■ INTRODUCTION

Solvated electrons have been of great interest recently because they provide a paradigm system for confronting the predictions of quantum simulations with experiment. Typically when excess electrons are injected into a neutral liquid, they localize in a cavity in the liquid due to Pauli repulsive interactions from the surrounding closed-shell solvent molecules. However, in liquid acetonitrile (CH 3 CN), an excess electron can also bind to one or more solvent molecules to create a solvated molecular anion. In fact, excess electrons in liquid acetonitrile take on two distinct forms that are in equilibrium with each other: a traditional solvated electron in a cavity in the liquid, which absorbs strongly in the near-infrared region, 1 and a solvated molecular anion, which absorbs weakly in the visible region. [2][3][4] At room temperature, the equilibrium constant acetonitrile cluster anions, (CH 3 CN) n -, which should serve as precursors to the fully solvated species in the bulk liquid.

Photoelectron spectroscopy experiments on acetonitrile cluster anions with sizes n = 10-100 revealed two peaks whose vertical electron detachment energies (VEDEs) differed by over 2 eV. 8 The lower-energy band, which is found between 0.4 and 1.0 eV depending on cluster size, is commonly labeled "isomer I", while the higher-energy peak, whose maximum is found between 2.5 and 3.0 eV, is termed "isomer II". For both isomers, the VEDE shifts to higher energies with increasing cluster size. 8 The same experiments found that smaller clusters (n ≤ 12) favored the formation of isomer I, while the isomer II band dominated the photoelectron spectrum for sizes n > 13. 8 Furthermore, an additional weak peak was observed near ∼0.8 eV for smaller cluster sizes, which has been assigned as a C-H vibronic excitation of isomer I. 8 Neumark and co-workers also applied time-resolved photoelectron imaging to acetonitrile cluster anions of sizes n = 20-50 to examine the excited-state dynamics of isomer II. These researchers found a lack of size dependence for the excited-state lifetime, suggesting a localized binding motif for this isomer. 9

Of course, it is tempting to assign the two isomers seen in gas-phase (CH 3 CN) n -cluster anions as precursors of the two distinct excess electron species observed in the bulk liquid. This type of extrapolation also has been attempted for water cluster anions, which similarly show multiple isomers in photoelectron spectroscopy, [10][11][12][13][14][15][16][17] even though only a single type of hydrated electron is observed in aqueous solution. [18][19][20][21] However, theoretical calculations suggest that at small cluster sizes (n ≤ 20) all of the different water anion cluster isomers have the excess electron residing on the surface of the cluster, so that the cluster behavior is not representative of interior states that would be present in bulk liquid water. 22 Moreover, calculations have shown that the different surface-bound isomers are created with different relative populations that depend on how the cluster anions were prepared; that is, the structural isomers observed depend on the temperature of the clusters, [22][23][24] which is generally not easily controllable or even known experimentally.

One previous theoretical attempt to understand the nature of excess electrons in acetonitrile cluster anions consisted of a mixed quantum-classical molecular dynamics simulation on clusters with sizes between n = 5 and 100. 25 These simulations employed a classical model for the acetonitrile molecules and a fixed pseudopotential for the classical acetonitriles' interaction with the quantum excess electron. 26,27 At larger cluster sizes, an internal cavity-solvated electron was observed, while metastable surface-bound states were seen for the smallest cluster sizes at low temperatures. 25 However, because an acetonitrile molecule's electron affinity increases as the molecule bends, such simulations are not capable of describing a solvated molecular anion. This is because the molecules that comprise the anion have a different electronic structure when they bend, allowing a partial C-C bond to be created between molecules, but this change in electronic structure cannot be described by using a pseudopotential optimized for the closed-shell, unbent molecule. Thus, the best that can be concluded from this study is that at larger sizes at room temperature a traditional cavity excess electron is a reasonable assignment for one of the two species observed in the bulk liquid.

