Infrared spectroscopic studies on the cluster size dependence of charge carrier structure in nitrous oxide cluster anions

The molecular anion of nitrous oxide, N₂O⁻, has been observed by mass spectrometry as early as the 1960s,^1–7 but its properties have been elusive, since it is difficult to generate as an isolated molecular ion. For example, the adiabatic electron affinity (AEA) of N₂O is still not well established. Early collision based experiments^8,9 gave widely varying results for the AEA and did not even agree on its sign. Photoelectron spectroscopy experiments on N₂O⁻ were only able to establish an upper limit of 0.76 eV for the AEA of N₂O.

Nitrous oxide is isoelectronic with carbon dioxide, CO₂. This similarity gives a first clue on the origin of the difficulties of generating bare N₂O⁻, since CO₂ does not have a stable negative ion (it has an AEA of −0.6 eV¹⁰). The Walsh diagram for N₂O, calculated as explained in Section II B, gives some insight into the molecular physics involved (see Figure 1). Inserting an electron into the lowest unoccupied molecular orbital (LUMO) of N₂O yields a negative ion which is stabilized as the molecule bends. The calculated minimum energy configuration of the anion is at ca. 135° (the exact value depending on the theoretical method used), leading to a large geometry change between anion and neutral. This results in a very small Franck-Condon factor for photodetachment from the vibrational ground state of the anion into the vibrational ground state of the neutral molecule, hence the difficulties of photoelectron spectroscopy to provide a good AEA value. Recent high-level ab initio calculations^11,12 predict a negative AEA for N₂O, i.e., they predict that the ground state of the anion lies above that of the neutral. This renders the anion electronically unstable against autodetachment.

Another reason why generating bare N₂O⁻ is difficult is that electron attachment to isolated N₂O molecules only produces products based on dissociative processes, predominantly yielding O⁻.^5,7,13–15 While bare N₂O⁻ has been observed, this ion is likely formed by charge transfer from O⁻ or NO⁻.^3,6 The calculated ground state geometry of N₂O⁻ is very close to a dissociative state leading to the formation of an O⁻ ion and a molecular N₂ fragment.^11,12,16

The instability of N₂O⁻ with respect to both electron loss and dissociation makes experiments on N₂O⁻ very challenging. As a consequence of these difficulties, no experimental data exist on the vibrational frequencies of N₂O⁻. Different from CO₂, matrix isolation work did not yield the vibrational frequencies of N₂O⁻ due to the overwhelming dissociative products of electron attachment to molecules and small clusters.^17–19 

Molecular clusters can support negative ion states even in cases where the molecular constituents do not have stable anions. In these cases, the question about the nature of the negative ion state is not straightforward to answer. In one limit, the electron can be bound in the collective field of the cluster constituents. Dipole-bound or network-bound states in hydrated electron clusters, (H₂O)_n⁻, are important examples for such electron binding motifs.²⁰ In another mode of electron binding, the excess electron is bound in a molecular valence state, but this state involves more than one molecular unit. The carbon dioxide dimer anion, (CO₂)₂⁻, is an example for this type of anion in (CO₂)_n⁻ clusters, at least for some cluster sizes (n = 2–6 and n > 13).^21–23 Finally, although the valence state of a molecular anion may be electronically unstable, it can be stabilized by the cluster environment. Again, carbon dioxide cluster anions, (CO₂)_n⁻, provide an example for this case in the size regime 6 ≤ n ≤ 13.^21–23 

Electron attachment to neutral (N₂O)_N clusters initially produces a transient negative cluster ion, which can dissipate the excess energy by evaporating weakly bound N₂O molecules, as well as through kinetic energy release in dissociative attachment.^7,15,24–31 While the main attachment pathway is dissociative, yielding ions of the form (N₂O)_nO⁻, a small fraction of the cluster anions produced are ions of the form (N₂O)_n⁻, as well as (N₂O)_nNO⁻ (n < N) at low kinetic energies. These ions only occur with specific cluster sizes, as has been demonstrated in several previous experiments on N₂O clusters.^24–29 

