Atmospheric new particle formation is the process by which atmospheric trace gases, typically acids and bases, cluster and grow into potentially climatically relevant particles. Here, we evaluate the structures and structural motifs present in small cationic ammonium and aminium bisulfate clusters that have been studied both experimentally and computationally as seeds for new particles. For several previously studied clusters, multiple different minimum-energy structures have been predicted. Vibrational spectra of mass-selected clusters and quantum chemical calculations allow us to assign the minimum-energy structure for the smallest cationic cluster of two ammonium ions and one bisulfate ion to a CS-symmetry structure that is persistent under amine substitution. We derive phenomenological vibrational frequency scaling factors for key bisulfate vibrations to aid in the comparison of experimental and computed spectra of larger clusters. Finally, we identify a previously unassigned spectral marker for intermolecular bisulfate–bisulfate hydrogen bonds and show that it is present in a class of structures that are all lower in energy than any previously reported structure. Tracking this marker suggests that this motif is prominent in larger clusters as well as ∼180 nm ammonium bisulfate particles. Taken together, these results establish a set of structural motifs responsible for binding of gases at the surface of growing clusters that fully explain the spectrum of large particles and provide benchmarks for efforts to improve structure predictions, which are critical for the accurate theoretical treatment of this process.
Atmospheric aerosols play a significant role in climate and health.1–3 Direct and indirect aerosol–radiation interactions are currently the largest sources of error in climate models. A significant portion of that error stems from difficulties in modeling new particle formation (NPF), the process by which trace atmospheric vapors cluster and grow to form aerosol particles.4 Prototypical mechanisms consider clusters containing sulfuric acid, ammonia,5,6 and nitrogen-containing bases,7–12 though the influence of organic and biogenic molecules is the subject of increasing studies.13–22 More than half the aerosols in the atmosphere are predicted to result from NPF,23 yet NPF remains the most difficult part of modeling climate change.24
Clusters at the size ranges relevant to NPF have been observed through ambient atmosphere mass spectrometry,22,25–27 atmospheric simulation chamber measurements,16,21,28,29 and flow tube experiments.9,30–32 Mass spectrometry and ion mobility studies have been used to probe the ammonia–amine exchange mechanism,33,34 and the energetics of NPF-relevant clusters have been probed experimentally and computationally.35–40 The incorporation of NPF into climate models does not fully account for the chemical complexity of the process,24 and more sophisticated modeling approaches such as the Atmospheric Cluster Dynamics Code (ACDC) require correct structures to yield accurate growth rates.41 While many structures have been proposed for clusters small than ∼10 molecules,42 concerns remain that the lowest energy structures are found.38,43–45 Figure 1 shows a selection of proposed structures for several small, cationic clusters.35,38,46 Even for very small clusters, such as (NH4)2+(HSO4)1−, different structure searches have produced different minimum-energy structures.38,46 As shown in Fig. 1, there are a number of reasonable structures for these small cationic clusters, and as the cluster size grows, the problem becomes exponentially more difficult to tackle with broad computational efforts alone.47
A variety of computational structure search techniques have emerged to probe minimum-energy structures for clusters.48–50 Many computational efforts, such as the recent adaptation of the ABCluster program51,52 for atmospherically relevant clusters, use algorithmic techniques developed initially across a wide variety of disciplines to explore the potential energy surface (PES) for cluster configurations at a computational cost significantly lower than that of typical high-level quantum chemical methods.53,54 The primary initial effort in these methods involves searching vast portions of the PES with lower-cost methods to identify promising structures, followed by interrogation of those structures with increasingly expensive and accurate methods. Biasing of algorithmic structure searches with information of what the suspected global minimum structure should look like can improve the accuracy of structure searches and allow the structure searches to scale to larger clusters when exploring specific classes of clusters.55,56 Spectroscopy, therefore, may be a useful tool to provide structural information about smaller clusters that can both be useful to bias algorithm-based structure searches and predict the behavior of these clusters without having to directly assign complete structures.
