to be interpreted cautiously, as the differences could simply stem from the lack of statistics. This subject was recently highlighted by Dawson and Gygi,[107] where uncertainties associated with several quantities of liquid water derived from FPMD simulations were accessed using a large dataset. Specifically, using 32 independent 64-molecule water simulations of 58 ps each, the authors showed that the variability of the pair correlation functions, number of hydrogen bonds, and diffusion coefficient across samples can be notably large. For example, as shown in Figure 4, the mean square displacement of the oxygen atoms was found to exhibit large variations from sample to sample, leading to a wide range of diffusion coefficients from 0.9 × 10−5 to 3.4 × 10−5 cm2/s. Hence, this study indicates that an accurate determination of these common quantities may require longer simulations and larger sample sizes than those typically employed.
FIGURE 3
Mean-squared displacement (MSD) of oxygen atoms in pure water (red solid line), 3M CsI (black dashed line), and NaCl (blue dashed and dotted lines) solutions simulated with classical force fields (A) and FPMD (B). Reprinted with permission from Ding et al.,[105] copyright 2014 National Academy of Sciences
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FIGURE 4
Simulations were performed as simultaneous runs for 32 independent 64-molecule water samples. A total simulation time was 58 ps for each sample. Mean square displacement of oxygen atoms in each sample computed using the entire simulation data is shown by red lines. The average value taken over all 32 samples is shown in black. Reprinted with permission from Dawson and Gygi,[107] copyright 2018 American Chemical Society
3.2 | Electronic structures The knowledge of the electronic structures of aqueous solutions, such as the ionization potential (IP) and electron affinity (EA) of liquid water, is important for understanding redox and photochemical reactions in aqueous environments. Here, we briefly summarize experimental measurements of the electronic structure of aqueous solutions, starting from liquid water to solutions with solvated ions, and we discuss recent progress in first-principles studies of the systems. The valence band of liquid water can be directly obtained from photoelectron spectroscopy. The first measurement by Delahay yielded an IP of 10.06 eV,[108] while more recent studies obtained a slightly smaller value of 9.9 eV,[109,110] leading to an overall agreement that the water IP is around 10 eV. Conversely, direct measurements of the EA are not available, and current estimates of the EA are based on thermodynamic arguments that involve specific assumptions on the behavior of photoionized electrons in water, which result in a wide range of 0-1.2 eV for the EA of liquid water.[111–114] With recent advances in highly accurate electronic structure methods, including MBPT within the GW approximation[115–117] and the development of novel hybrid density functionals,[97,98] several predictions of IP and EA of liquid water have been reported. However, the results significantly depend on the structural models and electronic-structure methods employed in the calculations. For example, using the structural configurations generated either by classical potentials or GGA-based FPMD simulations, “single-shot” G0W0 calculations with the wavefunctions derived from DFT and the PBE approximation yielded values of 0.7 eV and 8.8 eV for the EA and IP, respectively.[77] Conversely, using structural models derived from FPMD simulations with the inclusion of nuclear quantum effects (NQEs) and vdW corrections, self-consistent GW calculations report values of EA = 0.5 eV and IP = 9.4 eV.[118] Besides these MBPT studies, it has also been shown that self-consistent DDH functional calculations using structural configurations generated by FPMD simulations are able to recover the experimental value of IP for liquid water.[82,119] More recently, path-integral molecular dynamics simulations have been combined with MBPT to probe the electronic structures of liquid water and of its surface.[120] In this study, the molecular dynamics simulations were carried out with the many-body MB-pol potential energy function with the inclusion of NQEs, which accurately describes the structural properties of water in gaseous and condensed phases.[121–123] In addition, the electronic structures were calculated at the G0W0 level of theory, starting from the wavefunctions determined with the DDH hybrid functionals.[119] By combining these high-level theories, this study provides insight into the roles of NQEs in the determination of the electronic structures of liquid water, while revealing important differences between bulk water and its surface. As shown in Figure 5, the authors found that the inclusion of NQEs reduces the band gap by almost 0.5 eV. In addition, despite that the IPs of the bulk and surface are almost identical, their EAs were found to differ substantially, with the conduction band edge of the surface much deeper in energy than that of the bulk due to the presence of broken hydrogen bonds at the surface. Finally, by benchmarking the calculations of the EA with respect to pump-probe spectroscopy measurements of water surface,[124,125] the authors showed that the EA of liquid water is rather small, that is, 0.2 eV, which differs substantially from several results present in the literature. Based on this result, an updated energy-level diagram for an electron in water was presented, and the authors concluded that several existing experiments and assumptions used in constructing the diagram need to be revisited. Beyond liquid water, it has also been demonstrated that the DDH functionals can be used to accurately predict the electronic properties for a wide variety of aqueous solutions.[82] This is demonstrated in Figure 6, where Pham et al.[82] showed that the calculated IPs of 16 solvated ions is in good agreement with experimental measurements, yielding a mean absolute error of only 0.14 eV. Moreover, this level of theory was found to exhibit similar performance compared to more sophisticated, yet computationally more expensive, MBPT calculations. Accordingly, DFT calculations with DDH hybrid functionals provide an efficient and predictive tool for understanding the electronic structure of aqueous solutions.
