Dynamics of an excess hole in the 1-methyl-1-butyl-pyrrolidinium dicyanamide ionic-liquid

Ionic liquids (ILs) have received considerable attention for their use in energy-related problems. Some of this stems from the fact that whereas they are ionically conductive they are electronically insulating—in some cases with very large band-gaps (electrochemical windows). Applications range from Li^1–4 and sodium^5–8 battery technologies, solar cells,^9–11 spent nuclear fuel recycling^12–15 as well as tribology^16–19 and biomass processing.^20–22 In particular, ionic liquids based on the dicyanamide anion (DCA⁻)^23–32 appear to be appealing for many applications. Coupled with pyrrolidinium-based cations, they form liquids of low viscosity^23,33 at room temperature—high viscosity is one of the main drawbacks for the use of ILs in practical applications. Radiation chemistry studies have shown that anions commonly used in ILs tend to be the species most prone to degradation,³⁴ but of the most common small anions, DCA⁻ appears to be one of the most radiation resistant.^35,36 This makes the study of excess electrons and holes in 1-methyl-1-butyl-pyrrolidinium dicyanamide (⁠$Pyrr1,4+$/DCA⁻) most relevant.

During photoexcitation, radiolysis or when an IL is oxidized or reduced electrochemically, excess positive and negative charges are generated. At time zero before any solvent reorganization is possible, these are commonly referred to as “dry” electrons or holes; this is to distinguish them from the later solvent-equilibrated excess electron or hole species. Compared with common molecular solvents, the dynamics of excess electrons and holes in ILs is much slower,^37–39 making them a most attractive medium to study, among many other phenomena, charge transfer processes. A significant body of work already exists on the fate of excess charge in ILs.^40–53 In fact, the existence of long-lived solvated electrons with lifetimes longer than 100 ns and with the typical F-center spectrum in the near infrared (NIR) has been documented in several prior studies.^40–46,50 It is often the case that this peak, dominated by the excess electron,^{40,42,43,47,48} shifts to the blue over long time scales as solvation dynamics occurs.

In some ILs,^{40,45,47,48,54} another short-lived peak in the visible region of the spectrum can be observed. Blank and co-workers⁴⁸ showed that the photoionization transient absorption spectrum of $Pyrr1,4+$/$NTF2−$ has a sub-ps decay peak at around 500 nm; they also showed that $Pyrr1,4+$/DCA⁻ has a transient absorption peak at around 450 nm.⁵⁴ Kondoh and collaborators⁴⁵ also found an absorption peak at 480 nm for N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium coupled with $NTF2−$⁠, and this peak increased in intensity with the addition of pyrene as an electron scavenger. Wishart and co-workers⁵⁵ proposed that for an IL based on alkylammonium coupled with $NTF2−$⁠, this peak might have contributions from hole absorption. Our own work also predicted⁵¹ that, at least in the very early stages of solvation, both excess electrons and holes can contribute to peaks in the visible and near-IR regions of the absorption spectrum.

In general, the patterns of localization and dynamics of excess hole species in ILs are significantly more elusive than those of excess electrons. There simply is no generic signature in the transient absorption spectrum for holes like the broad near-IR band for electrons. We learn about excess holes from scavenging experiments and from electron paramagnetic resonance (EPR) measurements (see, for example, Ref. 32). However, EPR experiments are done on glassy or frozen matrices on macroscopic time scales under conditions that are obviously quite different from those used to collect transient absorption spectra in the liquid phase where time scales are much shorter on the order of ps to hundreds of ns.

For $Pyrr1,4+$/DCA⁻, Ref. 50 concluded that an excess electron could evolve to form a cavity species with its typical F-center type spectrum or could initially localize asymmetrically on a single DCA⁻. The transient signal of the excess electron could be observed both in the NIR and in the visible region. For the same IL, the current work will attempt to provide insight on the time scale for hole localization as compared to that for an excess electron, the contribution of hole species to the transient spectrum, and the nature of hole transitions giving rise to the different early transient spectral features. These results will be useful in the context of prior electrochemical and radiation chemistry results,^{28,30,31,36,56,57} as well as spectroscopy.⁵⁴ 

The classical and ab initio molecular dynamics (AIMD) techniques and protocols used to simulate neat $Pyrr1,4+$/DCA⁻ as well as the liquid in the presence of an excess hole follow closely those in our prior work on the excess electron in the same system.⁵⁰ Therefore, for completion, only a brief description will be provided here.