Vibrational spectroscopy has been used to obtain vibrational spectra of mass-selected NPF-relevant clusters generated through electrospray ionization.57–62 These linear action spectra have been used to confirm the structures of several ionic clusters and explore their hydration. Recent work has probed how surface features of small clusters impact their properties. For example, water uptake is proposed to be dominated by free NH sites,59,63 and bisulfate–bisulfate hydrogen bonds are proposed to be potentially reactive sites that are ubiquitous in neutrals.37,60,64 Identifying unique spectral markers of these features in smaller, easier to structurally define clusters is likely to facilitate an understanding of these same spectral markers in much larger clusters that will allow for inferences into the behavior of those clusters without knowing the core geometries. However, uncertainties remain regarding the structures of several small ammonium bisulfate clusters, and outstanding questions remain regarding how amine substitutions may influence these structures. Here, we synthesize NPF-relevant ammonium bisulfate clusters and spectroscopically analyze them using cryogenic ion vibrational predissociation (CIVP) spectroscopy. Using this technique and insights gleaned from a few well-characterized clusters, we are able to assign structures, or at least classify structural motifs, in several prototypical clusters. With these assignments, we are able to fully assign the dominant spectral features seen in larger dry particles.
A. Cluster synthesis
All clusters studied herein were generated via an atmospherically isolated electrospray ionization (ESI) source described previously.65 Briefly, a solution of 1 mM ammonium sulfate salt dissolved in 50/50 water/methanol was electrosprayed into a dry, ∼1 bar N2 atmosphere. Clusters containing alkylamines were obtained by ESI of the above solution in the presence of gaseous alkylamines added to the N2 atmosphere. The cluster distribution generated by this method is similar to the cluster distributions seen in chemical ionization mass spectrometry studies at the CLOUD chamber at CERN, suggesting this method does, indeed, prepare clusters relevant to NPF.10
B. Cryogenic ion vibrational predissociation spectroscopy
All experiments were conducted on a home-built guided ion beam/ion trap/tandem time-of-flight (TOF) photofragmentation mass spectrometer described previously.60 Briefly, ions generated from the electrospray ionization source at ambient pressure are introduced into the vacuum system and guided by a series of octopole guides into a cryogenically cooled octopole ion trap. The cryogenic trap is held at temperatures that yield the adsorption of two D2 molecules on the surface of the clusters, typically between 10 K and 15 K. The ions are then extracted into an orthogonal acceleration tandem time-of-flight mass spectrometer consisting of a linear stage and a reflectron stage. At the focus of the linear stage, the 2D2-tagged ions of interest are intersected by a pulse from an Nd:YAG pumped infrared OPO/OPA laser system from LaserVision. A measurable signal is generated by amplifying and digitizing the output of a microchannel plate detector. The signal is interpreted into meaningful data by recording the boxcar average of both the 2D2-tagged parent and the bare fragment generated by the laser as a function of wavelength. The laser power is monitored by directing a back reflection from the KBr window that couples the laser pulse in the vacuum system to a pyroelectric energy meter. A linear action spectrum is then created by dividing the boxcar average of the fragment by the sum of the boxcar averages of the parent and the fragment, and a laser power correction is applied by dividing by the laser pulse energy.
All calculations were carried out at the CAM-B3LYP/aug-cc-pVDZ level of theory using the Gaussian 16 suite of programs.66 This level of theory has been shown previously to produce computed vibrational spectra having good agreement with experimental data while maintaining a computational efficiency that allows for higher throughput to probe structures of up to seven components in a reasonable time.58 All starting structures were previously reported or developed by chemical intuition about optimal hydrogen-bonding networks derived from previous results on similar clusters. Structures were then optimized at the same level of theory, and basis set and harmonic frequency calculations were performed. The computed spectra as presented were convolved with 5 cm−1 Gaussian functions to reproduce experimental linewidths.