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FIGURE 5
Computed electronic energy levels of liquid water. Positions of the valence band maxima (VBM, blue) and conduction band minima (CBM, red) of the surface of the water and bulk water computed using the classical and path integral molecular dynamics with the MB-pol potential. All values are in eV. The energy levels were computed using the G0W0 approach, starting from the DDH functionals; the range given above (thick bars) corresponds to results obtained with range-separated and self-consistent hybrid density functionals. Reprinted by permission from Macmillan Publishers Ltd: Nature Communications, Gaiduk et al.,[120] copyright 2018
In addition, this approach can be used to interpret experimental photoelectron spectra and provide direct mapping between specific photoemission signals and chemical species. Collectively, recent development of advanced electronic structure methods, such as the DDH hybrid density functionals, has enabled the prediction of the electronic structure of aqueous solutions with high accuracy and fidelity. These developments can be readily extended to investigate other properties, including redox reactions of solvated ions in aqueous solutions. It is also important to emphasize that these methodologies are general and applicable to other liquids, thereby offering great promise in understanding and engineering electronic properties of solutions and liquid electrolytes for a variety of important energy technologies.
4 | ORGANIC ELECTROLYTES In this section, we discuss recent progress in the FPMD simulation of organic electrolytes, which are important components in ion batteries. For instance, it is known that the liquids form a solid electrolyte interphase (SEI) on graphitic anodes that prevents excessive electrolyte decomposition while promoting reversible ion intercalations in the systems.[126–129] In addition, a proper selection of the electrolytes could improve the ion diffusion,[130–134] which in turn leads to better performance of the ion battery, especially in the power density.[6] Compared to aqueous solutions, organic electrolytes have been less investigated by FPMD simulations, partly due to their complex structures that often require a large number of atoms in the simulation cell for a meaning representation of the liquid. For the same reason, most of the existing FPMD simulations of organic electrolytes were carried out with GGA exchange-correlation functionals to compromise the accuracy and computational expense.[53,135–138] At this level of theory, FPMD simulations have already provided valuable insights into the solvation and transport properties of Li+ and other relevant ions for battery applications in a variety of organic solvents.