Clearly, dynamical quantum chemistry studies on acetonitrile cluster anions would be of great help in identifying isomers I and II and their connection with the species in bulk 117 solution. To date, however, the calculations that have been 118 performed were limited to static energetic studies on gas-phase 119 molecular anions and clusters of small size (n ≤ 10). 7, 28-32 120 One set of cluster calculations at the MP2 and CCSD(T) level 121 of theory identified a wide variety of dipole-bound anions for 122 clusters with size n = 2 and 3. 28 Another set of calculations 123 using the B3LYP and PW91 functionals showed that the dimer 124 anion can become stable for clusters of size n = 4-6 if the 125 surrounding solvent molecules interacted with the dimer's N 126 atoms through an N•••H interaction. 29 These same workers 127 also demonstrated that if the geometry were appropriately 128 constrained, an interior (i.e., "cavity-like") excess electron 129 could be obtained for (CH 3 CN) 6

-, 29 The Journal of Physical Chemistry A ensemble at approximately room temperature starting from neutral configurations constructed with the Packmol software. 35 As discussed further below, we ran both roomtemperature-equilibrated trajectories of anionic clusters and trajectories of neutral acetonitrile clusters to which an electron was suddenly added. For detailed analysis, we then quenched (i.e., geometry-optimized) uncorrelated anion configurations taken from these trajectories using the same optimized BNL functional with the larger 6-311++G** basis set (although we found that for the n = 5 cluster anion dynamics, the geometry optimization step did not change the observed distribution of electron binding motifs or VEDEs; see the Supporting Information for more details). Corrections due to dispersion were accounted for with the D3 empirical potential developed by Grimme, 36 as implemented in the quantum chemistry package Q-Chem 5.2.1. 37 Before running any trajectories or extracting any configurations for geometry optimization, we first ensured that the range-separation parameter, ω, in the BNL functional was appropriately tuned for studying acetonitrile anion clusters. We began the functional optimization procedure by tuning the range-separation parameter to accurately describe both dipole and valence interactions between an excess electron and acetonitrile molecules in the gas phase. Two structures were considered for these initial gas-phase optimization calculations: a single linear acetonitrile dipole-bound anion and a bent antiparallel dimer anion. After individually optimizing the range-separation parameter for each anionic species, as described in more detail in the Supporting Information, we found that the optimally tuned parameter for the dimer anion was able to describe the ionization potential, dipole moment, and quadrupole moment of both the gas-phase dimer anion and the dipole-bound monomer species. Moreover, the optimally tuned functional also replicated the electronic properties of a bent monomer anion at the same level of theory.

We then optimized our long-range-corrected functional for cluster anion simulations by running an unbiased roomtemperature (CH 3 CN) 5

-trajectory using the dimer anion's optimally tuned range-separation parameter (ω = 0.320 bohr -1 ). Following a 1.5 ps initial equilibration period, we extracted eight uncorrelated (at least 1000 fs apart) cluster anion structures and performed a geometry optimization on each of them. We then applied the functional-tuning scheme described above to each of the collected structures and used the optimized values to compute an average optimized rangeseparation parameter. The mean value (ω = 0.151 bohr -1 ) for the optimally tuned functional obtained this way was then used to run another DFT-based (CH 3 CN) 5 -BOMD simulation.

We then extracted uncorrelated configurations from this latter run and reoptimized the range-separation parameter but found that the optimal average value of ω = 0.151 bohr -1 did not change. We then tested the new optimally tuned functional on the original gas-phase species and found that we were able to replicate their ionization potential and dipole moment to an acceptable degree of accuracy. Thus, we settled on ω = 0.151 bohr -1 as our optimally tuned range-separation parameter for all subsequent calculations and did not further adjust it for different cluster sizes or configurations.