All classical molecular dynamics (MD) simulations were carried out using the GROMACS package.^58,59 We used the Canongia-Lopes and Pádua force field parameters^60,61 as well as the All-Atom Optimized Potentials for Liquid Simulations (OPLS-AA) force field parameters⁶² as described in Ref. 50. All ab initio calculations were performed with the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) package^63–65 using the Perdew, Burke, and Ernzerhof (PBE) version of the generalized gradient approximation (GGA) and norm-conserving pseudopotentials. The pseudopotentials are those from Ref. 50. Unless otherwise noted, the split double zeta plus polarization basis sets with a 0.025 V energy shift and 100 K electronic temperature were used for all ab initio calculations using SIESTA. A mesh cutoff of 250 Ry, which corresponds to around 0.1 Å real-space grid resolution, was used and Brillouin sampling was conducted only on the Γ point.

In our prior work,⁵⁰ we had already equilibrated in the liquid phase first classically and then quantum mechanically a simulation box containing 10 $Pyrr1,4+$/DCA⁻ ion pairs. The outcome of that equilibration was used as initial condition for our calculations with an excess hole. For this, a positive charge was introduced in the system to generate a hole during a single point spin restricted calculation. The density matrix output together with the coordinates was used as ansatz for a spin unrestricted single point calculation. The outcome of this last calculation was then used as initial condition for our production AIMD run in the constant energy ensemble (NVE).

Noticing that the picosecond hole delocalization was over DCA⁻ anions, and since hole localization can be a process much longer than 3 ps, we followed a similar procedure to that outlined in Ref. 50 to extend our simulation classically to the several nanosecond time scale. The goal was to be able to access processes associated with longer-time solvation by the IL impossible to capture quantum mechanically. For this, one of the DCA⁻ ions in the classical simulation was made neutral to form the radical DCA ↑. A gas phase ab initio MP2/cc-PVTZ optimization and CHarges from ELectrostatic Potentials using a Grid-based method (CHELPG) charge assignment for the neutral radical using the Gaussian09⁶⁶ software resulted in bond lengths and angles that were similar to those of DCA⁻. Therefore all force field parameters for the neutral radical were approximated as identical to those of the ion except that charges were replaced by those resulting from the CHELPG calculation (see Fig. 1). The optical spectrum of the excess hole in the IL was computed using the same protocol as in Ref. 50.

In a recent article,⁵³ we showed that for ILs involving C, H, and N atoms, the density functional theory tight binding approach^67,68 in its latest implementation—DFTB3^69,70—in conjunction with the 3ob set of parameters,⁷¹ reproduced well different results obtained from full periodic DFT calculations but at a much lower computational cost. In addition to the previously described studies, and to bridge the gap between full DFT dynamics in the ps time scale and classical hole equilibration on the several nanoseconds time scale, we used the DFTB3 approach in conjunction with the Grimme corrections to van der Waals interactions^72–74 as coded in the dftb+ package⁷⁵ to access quantum mechanically hole dynamics on the 100 ps regime.

As demonstrated in Fig. 2 of Ref. 50, and consistent with mass spectroscopic results,⁷⁶ the HOMO band of neat $Pyrr1,4+$/DCA⁻ is almost completely dominated by the anionic subcomponent. For the same neat IL, Fig. 2 in the current article shows the anionic component of the projected density of states partitioned by atoms with labels as defined in Fig. 1. It is clear from this figure that the HOMO band is mostly contributed by the nitrogen atoms; the carbon contribution is much smaller. In other words, it is the anionic nitrogen that loses an electron to form the hole state.

For an excess electron, our prior study⁵⁰ discussed the different possible scenarios of localization in a cavity as well as on ions. We found that when an excess electron localized on ions it was on the DCA⁻ subcomponent and the process was rapid on a subpicosecond time scale. Localization came associated with a change in geometry of the doubly charged anion and noticeable energy changes of the Singly Occupied Molecular Orbital (SOMO). The situation is very different in the case of an excess hole where localization is slower and where energy changes associated with the process appear to also be smaller at least on the picosecond time scale.