FIGURE 6
The ionization potentials (IPs) of 16 solvated anions: Comparison between liquid-jet experimental data and DFT calculations with the self-consistent DDH functional. From Pham et al.,[82] reprinted with permission from AAAS
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Li OC and Li OE pair correlation functions (solid lines) and their integrals (dashed lines) for possible solvation structures of Li+ in the EC solvent: A, 4carbonyl and B, 3carbonylPF6. Here, OC and OE stand for the carbonyl and ether oxygen atoms of EC, respectively. Snapshots of the solvation structures and the average energies relative to the lowest-energy structure are shown in the insets. Reprinted with permission from Ong et al.,[137] copyright 2015 American Chemical Society
FIGURE 7
Solvation and diffusion of Li+ and its counter ion PF6− have been investigated for several organic solvents, including ethylene carbonate (EC), ethyl methyl carbonate (EMC), and a mixture of EC and EMC.[137] As demonstrated in Figure 7 for Li+ in EC, one of the most common organic solvent, the simulations showed that the ion is solvated by either carbonyl or ether oxygen atoms of the solvents and sometimes by the PF6− . In addition, Li+ prefers a tetrahedrally coordinated first solvation shell regardless of which species are involved, with the specific preferred solvation structure dependent on the organic solvent. An important finding of the study is that Li+ diffuses faster in the solvent that forms a weaker solvation shell with the ion. A similar conclusion was made in Ref. [135] when comparing propylene-carbonate (PC) and EC solvents, where the weaker solvation of Li+ in PC results in a relatively faster ion diffusion. Accordingly, these studies indicate a direct relationship between solvation structure and dynamics of Li+ in the solvent. Effects of vdW corrections on the solvation of Li+ in the EC solvent have also been investigated by Ganesh et al.[135] In Figure 8 the authors compared the Li-O(carbonyl) radial distribution function and the Li O C(carbonyl) bond-angle distribution function for simulations with and without vdW corrections.[139] It is found that the inclusion of the vdW interaction only slightly shifts the first peak in the radial distribution function, and Li+ remains its four EC molecules in the first solvation shell. In addition, the Li O C(carbonyl) distribution is very similar, suggesting that vdW interaction has a negligible effect on the structure of the Li+ solvation shell, and that the interaction between Li+ and the EC solvent is largely governed by electrostatics. In additional to Li+, solvations of Na+ and K+ in organic solvents, which are relevant for the study of sodium[140–144] and potassium[145–147] ion batteries, have been investigated. A systematic investigation of Na+ and K+ in EC using FPMD simulations was reported in Ref. [148], which revealed significant differences in the solvation structure and dynamical properties of Na+ and K+ compared to Li+. Specifically, in contrast to Li+ which exhibits a well-defined first solvation shell, the larger Na+ and K+ ions show more disordered and flexible solvation structures (see Figure 9). These differences in solvation were also found to significantly influence the ion dynamics, leading to larger diffusion coefficients of Na+
Comparison of the radial distribution function between Li and the carbonyl oxygen of EC, along with the Li+ coordination number (dashed lines), as obtained from simulations with (DFT-D2) and without (DFT) van der Waals corrections. Inset shows the histogram of He Li O C angle. Reprinted with permission from Ganesh et al.,[136] copyright 2012 American Chemical Society
FIGURE 8
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(C)
(B)
(A)
Na+ Li+
K+
Typical solvation structures of (A) Li+, (B) Na+, and (C) K+ in EC solvents. The solvation structures of Li+ and Na+ can be described as tetrahedral and distorted trigonal bipyramid (or square pyramidal), respectively, while the solvation structure of K+ is less well-defined. Thick solid and transparent lines denote bonds to carbonyl and ether EC oxygen atoms, respectively. Reproduced from Pham et al.,[148] copyright 2017 American Chemical Society
FIGURE 9