A. Overview of small cluster spectra and structural motifs
Here, we employ the notation (m, n) to denote the cluster structure, where the formula is given by (NH4+)m(HSO4−)n. Figure 2 compares the infrared spectra of the three smallest cationic clusters studied here to an attenuated total reflectance FTIR spectrum of ∼180 nm dry ammonium bisulfate particles from Cziczo and Abbatt.67 The similarity of the fingerprint regions of these spectra suggests that small cationic clusters ranging from (2, 1) to (4, 3) can provide a road map to analyzing the spectral features of larger particles. The progression from (2, 1) to (4, 3) creates a sufficient catalog of spectral bands that form the broader spectral features of the dry particle. These small clusters are computationally tractable and experimentally accessible, allowing them to serve as a basis to better inform predictions about less accessible clusters by allowing us to identify specific surface structural motifs based on spectral features present in larger structures. Currently, the structure of (3, 2) is known, and its spectral features are well defined.58 With the spectral assignments and structural motifs of (3, 2), we endeavor to determine the structure of (2, 1). We can then use structural motifs and chemical intuition gleaned from (2, 1) and (3, 2) to attempt to elucidate the structure of (4, 3). This is of particular significance, as it contains a new band that is also a major unassigned feature of the spectrum of a large dry particle, suggesting that (4, 3) contains a new structural motif that can inform our intuition about features of larger particles.
B. The (NH4+)2(HSO4−)1 cluster
1. Assignment of the structure
We initially consider three potential structures for the (2, 1) cluster, which are shown in Fig. 1. As shown in Fig. S1, isomer A is substantially higher in energy (8.5 kcal/mol) than the lowest energy structure, and the predicted harmonic vibrational spectrum is a poor match to the experimental (2, 1) · 2D2 spectrum. As such, we will focus our discussion on the other two previously proposed structures, isomers B and C, which have been depicted in the inset of Fig. 3.38,46 These isomers are found to lie close in energy, and their energetic ordering is sensitive to the specific level of theory used (see Table S1). The CIVP spectrum of the 2D2-tagged cluster and the unscaled computed vibrational spectra for both of these proposed structures, reoptimized at the level of theory described above, are also depicted in this figure. The lower-energy structural conformation, isomer B, contains four NH–OS hydrogen bonds, two of which are strong single donor/single acceptor hydrogen bonds and the other two are much weaker single donor/double acceptor hydrogen bonds. The higher-energy (+0.152 kcal/mol) structure, isomer C, only contains three NH–OS hydrogen bonds, all of which are single donors/single acceptors. Here, we wish to assign the spectrum to one of the two conformers, which we expect to be the true minimum-energy configuration (or at least the structure present in this experiment). We make this assignment by comparing the peak energies and band patterns between the calculated harmonic spectra and the experimental spectrum, rather than comparing all transition energies alone, since these spectra feature several overlapping bands and potentially significant anharmonic effects that complicate quantitative comparisons.57,68–70 Based on previous experience with these clusters,59,60,63,65 we find that fingerprint vibrations such as the bisulfate SO3 symmetric and nominally doubly degenerate SO3 asymmetric stretching modes shift characteristically according to the number and strengths of hydrogen bonds to bisulfate SO moieties. From these patterns, qualitative insight into the hydrogen-bond linkages can be inferred.
Two sets of two peaks located around 3400 cm−1 and 3600 cm−1 are typical of NH and OH stretching modes, respectively,57,58,60 suggesting that the higher-energy set of two peaks is likely related to the bisulfate OH stretching mode. While only one free OH stretch is expected, two are present here, suggesting an isomeric mixture. From previous results on closely related clusters, and a lack of other spectral indicators of an isomeric mixture, it is suspected that the isomers are tag isomers, which will be explored in depth later. The same splitting is observed for singly D2-tagged clusters, albeit with different relative intensities, suggesting that no new sites are populated by the second tag.58 The two sharp features around 3400 cm−1 are attributed to the symmetric and asymmetric (formally antisymmetric, but reduced in symmetry by proximity to the bisulfate) stretches of free NH2 groups. The broad, relatively intense feature located between 1800 cm−1 and 3000 cm−1 constitutes the shared proton region, a collection of anharmonic features arising from stretches of the hydrogen-bonded NH moieties.70–72 The fingerprint region, located from 600 cm−1 to 1800 cm−1, contains predominantly sharp features typically arising from bisulfate modes between 600 cm−1 and 1400 cm−1 and features typically related to ammonium modes between 1400 cm−1 and 1800 cm−1.