The nature of the charge carriers in N₂O based cluster ions has been the subject of earlier work, explored predominantly by using photoelectron spectroscopy.^32–35 Posey and Johnson used different precursor gas mixtures to create different forms of N₂O₂⁻.³² In expansions of neat N₂O and N₂O seeded in Ar, they predominantly found NNO₂⁻ (see Figure 2); in expansions of 5% O₂ in N₂ a van der Waals complex of the form N₂O₂⁻ was formed, and in expansions of NO in Ar, a dimer anion of NO was concluded to be the charge carrier.³² In a series of photoelectron spectroscopy work on N₂O based cluster anions, Sanov and co-workers studied (N₂O)_nO⁻ and (N₂O)_nNO⁻ clusters.^33–35 In the context of the present work, their most important finding is a change in the character of the charge carrier in (N₂O)_nO⁻ clusters from N₂O₂⁻ to O⁻ between cluster size n = 3 and 4.³⁴ This shift in charge carrier structure can be traced to the subtle balance between electronic stability and solvation energy. For example, in the simple case of a spherical ion, the free energy of solvation ΔG_solv is inversely proportional to the ion radius, R_i. In general, solvation energy favors smaller, more compact charge carriers, which has also been observed in the case of CO₂ based clusters.^21–23,36 The N₂O₂⁻ ion observed as a charge carrier for small clusters has three possible isomers (see Figure 2), and Pichugin et al. found that the isomer NNO₂⁻ was predominantly formed.³⁴ In contrast to (N₂O)_nO⁻ clusters, no size dependent change in structure was found in (N₂O)_nNO⁻ cluster ions in photoelectron spectroscopy experiments.^33,35

Infrared photodissociation spectroscopy has been particularly fruitful for characterizing the structural properties of cluster ions. For (N₂O)_n⁻ ions, the charge carrier has not been identified at all up to now, and there has not been any infrared spectroscopy work on (N₂O)_nO⁻, despite the interesting size-dependence of the photoelectron spectra of these species. In the present work, we use infrared photodissociation spectroscopy to study the nature of the charge carrier in (N₂O)_nO⁻ and (N₂O)_n⁻ cluster ions.

We generated (N₂O)_n⁻ and (N₂O)_nO⁻ ions by combining an electron impact plasma with supersonic expansion of neat N₂O in a pulsed valve. While (N₂O)_nO⁻ ions were formed in large abundance, we note that we observed (N₂O)_n⁻ clusters down to n = 5, but we only had sufficient ion abundance for infrared photodissociation spectroscopy in the size region 7 ≤ n ≤ 15. This is consistent with the size distributions observed by others in earlier work.^27–29 A typical mass spectrum is shown in Figure 3. Using entrainment of N₂O into a supersonic expansion of Ar, we were also able to generate Ar-tagged (N₂O)_nO⁻ ions for small cluster sizes (up to n = 5) in sufficient quantities to perform Ar predissociation spectroscopy of (N₂O)_nO⁻ ⋅ Ar₂ clusters.

The ions were injected into a photodissociation spectrometer based on an idea developed by Lineberger and co-workers³⁷ and described in detail in an earlier work.^38,39 Briefly, the ions were accelerated to ca. 3.5 keV kinetic energy. At the first space focus of a Wiley-McLaren time-of-flight mass spectrometer, we mass selected the ions under study using a pulsed mass gate.⁴⁰ Shortly behind the mass gate, we irradiated the ions with radiation from a tunable optical parametric converter system capable of producing photons in the mid- to far-infrared spectral region (600–4500 cm⁻¹, bandwidth 2 cm⁻¹). Irradiation occurred in a multipass cell based on a design by Liu and co-workers.⁴¹ If a cluster absorbs a photon with sufficient energy, it can evaporate one or more weakly bound constituent molecules. To distinguish fragment ions from the undissociated parent ions, the ion beam entered a two-stage reflectron, which was used as a secondary mass spectrometer. The ions were detected using a dual microchannel plate detector. Sixteen laser shots were averaged per data point, and the photofragment signal was corrected for laser fluence. Several spectra were taken on different days to ensure reproducibility and were averaged to improve the signal-to-noise ratio. The spectra were calibrated using a fiber-optic spectrometer suite which in turn was calibrated to the emission lines of Ar and Fe discharge lamps. We conservatively estimate the wavenumber uncertainty to be 2 cm⁻¹.