With our chosen long-range-corrected BNL functional optimally tuned, we then studied the dynamics and energetics of (CH 3 CN) n -cluster anions of sizes n = 5, 7, and 10. The largest cluster size of 10 was chosen as a compromise between The Journal of Physical Chemistry A (CH 3 CN) n -trajectories described above. Second, as indicated in the lower part of the figure, using the classical molecular dynamics code LAMMPS, 39 we simulated poor thermal equilibration conditions/colder cluster temperatures by starting with classical MD trajectories of neutral acetonitrile clusters with sizes n = 5 and 10 using a flexible all-atom force field. 26,40 We then extracted uncorrelated neutral CH 3 CN cluster configurations every 0.5 ps, added an excess electron, and then immediately quenched (i.e., geometry-optimized) these configurations using the methodology described above without running any ab initio dynamics. We note that we used a similar methodology in our previous study of water cluster anions and were able to successfully reproduce photoelectron spectroscopy experiments from different groups that used different cluster expansions conditions. 22 Finally, to ensure that the use of classical trajectories on neutral acetonitrile cluster dynamics was a reasonable approach for the production of poorly equilibrated (CH 3 CN) n -cluster anions, we also produced poorly equilibrated cluster anions by first running DFT-based ab initio trajectories for neutral n = 5 clusters and then added the excess electron and immediately performed a geometry optimization. We then compared the results from preparing the neutral clusters with classical mechanics versus preparing them using DFT and found no statistically significant difference between the distribution of different binding motifs observed or in the range of calculated VEDEs, as described in more detail in the Supporting Information. This gave us confidence that the use of classical mechanics for generating poorly equilibrated cluster anions at the larger n = 10 size produced meaningful configurations.

■ RESULTS AND DISCUSSION

Categorizing the Electron Binding Motifs in (CH 3 CN) n -Cluster Anions. After running trajectories and collecting both room-temperature-equilibrated and poorly equilibrated acetonitrile cluster anion configurations for clusters with sizes 5 and 10 (as well as equilibrated trajectories for size 7), we began our analysis by examining the dynamics of the individual acetonitrile molecules that make up each cluster anion. What we found is that the C-C-N bond angle, Θ CCN , serves as a chemically meaningful order parameter that is capable of differentiating the binding motifs that we observe for the excess electron. The choice of Θ CCN as an order parameter for understanding the excess electron behavior makes sense because this bond angle is strongly correlated to the electron affinity of the molecule: a single CH 3 CN -anion changes from dipole bound to valence bound as Θ CCN changes from 180°to 130°. 6

f2

Figure 2 provides a limited sampling of how this bond angle typically changes as a function of time for all of the CH 3 CN molecules in each of the cluster sizes tackled in the study; for the data displayed here, the dynamics were collected for (CH 3 CN) n -clusters at thermal equilibrium at roughly room temperature. What the data show is that there are three distinct distributions of Θ CCN . For the n = 5 cluster anion, we see that at many times (for example, for the first ∼0.5 ps of the trajectory plotted) all five acetonitrile molecules have bond angles ≥155°, which we will refer to as "straight" molecules. What we will show below is that when all the molecules are straight, the electron is dipole bound to the surface of the cluster. Next, we see many configurations in both the n = 5 and n = 10 cluster anions where a single CH 3 CN molecule had a bond angle between 125°and 155°, which we will refer to as To further understand the different types of excess electron binding motifs, we quantified the excess electron's spatial extent by investigating how the center of mass and radius of gyration of the excess electron's spin density compare to those of the entire cluster. We find (see the Supporting Information for more details) that solvated monomer and dimer anions (with one or two bent molecules, respectively) had relatively compact electron radii of gyration compared to the size of the cluster and that the center of the electron was on average located inside the cluster's radius of gyration. For surfacebound excess electrons (clusters with only straight molecules), we found that the electron's radius of gyration was comparable to or larger than that of the cluster and that the center of mass of the electron generally resided outside the cluster's radius of gyration. Thus, our assignment of these species as molecular and dipole-bound fits well with the position and spatial extent of the electron's spin density. f4 Figure 4 shows the relative abundance of the different types of electron binding motifs in clusters with different sizes and different production methodologies. The data in the leftmost panels were constructed from 78 and 32 poorly thermalized cluster anions for sizes n = 5 and n = 10, respectively. Those plots in the rightmost panels consist of 964 and 192 thermally equilibrated configurations directly taken from the cluster anion trajectories every 50 fs for sizes n = 5 and n = 10, respectively (Figure S5 shows similar data for thermally equilibrated n = 7 cluster anions). We find the surface-bound species predominates in clusters that were prepared with poor thermal equilibration, while the valence-bound monomer and dimer anion species appear to a greater extent in clusters that were thermally equilibrated. We also see that larger cluster sizes favor the dimer anion over the monomer anion and disfavor the surface-bound species. Finally, as discussed in the next section, we also examined the VEDEs of our cluster anions and find that each electron binding motif corresponds to a unique VEDE range, allowing us to make a tentative assignments of the peaks seen in the (CH 3 CN) n -cluster anion photoelectron spectroscopy experiments.