and K+ compared to Li+. In particular, the simulations indicated that the diffusion coefficient of Li+ is about 3 times smaller than those of either Na+ or K+, which can be directly related to a significantly stronger solvation shell of Li+. Interestingly, the dynamics of EC molecules is also be affected by the presence of the ion. As the authors demonstrated in Figure 10, a slight suppression of the EC diffusion in the electrolyte containing Li+ was found compared to those with Na+ and K+. Investigation of the dynamics of EC molecules in the first ion solvation shell indicated that the low diffusivity of the EC molecules near Li+ is responsible for this difference in EC diffusion, and further highlights the specific ion effects in the transport of solvent molecules. Overall, recent FPMD simulations of Li+ and other ions in organic electrolytes all point to a close correlation between the ion solvation strength and ion diffusion. Furthermore, these studies reveal an interesting and important analog in the behavior of the ions in organic electrolytes and aqueous environments, particularly in the specific ion effects on the solvent dynamics. For example, the strong ion–solvent interactions of Li+ reflect the “structure-maker” nature of the ion in the EC solvent, which is similar to the behavior of solvated ions in aqueous electrolytes.[27]
5 | OTHER LIQUIDS While this review has focused on the simulation of aqueous solutions and organic electrolytes, FPMD methods have also been employed to investigate more complex liquids. A primary example is ionic liquids (ILs) that have emerged as highly promising electrolyte candidates for electrochemical devices due to their nonvolatility and inflammability that offer enhanced safety and stability.[149–151] In recent years, FPMD simulations have been increasingly utilized to investigate the atomistic structure of ILs.[152–159] For instance, significant efforts have been devoted to elucidate the nature of the hydrogen bond network in ILs,[160–165] and its relevance for, that is, transport properties, such as ion diffusion and ionic conductivity of the liquids.[158] In addition, first-principles calculations have been extended further to predict the electrochemical window for several ILs.[166,167] Conversely, applications of FPMD simulations to the study of several other properties of ILs remain prohibitive, largely due to the high complexity of the systems. For instance, direct simulations of the transport properties of ILs are currently beyond the reach of first-principles techniques due to the sluggish nature of the liquids that requires significantly longer simulation times. In additional to ILs, development of ultrahigh concentration electrolytes for energy storage systems is an emerging field. These electrolytes exhibit extraordinary properties beneficial to electrochemical performances that are unavailable at low salt concentration.[168–170] For instance,
Mean square displacement computed for all EC molecules in the electrolyte with Li+ (black), Na+ (red), and K+ (blue) ions. The MSD computed for EC molecules only in the first solvation shell of Li+ is presented by the dashed line. Reprinted with permission from Pham et al.,[148] copyright 2017 American Chemical Society FIGURE 10
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Ogumi and coworkers found that graphite electrodes drastically change their behavior to reversibly accommodate Li+ in highly-concentrated PC electrolytes, which is otherwise impossible in the dilute electrolytes.[171,172] In addition, the use of ultrahigh concentration electrolytes has enabled the rapid formation of the SEI in ion batteries, thereby significantly improving the stability of the anode.[173] More recently, Suo et al.[13] developed highly concentrated aqueous mixtures of lithium bis(trifluoromethane sulfonyl)imide that yield a voltage stability window far beyond that of typical aqueous electrolytes, and hence could be used as alternative to replace traditional flammable organic electrolytes. In additional to extensive experimental studies, FPMD simulations have started to be utilized to investigate properties of this new class of electrolytes.[170,173–175] For instance, Yamada et al.[173] employed FPMD simulations to unravel the unique electronic structures of the superconcentrated acetonitrile solution, which can be directly related to the enhanced reductive stability of the solution in lithium-ion batteries. However, the fundamental understanding of these complex electrolytes is generally still in its infancy, which continues to stimulate further theoretical studies in the near future. Finally, solid electrolyte materials have also been a topic of increasing interest. This is related to ongoing efforts in the development of novel all-solid-state batteries,[176] where the replacement of an organic liquid with an inorganic solid promises superior safety as well as mechanical and thermal stability. In this context, many candidates have been investigated, including polyborate salts that exhibit exceptional ionic conductivities.[177–179] For these materials, FPMD simulations have elucidated the fundamental mechanisms that govern their ultrafast ion conduction, and provided general strategies for improved ionic conductivity.[180–182] These studies demonstrate how the fundamental understanding provided by FPMD simulations could be leveraged to establish a more rational design approach for electrolyte selection.