In the present work, we measured infrared spectra of mass-selected (N₂O)_nO⁻ ⋅ Ar₂ (n = 1–5), (N₂O)_nO⁻ (n = 5–12), and (N₂O)_n⁻ ions (n = 7–15) in the spectral region 800–2150 cm⁻¹. This region was chosen because we expect the fundamental transitions of N–N and N–O vibrations of the clusters under study here. Infrared photodissociation spectra were measured by monitoring the fragment ion signal resulting from the loss of the Ar tags (where applicable) or of a single N₂O molecule from the parent cluster ion, corrected for laser fluence. We note that—assuming that the clusters are formed as an evaporative ensemble⁴²—the internal energy of the parent clusters without Ar tagging is expected to be of the order of the binding energy of an N₂O molecule in the cluster, which can be estimated from calculations (see below) to be around 1600 cm⁻¹ for small clusters (n ≤ 5) and around 1000 cm⁻¹ or lower in larger clusters (n ≥ 7). In the untagged ions, we only observed the evaporation of one N₂O molecule upon photon absorption, in line with this estimate. Based on previous experiments with other clusters that have similar binding energies,^36,43–47 we expect that infrared signatures below 1000 cm⁻¹ will be strongly suppressed. In the case of Ar-tagged species (N₂O)_nO⁻ ⋅ Ar₂, we monitored the loss of both Ar atoms.

The Walsh diagram of N₂O (Figure 1) was generated using the RI-MP2 method (second-order Møller–Plesset perturbation theory applying the resolution-of-identity approximation for evaluation of two electron integrals^48,49) with def2-TZVPP basis sets⁵⁰ for all atoms. Structures and vibrational spectra of N₂O based anionic species were calculated based on density functional theory using the B3-LYP functional^51,52 with dispersion correction,⁵³ again using def2-TZVPP basis sets for all atoms. All computational work was performed using the turbomole suite of programs.⁵⁴ Vibrational spectra were calculated with the aoforce program.^55,56 In general, no symmetry restrictions were used, except for the Walsh diagram (Figure 1) and for establishing that the NNO₂⁻ ion is of C_2v symmetry. Charge distributions were calculated using natural population analysis.⁵⁷ 

Clusters of the form (N₂O)_nO⁻ were the most abundant in the present experiments (see Figure 3). Figure 4 shows the infrared spectra of (N₂O)_nO⁻ ions. For the smaller ions (n ≤ 5), these spectra were obtained by monitoring the loss of both Ar tags from (N₂O)_nO⁻ ⋅ Ar₂, while for the larger ions, spectra were acquired by monitoring loss of a single N₂O molecule from (N₂O)_nO⁻. We note that we acquired spectra for n = 5 with and without the presence of Ar atoms and found no differences in the peak positions or relative intensities within experimental uncertainty.