While the two isomers share many spectral features, isomer B appears to most closely represent the experimental spectrum. Analyzing the SO3 asymmetric stretches around 1150 cm−1 and 1200 cm−1 in both isomers, the relative intensities of the lower- and higher-energy peaks are interchanged. Beyond that, looking at the S–OH stretch around 800 cm−1 and the SO3 symmetric stretch around 1000 cm−1, it can be seen that the relative intensity patterns of these two modes are inverted in the higher-energy calculated spectrum as compared with the experimental spectrum. These notable discrepancies between the isomer C calculated spectrum and the experimental spectrum suggest that isomer C is most likely not the major isomer conformation of the (2, 1) cluster.
Upon closer inspection of the S–OH bend and SO3 asymmetric stretching region, it appears as though the S–OH bend around 1100 cm−1 and the SO3 higher-energy asymmetric stretch just past 1200 cm−1 are slightly more intense in comparison to the very intense SO3 asymmetric stretch around 1150 cm−1 in the isomer B calculation compared with the experimental spectrum. This is most likely due to tag effects that can be observed in Fig. S2, where the experimental spectrum, the calculated lower-energy conformation with no tags, and the calculated lower-energy conformation with 2D2 tags in various locations are compared. Within Fig. S2, it can be observed that in the S–OH bending and SO3 asymmetric stretching region, there is a slight shift in frequency between the calculated spectra that contain a D2 molecule tagged to an OH and those that do not. If both tag isomers are present in the experimental spectrum (as suggested by the OH stretching region discussed in more detail later), this could result in a slight broadening and reduction in the intensity of the peaks corresponding to the S–OH bending and SO3 asymmetric stretching modes in the experimental spectrum as compared to the untagged calculated spectrum.
Some notable regions, where the calculated spectrum of either isomer did not appear to capture the experimental spectrum as adequately, are in the NH and OH stretching regions around 3400 cm−1 and 3600 cm−1 and the H-bonded NH stretch region from about 1800 cm−1 to 3000 cm−1. Free NH and OH stretches are typically overestimated by harmonic frequency calculations, and thus, scaling factors are often applied.58,69,70,73 In the OH stretching region, two peaks are found in the experimental spectrum compared with the calculated spectra that both only contain a single peak in that region, as expected for a single OH oscillator. This is due to tag effects that can be observed in Fig. S2, as mentioned previously. In tag isomers containing a D2 bound to an OH, there is a red-shift in the free OH stretch, so an isomeric mixture of tag-binding locations would then lead to two apparent free OH stretches in this region of the spectrum. Additionally, the relative intensities of the peaks in the NH stretching region in the isomer B conformation show the symmetric stretch peak as more intense than the asymmetric stretch peak, which is the opposite relative intensity pattern found in the experimental spectrum. However, the integrated intensity of the symmetric stretch is larger than that of the asymmetric stretch, even though the peak intensity is lower. The harmonic calculation intensity is proportional to the integrated intensity, so although the symmetric stretch relative intensity appears lower than that of the asymmetric stretch in the experimental spectrum, the integrated intensity is likely similar to that of the symmetric stretch in the calculated spectrum. The broad, relatively intense feature in the experimental spectrum is not reproduced in any of the calculated spectra. This broad region is attributed to the hydrogen-bonded proton stretching region and is typically not well represented in harmonic frequency calculations.69,70,72 Broad features such as these are commonly found in the spectra of hydrogen-bonded ionic clusters and arise from strong anharmonic couplings between allowed fundamentals and formally disallowed combination bands and overtones due to large amplitude motions.