The relatively low abundance of the molecular anion species in the poorly equilibrated clusters is related to the need for these species to be stabilized by solvation. Upon examination of the different binding motifs (see the Supporting Information for details), we find that the bent molecules of the valencebound molecular anions, and particularly the dimer anion, are stabilized by coordination of the H atoms on their methyl On the basis of the generally good agreement between experiment and theory, we are now able to assign the peaks present in the experimental photoelectron spectroscopy of (CH 3 CN) n -cluster anions. First, the simulations clearly suggest that the weakly bound isomer I species is a surfacebound electron, similar to the species observed in previous studies of small water cluster anions. [22][23][24] We find no evidence that isomer I could be the cluster-phase counterpart to the bulk The Journal of Physical Chemistry A F the associated shoulder shift to higher binding energies with increasing cluster size also supports our assignment of the two features to the surface-bound electron and monomer anion.

Finally, in agreement with the general consensus in the literature, 5,8,9,38 we believe that the isomer II peak, which becomes prominent at higher binding energies in the experimental photoelectron spectra at cluster sizes n ≥ 12, is due to the (CH 3 CN) 2 -dimer anion. We note that experimental studies on low-temperature solid-state α-acetonitrile crystals have also argued that absorption band observed in the UV/blue portion of the spectrum for the bulk solvated electron can be explained as arising from the dimer anion. 5 Figure 6 also compares the high-energy range of our simulated spectrum for n = 10 with the experimental photoelectron spectrum for n = 11 (dashed black curve). 8 We make this comparison because n = 11 is the smallest cluster size for which the isomer II peak is somewhat visible, and we see that the position and relative intensity of this peak agree reasonably well with the predictions for the dimer anion from our poorly thermally equilibrated simulations. What this comparison suggests is that the experimental clusters of this size are even more poorly equilibrated (or at a colder average temperature) then the way we simulated them from room-temperature neutral cluster configurations: we see a slightly larger population of dimer anions in our simulations because the geometry-optimization procedure we use is better able to provide the requisite H•••N interactions needed to stabilize this species than the colder cluster anions created experimentally. We note that the experiments also show that the isomer II peak becomes predominant by size n ≥ 13. We believe that this occurs for two reasons. First, the larger clusters have more straight molecules that can provide favorable solvation interactions to help stabilize the formation of a dimer anion. Second, the larger clusters in the experiments are also likely more thermally equilibrated than the smaller clusters, so that the relative distribution of electron binding motifs for clusters with n ≥ 13 starts to resemble that of the thermally equilibrated trajectories in our simulations more than the poorly equilibrated trajectories, again favoring the dimer anion.

■ CONCLUSIONS

In summary, we have carefully tuned the range-separation parameter of the BNL functional to capture the chemistry of acetonitrile cluster anions to a reasonable level of quantum chemical accuracy. With the optimally tuned functional, we studied the energetics and dynamics of (CH 3 CN) n -cluster anions with sizes n = 5, 7, and 10. The simulations revealed that the electron has three chemically distinct binding motifs.

For the weakest binding motif, the surface-bound anion, the electron is attached to the cluster largely through dipole interactions. The other two binding motifs have the electron valence bound as part of solvated molecular anions consisting of either one or two bent acetonitrile molecules stabilized through N•••H interactions with the neighboring solvent molecules. The molecular dimer anion adopts an antiparallel structure and has a much higher electron binding energy than the monomer anion. In agreement with experiment, we observed a systematic shift toward higher energies in the distribution of binding energies with increasing cluster size for all three binding motifs.

We also compared the electron-binding behavior of acetonitrile cluster anions with sizes n = 5 and n = 10 when the clusters were either thermally equilibrated at room 561 temperature or poorly equilibrated. We found that the 562 formation of the valence-bound monomer and dimer anions 563 was favored with thermal equilibration, while clusters that were