A Quantum Chemical View on the Growth Mechanisms of Odd-Sized

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

A Quantum Chemical View on the Growth Mechanisms of Odd-Sized Nitrogen Cluster Anions Ersin Yurtsever, and Florent Calvo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08822 • Publication Date (Web): 07 Dec 2018 Downloaded from http://pubs.acs.org on December 16, 2018

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The Journal of Physical Chemistry

A Quantum Chemical View on the Growth Mechanisms of Odd-Sized Nitrogen Cluster Anions E. Yurtsever1* and F. Calvo2 1 Chemistry Department, Koç University, 34450 Istanbul, Turkey 2 Univ. Grenoble Alpes, CNRS, LiPhy, 38000 Grenoble, France

Abstract The stable structures of odd-numbered anionic nitrogen clusters, N2n+3-, have been theoretically investigated in the size range n=1–9 using a variety of quantum chemistry methods that include perturbation theory, coupled cluster, and density-functional theory with different exchange correlation functionals. We generally find that the clusters are composed of an azide chromophore N3surrounded by essentially neutral nitrogen molecules. The growth initially proceeds by placing the neutral molecules parallel to the azide anion, completing a first shell at N13-, above which the extra molecules arrange on the side but with a significantly lesser binding energy. Comparison with the cyclic N5- anionic core shows that the latter is unfavorable, the spectral signatures of both N5- and N2N3being provided in both the infrared and ultraviolet ranges. The trend of these clusters to be highly stable as (N2)nN3- agrees with recent mass spectrometry experiments under the cryogenic environment of helium droplets. The issues associated with the successful development of a nonreactive force field for such clusters are also highlighted.

Graphical abstract

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

I.

INTRODUCTION

There is currently a growing interest in polynitrogen molecules as a potential ingredient for highenergy density materials. The triple bond of N2 has a dissociation energy of nearly 10 eV, hence it is very difficult to break and convert into materials consisting of singly bonded nitrogen atoms. This process can release large amounts of energy as the bond energy of a single N-N bond is around 1.7 eV only. Therefore, it could be valuable for green energy sources or propellants. The synthesis of polynitrogen under ambient conditions is known to be very challenging. The intermediate use of HeN compounds to form polymeric nitrogen was recently suggested from ab initio calculations.1 In cubic gauche phase, polynitrogen could be synthesized in small amounts,2 later also by chemical vapor decomposition.3 An allotrope in the form of N6 molecules was shown to be stable4 and it was proposed to confine such molecules inside BN nanotubes.5 A comprehensive review of polymeric nitrogen compounds including their ionic forms has been given by Samartzis and Wodke.6 Cationic nitrogen clusters have been produced and observed in various experiments,7-9 and their structure and stability have been discussed extensively based on computational investigations.10-13 In comparison, anionic clusters have received much scarcer attention. One of the controversial anions is N5-, whose presence was reported in several communications.14-16 The structure of this cyclic ion was predicted by various quantum chemical methodologies.10,17-19 Much larger anionic clusters with hundreds of nitrogen atoms could be observed in a supersonic jet,20 while smaller clusters were detected upon bombardment of N2 with Ar13+. 21 A detailed study of the formation of anionic nitrogen clusters was recently reported.22 In this experiment, helium nanodroplets were doped with nitrogen and Nm- anions could be formed by electron attachment. The abundance of Nm- as a function of m, the number of nitrogen atoms, shows two main features. First, anions with even m are found to be much less abundant than anions with odd m. In addition, certain sizes such as m=4, 11, or 23 exhibit higher abundances and can be considered as magic numbers. In this work we propose a growth model for small anionic nitrogen clusters with an odd number of atoms. For such clusters Weinberger et al.22 suggested that anionic clusters are formed from an azide ion N3- as the chromophore and N2 molecules surrounding it, in a picture rather similar to cationic rare gas clusters.23 The azide anion is highly stable with a linear structure and is isoelectronic with CO2 and N2O, making it indeed plausible that clusters with odd numbers of nitrogen atoms have (N2)nN3- type structures. Our exploration of cluster geometries is essentially based on chemical intuition guided by information about the interaction between azide and nitrogen that we carefully mapped from quantum chemical calculations. Our results support the picture of odd-sized clusters being indeed of the (N2)nN3- form, although the peculiar arrangements we found happen to represent a challenge for modeling with a force field, which we interpret as originating from the significant magnitude of intermolecular charge transfer, the electron on the azide ion spilling away onto the surrounding molecules. The article is organized as follows. In section 2, we describe the interaction between azide and a single nitrogen molecule. In section 3, we present the structures and energetics for (N2)nN3- clusters up to n=9 and use these results to explain the ion abundances given by Weinberger et al.22 Vibrational and optical spectra of selected clusters are also provided in order to provide support for possible experimental characterization. Finally, we give some concluding remarks in section 4.