2. Structural impacts of alkylamine substitution
Substitution of methylamine, dimethylamine, and trimethylamine for ammonia has been proposed to accelerate NPF9,10,74 and, thus, raises the question of what structural deformations are suffered by an initially ammonia-rich cluster upon substitution. These amine species allow for the modulation of the number of available hydrogen-bond donors, which in turn allows for the structural configuration to be probed by varying cluster compositions. CIVP spectra of alkylamine-substituted (2, 1) clusters were collected and are displayed in Fig. 4, where the alkylaminium-bisulfate clusters are labeled in the following manner: (k, m, n)l = (alkylaminium+)k (NH4+)m(HSO4−)n, where l = methylaminium (MA), dimethylaminium (DMA), or trimethylaminium (TMA). We see that the number of transitions in the free NH stretching region is reduced from two (the aforementioned NH2 symmetric and asymmetric stretches) in the ammonium-containing cluster to one in the methylaminium-containing cluster and zero in the dimethylaminium-containing cluster. This is consistent with these structures maintaining an isomer B-like configuration. The MA- and DMA-substituted clusters both have at least two possible hydrogen-bond donor sites on each of the two cations in each cluster, which allows for the four hydrogen bonds necessary for an isomer B-like configuration to form. In the case of the MA-substituted cluster, this leaves one free NH, responsible for the single stretch in the free NH region. In DMA, there are no free NH groups remaining, and therefore, no free NH stretches. In the TMA-substituted cluster, there is only one possible hydrogen-bond donor site per cation in the cluster, and as such, no free NH stretches are expected for either of the considered structures.
Focusing on the bisulfate fingerprint modes at lower energy, we find that the spectra are essentially conserved, with discernible shifts in the S–OH stretching, SO3 symmetric stretching, S–OH bending, and SO3 asymmetric stretching regions. This suggests that substitution most likely does not perturb the overall symmetry of the (2, 1) cluster structure, with the shifts likely reflective of modulation of the hydrogen-bond strengths with increasing amine basicity. It appears as though the same structural conformation is preserved throughout all of the substituted clusters, even the TMA-substituted cluster. This indicates that, while the two weaker hydrogen bonds enhance cluster stability, they are not an essential component in maintaining the general conformation.
Further evidence that the structure is preserved comes from calculations. Figures S3, S4, and S5 compare the experimental and computed spectra of MA-, DMA-, and TMA-substituted clusters, respectively, for both low-energy isomers. The calculated structures compared in these figures contain the same hydrogen-bonding motifs as the (2, 1) ammonium cluster calculations depicted in Fig. 3. Once again, the lowest energy structural conformations appear to most closely represent the experimental spectra of each of these clusters based on relative peak intensity patterns, most notably in the fingerprint region. For all three of these substituted clusters, the lowest energy structure involves a hydrogen-bonding motif most similar to that of isomer B, further supporting the case that the substituted protonated amines only minimally perturb the structural conformation of the (2, 1) cluster. Tag isomers are apparent in the MA- and DMA-substituted spectra, as was the case in the (2, 1) cluster. Evidence supporting this claim can be observed in Figs. S6 and S7, where once again tag isomers that contain D2 molecules adsorbed on the bisulfate OH induce a red-shift in the free OH stretch frequency.
C. Ad hoc corrections for anharmonic effects
While harmonic calculations provide qualitatively good agreement in terms of pattern reproduction for the observed vibrational spectra of these clusters, the predicted frequencies of the fingerprint bisulfate-related modes are reproducibly shifted from the measured frequencies. Particularly for amine-containing clusters, lower-energy amine modes overlap with, for instance, the SO3 symmetric stretching band in the computed spectra, hampering efforts to reliably determine structures. Similar to methodologies proposed across a wide variety of systems such as organics, biological molecules, and transition metal complexes,75–77 we propose a method in which we derive frequency-dependent scaling factors for predominantly bisulfate-related modes based on the difference between computed and experimental spectra for the (2, 1) cluster.