The spectrum for n = 1 shows two intense peaks at 1197 cm⁻¹ and 1352 cm⁻¹. If the charge carrier were O⁻ solvated by a single N₂O molecule, we would expect to find the signature of the N–O stretching mode of the solvent molecule around 1285 cm⁻¹.⁵⁸ The absence of this signature suggests that the charge carrier is of the form N₂O₂⁻, consistent with the photoelectron spectroscopy results of Sanov and co-workers.³⁴ Comparison of the two observed peaks with the calculated spectra of the three isomers of N₂O₂⁻ (see Figure 5) allows unambiguous identification of the charge carrier as the NNO₂⁻ isomer. We assign the lower energy peak to the asymmetric NO₂ stretching mode, while the high energy feature is due to the N–N stretching mode. Note that the sharp peaks and the absence of weak satellites imply that no other isomers are significantly populated. While this is consistent with the observations by Posey and Johnson,³² it is surprising to some extent, since the NNO₂⁻ isomer is higher in energy than the cis and trans isomers, and signatures of ONNO⁻ ions have been found in previous experiments by Sanov and co-workers. We assume that the structure is due to the charge distribution in neutral N₂O. Our calculations yield a natural charge of +0.513 e on the central N atom, while the terminal N atom is slightly negative (−0.071 e), as is the O atom (−0.442 e). In line with the argument raised by Posey and Johnson,³² an O⁻ ion is created first by dissociative attachment to an N₂O moiety in an (N₂O)_N cluster or to a free N₂O molecule in the expansion. The nascent O⁻ anion then reacts with N₂O in the cluster to form NNO₂⁻.

For n > 1, we observe a peak in the general region where we expect the solvent signature to appear, and this peak persists for all cluster sizes under study. For n = 2, this peak is at 1292 cm⁻¹, but it shifts slightly to lower wavenumbers as cluster size increases and converges to (1282 ± 3) cm⁻¹ for the largest clusters studied here. We assign this peak to the N–O stretching mode of solvent N₂O molecules. For some of the small clusters (in particular, n = 3), we observe that the solvent signature has some substructure, which we attribute to small differences in solvent position and orientation to the charge carrier.

The signature of the solvent peak grows in intensity relative to the NNO₂⁻ features. This is to be expected, since the number of solvent molecules grows, while there is (at most) a single NNO₂⁻ ion in the cluster. Sanov and co-workers have observed that the charge carrier changes from NNO₂⁻ to O⁻ at cluster size n = 4. Since no other signatures appear as cluster size changes, any core ion switch will result in the formation of an atomic ion, or one that has no (or too weak) vibrational signatures. A possible example for the latter would be O₂⁻, whose infrared absorption cross section in the cluster would presumably be very small, as the cluster environment would only minimally lift the symmetry forbidden character of vibrational excitation by electric dipole transitions in free O₂⁻. The O₂⁻ charge carrier should not be formed significantly in our ion source, since it is not generated in significant amounts using pure or seeded expansions of N₂O.³² Consequently, if a core ion switch occurs, it will most likely result in the formation of O⁻ as a charge carrier. In this case, the core ion switch would be marked by the disappearance of the NNO₂⁻ signatures. In our experiment, we see that this change in charge carrier is not quite complete, since we observe traces of the NNO₂⁻ signatures up to the largest clusters under study (see Figure 4). However, if a large fraction of the core ions would be based on O⁻, we would find a disproportional loss of intensity in the NNO₂⁻ signature compared to the solvent signature as cluster size grows. We can analyze the integrated peak areas with reasonable signal-to-noise ratios for cluster sizes up to n = 7. If NNO₂⁻ were to remain the only charge carrier for all cluster sizes, the ratio of the NNO₂⁻ features to the solvent feature would change with increasing cluster size according to

since one N₂O moiety is part of the core ion in the notation (N₂O)_nO⁻. This relationship assumes that the infrared absorption cross section per monomer for either feature does not change with cluster size. Our infrared spectra suggest that none of the ONNO⁻ isomers are significantly populated in our ion beam. Based on the results of Sanov and co-workers,³⁴ we further assume that NNO₂⁻ is the only charge carrier at n = 2, allowing us to quantitatively compare the prediction from this model to the experimentally observed ratios (see Figure 6). We observe that the fraction of clusters with NNO₂⁻ core drops to ca. 30% going from n = 2 to n = 3, staying roughly at this level before dropping below 15% at cluster sizes n ≥ 6. Sanov and co-workers observed the core ion change taking place rather abruptly between n = 3 and 4.³⁴ We assume that the differences between the experimental conditions in the different ion sources are at the heart of the minor discrepancies between our results and those of Sanov and co-workers, but these small differences do not detract from the main conclusions for (N₂O)_nO⁻ clusters: (i) we can unambiguously observe the NNO₂⁻ isomer of $N2O2−$ as the dominant charge carrier in small (N₂O)_nO⁻ clusters and (ii) we also observe a clear change of the nature of the dominant core ion, presumably to O⁻. We note that these conclusions apply to (N₂O)_nO⁻ clusters generated by electron injection into supersonic expansions of N₂O, and other precursor gas mixtures can have other structural motifs of the charge carrier.^32–35 