6 | CO NCLUSIO NS A ND OU TLOOK In summary, we reviewed some recent progress in the FPMD simulation of liquid electrolytes for energy conversion and storage. We mainly discussed the structural, dynamical, and electronic properties, which are important factors in optimizing device performance for several energy technologies. While this review has largely focused on the studies of bulk liquid electrolytes, it is important to emphasize that FPMD simulations have been increasingly utilized to provide a reliable microscopic description of electrolytes in more complex environments. For example, a large number of first-principles simulations have been reported for solid/liquid interfaces in ion batteries[53,138,183–187] and photoelectrochemical cells for solarwater-splitting.[31,32,59,77,188–196] Despite the impressive development in the FPMD method, making the connection between theoretical observables and experimental measurements remains a challenging task, which motivates further developments in the community. A primary example is the electrode/electrolyte interface, a key component in several energy conversion and storage devices, for which additional physical factors should be considered to provide a realistic description of the systems. In particular, effects of applied bias potentials, which play a critical role in determining device performance under working conditions, need to be included. Modeling these effects, however, is not straightforward in conventional DFT and quantum chemistry calculations, where a fixed number of electrons are often employed. Although recent developments in first-principles techniques, such as the effective screening medium (ESM) method,[197–199] have made it possible to carry out first-principles calculations at a constant electron chemical potential instead of at a fixed number of electrons, direct applications of such methods to complex interfaces are often limited by the high computational expense. Similarly, the formation of the electric double layer at the electrode/electrolyte interface needs to be considered, which involves not only solvent molecules but also solvated ions. Although some attempts have been made to understand the behavior of solvated ions at the interface with solids,[200–205] these types of studies are rather sparse due to limitations in the time and length scales accessible by FPMD approaches. In this regard, coupling FPMD to advanced sampling methods[206–208] and continuum solvation models[209,210] offers promising means to alleviate these problems. In addition, significant efforts are needed to improve the accuracy of FPMD simulations for a faithful description of complex electrolytes and their interfaces with solid electrodes. In contrast to liquid water that has been a topic of intense study, the accuracy of GGAs in describing the physiochemical properties of ultrahigh concentration electrolytes and solid-electrolyte materials has been largely unexplored. For example, the effects of vdW corrections and delocalization error in the simulation of these complex electrolytes have not been addressed. Similarly, the development of a single density functional capable of providing an equally accurate description of solid electrode materials and electrolytes in heterogeneous interfaces remains a significant challenge.[31] In this regard, integrating simulations and experimental validations through in situ characterization techniques will play a key role in understanding and advancing the accuracy of the FPMD method.[42] Overcoming the limitation in the length and time scales accessible in FPMD simulations continues to be a main effort of the community. In particular, developing novel algorithms and efficient electronic structure methods for enabling massively parallel first-principles simulations is one of the most active research areas in the field.[211–216] Other approaches for alleviating this shortcoming of FPMD methods include the development of sophisticated force fields that are capable of accessing a broader range of length and time scale based on high level quantum chemistry methods.[121–123,217–220] In addition, Monte Carlo simulation methods represent a promising direction, where advanced sampling techniques can be employed to efficiently equilibrate and probe configurational space of complex and strongly interacting electrolytes.[221,222] Finally, together with advancements in these theoretical approaches, we emphasize again that a close integration between computational and experimental approaches will play a decisive role in understanding electrolytes and electrolyte interfaces for energy conversion and storage.
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ACKNOWLEDGMENTS This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. The author acknowledges support from the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office; the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences; and LLNL Laboratory Directed Research and Development Program Grant No. 18-LW-064. Many thanks to Alex Gaiduk, Giulia Galli, Eric Schwegler, John Pask, Vincenzo Lordi, Brandon Wood, and Tadashi Ogitsu for fruitful discussions, and to Liam Krauss for a critical reading of the manuscript. The author is indebted to his Ph.D. advisor at UC Davis, Giulia Galli (now at the University of Chicago) for introducing him to the world of liquid water. ORCID Tuan Anh Pham
http://orcid.org/0000-0003-0025-7263
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AUTHOR'S BIOGRAPHY TUAN ANH PHAM is a staff scientist in the Quantum Simulations Group and Materials Science Division at the Lawrence Livermore National Laboratory (LLNL). He joined LLNL as a Lawrence Fellow in 2014 after receiving a Ph.D. in Physical Chemistry at the University of California, Davis, under the supervision of Dr. Giulia Galli. He is also the recipient of the 2014 UC Davis Outstanding Chemistry Dissertation Award and 2017 PCTC Postdoctoral Fellow Award. His research interests include the development and application of first-principles techniques to validate, understand, and predict material properties for energy technologies.
How to cite this article: Pham TA. Ab initio simulations of liquid electrolytes for energy conversion and storage. Int J Quantum Chem. 2018;e25795. https://doi.org/10.1002/qua.25795