Frequency-dependent scaling factors were created by assigning vibrational modes of the CIVP spectrum of the (2, 1) cluster to the computed vibrational frequency of the same motion from the lowest energy structure, isomer B. The scaling factors for a given vibrational mode are then the ratio of the frequency of the experimental peak center to the computed frequency of the same motion, as shown in Table I. The same procedure was done for the fully substituted (2, 0, 1) clusters containing MA, DMA, and TMA, and the scaling factors from the four clusters for each mode were averaged. As shown in Fig. 5, we can apply those scaling factors to the appropriate transitions in the (3, 2) computed spectrum as a test of concept. We find significantly improved agreement between predicted and measured frequencies, suggesting that this process appears promising as a way to utilize lower computational cost methods with a smaller sacrifice to accuracy.
|.||Calculated vibrational .||Measured vibrational .||scaling factor .|
|(2, 1) modes .||frequency (cm−1) .||frequency (cm−1) .||(measured/calculated) .|
|SO3 symmetric stretch||1002||1050||1.048|
|SO3 asymmetric stretches||1152||1165||1.012|
|.||Calculated vibrational .||Measured vibrational .||scaling factor .|
|(2, 1) modes .||frequency (cm−1) .||frequency (cm−1) .||(measured/calculated) .|
|SO3 symmetric stretch||1002||1050||1.048|
|SO3 asymmetric stretches||1152||1165||1.012|
We can apply scaling factors derived from only the unsubstituted (2, 1) cluster to the lowest energy calculations for the (2, 0, 1)MA, (2, 0, 1)DMA, and (2, 0, 1)TMA clusters (Figs. S8, S9, and S10, respectively) as a methodology for quickly discerning between bisulfate features native to the structure and emergent alkylamine related features that may be coincidentally appearing in the bisulfate feature region of the spectrum. Amine related motions, and, particularly, alkylamine related motions, tend to agree between the computed frequency of the harmonic spectrum at this level of theory and the experimental frequency, and applying these ad hoc scaling factors to the bisulfate modes can separate amine and bisulfate modes that are predicted to overlap but, experimentally, are separated (or in the case of Fig. S9, modes that are predicted to be separate but experimentally overlapped become overlapped when the scaling factors are applied). For all three alkylamine substituted clusters, we find that the predicted bisulfate motions much more closely match the experimental spectra. We also find that in the region between 800 cm−1 and 1200 cm−1 that we typically assign as belonging only to bisulfate motions, there are several unshifted NH motions that are more easily identified with the bisulfate motions being shifted, particularly in (2, 0, 1)MA, as shown in Fig. S8. This method appears useful as a means for quicker screening of features that emerge as cluster composition changes, and new motifs appear and improve the ability to use pattern recognition to identify matches between experimental and calculated harmonic spectra.
D. Elucidating structural motifs in (4, 3)
Previous work has been done to elucidate the structure of the (4, 3) cluster.35,58 In particular, Froyd and Lovejoy35 proposed and Johnson and Johnson58 further interrogated two likely structures—one that maximizes the total number of hydrogen bonds and the other that maximizes the number of single hydrogen-bond acceptors and represents an open, largely symmetric structure more reminiscent of (3, 2). The computed harmonic vibrational spectra for these structures do not yield compelling matches to the experimental vibrational spectrum. In particular, neither calculation captures a key band at 1315 cm−1. A CIVP spectrum of the (4, 3) cluster upon 15N substitution (Figs. S11 and S12) shows no measurable shift for this band, suggesting that it is related to the bisulfate moieties of the cluster.