Fig. 7 shows the infrared photodissociation action spectra of (N₂O)_n⁻ cluster ions (n = 7–15) in the region 890–2150 cm⁻¹ (800–2150 cm⁻¹ in the case of n = 10), obtained by monitoring the loss of a single N₂O molecule from the cluster. We note that we did not observe the formation of (N₂O)_mO⁻ or (N₂O)_mNO⁻ cluster ions (m < n) which would indicate vibrationally induced dissociation of the charge carrier. The spectra are dominated by a peak at 1282 cm⁻¹, and the peak position of this feature does not vary within the uncertainty of the experiment. It nearly coincides with the NO stretching vibration of free, neutral N₂O (see Table I), and we therefore ascribe it to N₂O molecules playing the role of solvent molecules, solvating the charge carrier of the cluster ion. The only other signatures are around 1600 cm⁻¹. Neutral N₂O molecules do not have vibrational modes in this region, so we assume that these signatures are due to the charge carrying species. At the smallest cluster size (n = 7) probed in the present work, we observe a signature at 1643 cm⁻¹. At n = 8, there are two weak features, one at 1665 cm⁻¹ and a broad peak at ca. 1585 cm⁻¹. For n ≥ 9, only a single feature at slightly varying positions (1592–1598 cm⁻¹) remains in this region.

The first question arising here is which charge carrier is present in the clusters. For a delocalized excess electron, one would expect that the excess charge is either delocalized over the whole cluster or bound to the net dipole moment of the cluster in a dipole-bound anionic state. Neither scenario would lead to a clearly distinguishable set of solvent vs. charge carrier signatures. A charge carrier where the charge is shared by several N₂O molecules forming a dimer, trimer, or other subcluster would lead to multiple lines corresponding to combinations of “local” N–N and N–O oscillators. The observation of a single feature characteristic for the charge carrier for n ≥ 9 suggests that the charge carrier is a single N₂O⁻ ion stabilized by solvation in the cluster environment. The observed signature at (1595 ± 3) cm⁻¹ can be assigned to the N–N stretching fundamental of a solvated N₂O⁻ ion by comparison with DFT and ab initio calculations (see Table I). The ratio of experimental to calculated transition wavenumber for the N–N stretching mode of neutral N₂O in the present work is 0.949. Using this factor to scale the calculated value for the N–N stretching mode of the N₂O⁻ ion yields 1595 cm⁻¹, which is exactly the experimentally measured value. While the quality of agreement between the scaled computational and experimental values is certainly fortuitous, there is no doubt about the validity of the assignment.