As in prior studies,^49,50,53 we use Mulliken charges (see Fig. 3) to follow the charge distribution for all the ions as a function of time after introducing an excess hole during our AIMD. Whereas the Mulliken method for charges is not the most accurate, it proves very useful to follow as a function of time changes in charge distribution and possible localization-delocalization events.^49,50,53 Charges for the ions obtained with this method are non-integer; this is expected for a non-minimal and non-orthogonal basis set.^49,50,53 Instead, with the smaller basis set used in our DFTB calculations (vide infra), these are much closer to unity. Figure 3 shows the time evolution of charges for all ions. At time zero, the “dry” hole is distributed broadly over the nitrogen atoms in different DCA⁻ ions, but already on a subpicosecond time scale at around 0.7 ps (see Fig. 3), a pair or a few DCA⁻ ions share a larger portion of the extra positive charge. Within 3 ps of dynamics, at least two such periods can be observed where the excess hole is more localized. As opposed to the case of the excess electron in the same system where a significant change in the SOMO energy was observed upon early localization on a DCA⁻ anion (see Figs. 3 and 8 in Ref. 50), no significant SOMO ↓ energy changes appear to correlate with early partial localization events for the hole; this can be appreciated from Fig. 4. In the current article, we explicitly utilize the expression SOMO ↓ in reference to the unoccupied spin down channel state associated with the excess hole.

To investigate whether longer time solvent relaxation would significantly impact the energy of SOMO ↓ and the nature of the hole species, we extended our simulations in two different ways. In one case, we extended our simulations using the tight-binding DFT methodology. In the other, we performed classical simulations up to 6 ns where one DCA⁻ anion was converted into the neutral radical hole species DCA ↑; we did this by adjusting charges as indicated in Fig. 1 (see Sec. II).

Figure 5 shows the time evolution of charges for all ions during our 100 ps-long tight-binding DFT calculation using as initial conditions the 3 ps frame of our full DFT dynamics. It is clear from Fig. 5 that the patterns of partial localization and delocalization over the DCA⁻ component of the liquid persist much longer than a few picoseconds. As an example, Fig. 6 shows a frame at 63.8 ps in which three DCA⁻ ions share most of the hole density and later at 90.0 ps the density of the hole is significantly more delocalized.

During a 6 ns extension of our original 3 ps DFT trajectory using classical MD including a single radical DCA ↑ species, snapshots of the system were minimized quantum mechanically in the condensed phase every 2 ns. Resulting Mulliken charges, state energies, and spin densities are shown in Figs. 3, 4, and 7, respectively. In Figs. 3 and 4 data up to 3 ps correspond to those of our DFT dynamics whereas data points at 2, 4, and 6 ns to those of the extended 6 ns trajectory. In Fig. 7 the first two snapshots are for the DFT dynamics and the last three snapshots for the extended trajectory. For the extended trajectory, we find that the energy of SOMO ↓ is quite consistent with values observed during the first 3 ps of AIMD. Notably, the density shows the same pattern of partial localization and delocalization that was previously observed in the picosecond regime. For example, in Fig. 7, at 2 ns and at 6 ns the hole appears to be more localized but at 4 ns more delocalized.

When analyzed quantum mechanically, the final snapshot of a classical simulation that biased the excess hole to localize on a single DCA ↑ resulted instead in what is possibly a dimer radical anion where two ions unevenly share the excess positive charge. This finding may be consistent with predictions by Wishart and Shkrob³¹ based on EPR measurements at low temperature in the glass state and their gas phase DFT calculations. However, one must be cautious in making this assignment since (1) the SOMO ↓ orbital also includes contributions from several other anions (vide infra) and (2) extending the dynamics beyond 6 ns using the DFTB methodology still results in time-dependent patterns of partial localization and delocalization (data not shown). It would therefore appear that even on the several nanoseconds time scale the system is unable to find a deep trap with sufficient energy separation between localized and delocalized states.