We have previously shown that the formation of bisulfate–bisulfate hydrogen bonds in such clusters causes significant disruption of the spectrum in this region.60 We, thus, hypothesize that the missing structural feature in the present spectrum is a bisulfate–bisulfate hydrogen bond, in which the hydroxyl group of one bisulfate acts as a hydrogen-bond donor to the SO group of another bisulfate. The larger size and potentially greater flexibility of the (4, 3) cluster may allow for the individual bisulfate groups to more freely interact with one another, forming bridging bisulfate–bisulfate hydrogen bonds as a means of stabilizing the otherwise large and open cluster structures previously proposed, akin to a form of tertiary structure. To interrogate this hypothesis, we proposed a variety of structures containing bisulfate–bisulfate interactions, as shown in Fig. 6, and computed their vibrational spectra, as shown in Fig. 7. We find that each low-lying structure contains such a bisulfate–bisulfate interaction and that two are notably lower in energy than the previously reported structures. The computed vibrational spectra show a band associated with an out-of-plane (with respect to the cluster surface) bending motion of the OH involved in the bisulfate–bisulfate hydrogen bond that appears at approximately the same frequency as the unassigned band in the experimental spectrum, resolving this outstanding question. Features with substantial H-motion are also found at similar energies in bisulfate/sulfuric acid clusters, though they were not assigned.62 We further assign the comparable feature in the ∼180 nm dry ammonium bisulfate particle spectrum to this motion as well, suggesting that this structural motif is pervasive in larger particles. Given the surface area to volume ratio of such a particle, this feature must at least be found in the core; the signal from any surface-localized bisulfate–bisulfate hydrogen bonds would not be detectable. However, the existence of such a motif on the surface of the cluster studied here suggests that this is a possibility and that such motifs may play a role in the accommodation of incoming molecules during NPF.
Structure L (depicted in Fig. 6), a derivative of an H-like structure that has “folded” to form a single bisulfate–bisulfate hydrogen bond, is the lowest in computed energy and reproduces this previously unassigned band. However, it still does not satisfactorily reproduce other bands of the experimental spectrum, particularly the SO3 stretching region. Structure K, while slightly higher in energy than structure L (though within the error of the calculation), possesses both the key bisulfate–bisulfate mode and a narrow SO3 symmetric stretching mode, suggesting that the bisulfate oxygen environments in this particular structure more closely resemble the true structure of (4, 3). Exact agreement between calculation and experiment may also be hampered by unexplored tag effects. While this leaves open the possibility that the true minimum-energy (4, 3) cluster structure remains to be found, we conclude that the previously unassigned band at 1315 cm−1 represents a bending motion of an OH that acts as a hydrogen-bond donor to an SO group of a neighboring bisulfate and that structures L and K capture the majority of the structural motifs present in the cluster. With this assignment, we have a sufficient set of spectral markers to explain the spectra of larger particles with well-assigned structural motifs.
Following the methodology outlined previously, we can create frequency-dependent scaling factors for the bisulfate modes of the (3, 2) cluster and apply those scaling factors to (4, 3) computed spectra, as shown in Fig. 8. We choose to use (3, 2) as our model rather than (2, 1) because (3, 2) more likely contains binding arrangements similar to the (4, 3), as its larger size allows for more folding-like interactions. We apply these corrections to structure K from Fig. 7. Again, we find that the shifted computed spectra closely match the experimental data.
Using cryogenic ion predissociation vibrational spectroscopy, we measured infrared vibrational spectra for several small cationic clusters relevant to NPF. We were able to differentiate between two previously proposed minimum-energy structures for (2, 1), the smallest cationic cluster. With the aid of computational results, we assigned the true minimum-energy structure to a CS-symmetry structure that is robust upon alkylamine substitution with methylaminium, dimethylaminium, and trimethylaminium. We examined the (4, 3) cluster, the smallest cluster that contains all the spectral features of large, dry particles. While we make no definitive structural assignment, we have identified and assigned a previously unidentified spectral band as an out-of-plane OH bending motion for an OH participating in an intermolecular bisulfate–bisulfate hydrogen bond. This band is the final assignment for all the fingerprint spectral features of the large dry particle, giving us a seemingly complete library mapping structural features to spectral markers. Making note of consistent trends in shifts between the experimental vibrational frequency and the computed vibrational frequency for several modes in the fingerprint region, we proposed ad hoc scaling factors derived from a small database of our structurally well-assigned clusters. While this database of structures is currently small, it can be improved as more structures become well assigned and the methodology shows promise for improving the informational quality of less expensive computational methods, particularly as clusters grow larger and exact structural assignments become more difficult.
See the supplementary material for additional spectra and coordinates for all computed structures.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
The authors acknowledge support from the National Science Foundation of the U.S. under Grant Nos. CHE-1566019 and CHE-1905172.