The variation of the N–N stretching signature with cluster size is an interesting observation that warrants discussion. At small cluster sizes, solvent N₂O molecules are likely to form a subcluster, since they can interact favorably through their dipole and quadrupole moments. This subcluster will preferentially solvate the charge carrier on one side, and it will polarize the charge carrier so that even more negative charge will be localized on the solvated side, similar to the case of some CO₂ containing clusters.^23,36 As cluster size grows, the charge carrier will be solvated more symmetrically, leading to a redistribution of charge. This redistribution will in turn result in a change in the vibrational frequencies of the charge carrier. The excess electron in N₂O⁻ resides in an antibonding orbital (see Figure 1) that weakens both the N–O bond and the N–N bond, which is reflected in the calculated frequencies (see Table I). Since we assign the signature at 1595 cm⁻¹ to the N–N stretching mode, and this signature is shifted to lower wavenumbers as the cluster size increases from n = 7 to n = 9, we assume that solvation will preferentially occur closer to the O atom of N₂O⁻ for small clusters, polarizing the excess charge more into the N–O bond. Upon increasing solvation, redistribution of the excess charge will progressively weaken the N–N bond as the solvation shell grows onto the other side of the charge carrier, shifting the N–N stretching frequency to the red, as observed. The size region where this change occurs is reminiscent of IBr⁻ ⋅ (CO₂)_n cluster ions,⁶¹ where the initial CO₂ solvent subcluster grows around the Br atom of the dihalide ion with a half-shell forming at n ≈ 8. Unfortunately, there is a plethora of possible structures at the cluster sizes experimentally studied in our experiment, and attempts to construct specific solvation geometries, e.g., n = 7, were unsuccessful. However, we were able to construct symmetric and asymmetric solvation environments for smaller species. At n = 3 and 4, an N₂O subcluster solvating the O atom of N₂O⁻ is calculated to be 50–60 meV more favorable than a more symmetric arrangement, qualitatively corroborating the above argument. The vibrational analysis is less clear, as the N–N stretching mode for asymmetric solvation on the O atom is calculated to be only ≤10 cm⁻¹ higher than for symmetric solvation. While the trend is consistent with the idea outlined above that the red shift of the N–N stretching mode between n = 7 and n = 9 is due to an increasingly symmetric solvation environment, the magnitude of the shift is much smaller than experimentally observed. Nonetheless, we tentatively attribute the change in the N–N stretching frequency to a change in the solvation environment.

In principle, one would expect two vibrational signatures for the N₂O⁻ ion in the wavenumber region addressed by the present work (see Table I), one due to the N–N stretch as observed and one due to the N–O stretch. However, the N–O stretching fundamental is expected to be below 1000 cm⁻¹, a region that our present experiment is rather insensitive to, since the binding energy of a single N₂O molecule to the cluster is sufficiently high to suppress N₂O evaporation (≈1000 cm⁻¹ for the cluster sizes under study). For the most abundant ion in the (N₂O)_n⁻ series, n = 10, we extended the wavenumber range down to 800 cm⁻¹ in search of an experimental signature of the N–O stretching mode. We were able to observe a very weak peak at (894 ± 5) cm⁻¹, which we assign to this vibrational mode. The calculated intensities of the N–N and N–O stretching modes in N₂O⁻ are comparable, but the suppression of N₂O evaporation at these low photon energies obscures this feature almost completely. Using the same strategy for anharmonic correction as for the N–N stretching mode, we would expect the N–O stretching signature to appear at 960 cm⁻¹ (with a scaling factor of 0.967). Obviously, this simple procedure underestimates the anharmonicity of the N–O stretching mode induced by incorporating an excess electron into the molecule. In light of the instability of bare N₂O against dissociative attachment forming O⁻, this is not unexpected.

We have shown infrared photodissociation spectra of (N₂O)_nO⁻ and (N₂O)_n⁻ cluster anions generated by electron injection into a supersonic expansion of N₂O. In clusters of the form (N₂O)_nO⁻, we observe that the NNO₂⁻ isomer of N₂O₂⁻ is the only significantly populated core ion for n = 1. With increasing cluster size, the core ion changes to a species that is not infrared active, presumably to O⁻. In clusters of the form (N₂O)_n⁻, the excess negative charge is localized on a single N₂O molecule, giving rise to a solvated N₂O⁻ ion. We report for the first time an experimental value for the N–N stretching vibration of this elusive species at (1595 ± 3) cm⁻¹ and for the N–O stretching vibration at (894 ± 5) cm⁻¹. Asymmetric solvation of the N₂O⁻ core ion leads to an abrupt red shift of the N–N stretching mode by ca. 20 cm⁻¹ at n ≈ 8, suggesting the formation of a half-shell at this cluster size.

We gratefully acknowledge funding from the National Science Foundation (NSF) through the NSF AMO Physics Frontier Center at JILA (No. PHY-1125844).