From Fig. 4 (see also Ref. 50), we see that before the introduction of an excess hole the band gap for neat $Pyrr1,4+$/DCA⁻ is computed to be about 4 eV (Molins i Domenech reports the onset for absorption at 4.1 eV⁵⁴). Therefore, in this study, transient transitions observed that are less than this energy must be solely from the excess hole species (in a real system, transient transitions can be either from excess electrons or holes; for a description of transitions of the excess electron see Ref. 50). From Fig. 4, we notice that there are three bands that can contribute to transitions below this threshold. These transitions which are for electrons in lower energy states into SOMO ↓ contribute to the transient optical spectrum of the excess hole.

Figure 8 shows the optical spectrum for an excess hole in $Pyrr1,4+$/DCA⁻, after 6 ns of classical MD simulation and quantum mechanical optimization. The spectrum for earlier times in the ps regime is qualitatively similar (data not shown). The spectrum is characterized by a sharp peak in the visible region, a broad peak in the near-IR, and transitions in the ultraviolet (UV). For the same system, peaks in these ranges were observed experimentally by Molins i Domenech.⁵⁴ Since the liquid is transparent in the visible and near-IR regions, in our study all transitions in these regions are from the excess hole. Instead, transitions in the UV at energies larger than 4 eV can have multiple origins including from low-energy electrons into SOMO ↓, as well as from electrons crossing the liquid band gap. Therefore, we focus solely on the transitions of the hole at energies below 4 eV.

From Figs. 8 and 4, we observe that at low energies in the region between 0 and 1.5 eV two types of transitions are possible. The ones at lowest energy correspond to intraband transitions where the hole can be transferred to orbitals that are very similar to SOMO ↓ but localized on different ions. We have referred to such transitions in prior articles^49–51 as translational electronic transitions. An example of such transitions is between SOMO ↓ [Fig. 9(a)] and HOMO-4 [Fig. 9(b)] belonging to the same band. Notice that this band corresponds to orbitals that are qualitatively similar to the gas phase HOMO of DCA⁻ [Fig. 9(c)].

Transitions in the 1 eV range are from states in the first band below SOMO ↓ (see Fig. 4) into SOMO ↓. As can be appreciated from Figs. 9(d) and 9(e), the wave function nature of these states, where some orbitals appear to have more bonding character, is quite different from SOMO ↓. As can be seen from Fig. 9(f), this band is associated with the gas-phase HOMO-1 orbital of DCA⁻. Transitions in the visible region are from states in the second liquid band below SOMO ↓ into SOMO ↓. Figures 9(g) and 9(h) show that transitions from this band into SOMO ↓ are from states where the electron is associated with terminal CN in DCA⁻, as well as from non-nitrogen cationic contributions. Figure 9(i) shows that the anionic subcomponent of this band corresponds to the gas-phase HOMO-2 state of DCA⁻.

In a conventional liquid, ejecting an electron either via photolysis or radiolysis results in a positive radical species. Instead, when electrons are ejected from an ionic liquid, these may originate from cationic or anionic species. If the origin is anionic as in the case of $Pyrr1,4+$/DCA⁻, at least nominally what is left behind is a neutral radical. We find that in this IL, hole localization is almost exclusively on anionic nitrogen. When comparing to excess electron localization on ions in $Pyrr1,4+$/DCA⁻ on the picosecond time scale, the driving force for localization appears to be smaller for the hole species. Specifically, in our prior study, we had observed a drop in SOMO energy on the order of 0.5 eV in less than a picosecond for an electron that localizes on a single DCA⁻ forming an asymmetric and doubly charged radical anion. Nothing like this is observed for an excess hole where short-time partial localization and delocalization do not appear to be separated by large energies. However, we must be cautious with this analysis as electrons will also localize in cavities and radical hole species will react, leading to long-time localization which can be energetically favorable.

We predict that the transient optical spectrum of an excess hole in $Pyrr1,4+$/DCA⁻ will show absorption in the near-IR, visible, and UV regions. The transitions in the near-IR and visible regions are from the same band as SOMO ↓ and from the two bulk liquid bands of lower energy into SOMO ↓. Instead, transitions with energies larger than about 4 eV can have a myriad of different origins as they are consistent with energies larger than the liquid band gap.

The authors would like to thank Dr. James Wishart and Professor David Blank for useful discussions. Support from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract No. DE-SC0001780 is acknowledged.