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2. POTENTIAL ENERGY SURFACE OF N3-+N2 We calculate a restricted potential energy surface (RPES) between N3- and N2 using highly accurate quantum mechanical methods. For obtaining the RPES, N-N bond lengths were fixed and chosen as 1.096 Å for N2 and 1.183 Å for N3-, as predicted from the B3LYP/6-311++G** method. The complete survey of the energy surface between two nonvibrating species requires 4 coordinates. Keeping the center of mass of N3- at the origin of the reference frame, 2 coordinates are needed to place the center of mass of N2 and two angular coordinates to specify the orientation of N2. Here 20 different angular orientations and around 80 distances between the centers of mass were chosen. At each point, the interaction energy is calculated at coupled cluster level with single, double and perturbative triple excitations [CCSD(T)]24 using the aug-cc-pVTZ basis set. All energies are corrected for basis set superposition error using the standard counterpoise method of Boys and Bernardi. The relative position of the center of mass of N2 is denoted by polar coordinates (R,Θ), Θ=0 corresponding to N2N3- being collinear while Θ=90o when N2 and N3- are parallel. For each set of (R,Θ) values, three calculations were performed with N2 being aligned along the x, y, and z directions (N3- is aligned along x with y=z=0 while the two centers of mass are in the z=0 plane). For visualization purposes, the interaction energy was averaged over the three orientations of nitrogen along x, y, or z axes.

Fig. 1. Interaction potential between rigid N3- and N2 as a function of the intermolecular distance between centers of mass and for several relative orientations of N2 relative to the azide axis. In Fig. 1 we show the variations of the averaged interaction between the azide and nitrogen molecules with the distance between their centers of mass. Even with this averaging, it is clear that the interaction is the strongest for Θ=90o, when the two molecules are parallel. For this configuration the interactions at three orientations of N2 also show some variations. Obviously, the case where N2 is approaching N3- perpendicularly but in the same plane shows a weak interaction whereas the other two orientations yield very similar energies. In Fig. 2 we show the effects of different relative orientations along x, y, or z on the resulting interaction at fixed Θ. The relatively large difference of 80 meV for different configurations shows that orientational effects are important and that a coarse-grained, united atom description as used e.g. for hydrogen clusters25 may not be suitable here. 3 ACS Paragon Plus Environment


Fig. 2. Interaction energy between N3- and N2 at Θ=90o and for several relative orientations of the molecular axes. The parallel and crossed orientations correspond to structures depicted in Fig. 3(a) and (b), respectively, while the T shape orientation is similar to (a) but with N2 rotated by 90o but with all nitrogen atoms in the same plane.

Based on the above results, the most stable configuration for N5- appears to be made of the azide anion and nitrogen molecule lying alongside and parallel to each other, as depicted in Fig. 3(a).

Fig. 3. Possible structures of N5-. (a-c) N2N3- with different relative positions and orientations: (a) parallel; (b) crossed; (c) T-shape; (d) cyclic conformer of N5-.


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3. STABLE STRUCTURES 3.1. A tentative force field for structural exploration A complete global optimization of anionic nitrogen clusters using full quantum mechanical methods is a daunting computational task without assuming some particular bonding patterns. In a first attempt and to alleviate most of the numerical burden, we began our structural exploration of the energy landscapes of N2n+3- clusters (n>0) by constructing an efficient force field based on an existing model for pure nitrogen clusters26 in which the n nitrogen molecules are rigid and carry 3 partial charges, one on each atom with magnitude qN=0.473e and one at the center equal to -2qN. Besides Coulomb forces between the partial charges, nitrogen atoms from different molecules interact through a Buckingham potential detailed in Ref. 26. This potential was extended to account for the azide anion, also treated as rigid and whose geometry was taken from the CCSD(T) calculations reported in the previous section. Partial charges on the three nitrogen atoms were evaluated from an additional DFT calculation using the M06-2x/aug-cc-pVDZ method and the RESP procedure to eventually yield values of -0.947e on the outer atoms and 0.894e on the central atom. For simplicity we first used the same Buckingham pairwise potential between the nitrogen atoms of azide and nitrogen molecules. To describe the interaction between azide and nitrogen more accurately, we also considered adding a polarization contribution by placing an isotropic polarization site at the center of all nitrogen molecules with polarizability α=1.710 Å3 as borrowed from experimental data.27 The polarization energy was then evaluated by solving the induced dipoles self consistently. Unfortunately, the nonpolarizable and polarizable potentials predict most stable geometries for N2N3that both disagree qualitatively with the results of the quantum chemical exploration. In the polarizable version, the electric field is much stronger near the extremities of the azide ion, and the nitrogen molecules place themselves along the azide axis but rotate into a T shape to maximize polarization energy [Fig. 3(c)]. In the nonpolarizable version, the nitrogen molecule is correctly placed perpendicularly to the azide axis, although the two molecules are not parallel to each other but again perpendicular in a crossed fashion [see Fig. 3(b)]. The nonpolarizable version of the potential, in which the electrostatic interaction between azide and nitrogen is mainly of the charge-quadrupole type, thus appears somewhat more realistic but still insufficiently accurate. The form chosen for the potential has a very limited number of free parameters, and we tried to systematically refine those associated with the Buckingham interaction between azide and nitrogen, without significant success. In order to obtain the global minimum with N2 and N3- that are parallel to each other, higher order multipolar effects or intermolecular charge transfer should thus be probably considered. The likely importance of charge transfer will be discussed later based on quantum chemical analysis of the proposed structures.

3.2 Results from electronic structure calculations Considering the difficulties arising from using nonreactive potentials, the candidate structures for larger clusters were produced by chemical intuition and previously proposed geometries,10-13 5 ACS Paragon Plus Environment


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optimizing the structures using both DFT and relatively inexpensive MP2 calculations, at least for geometry optimizations. In this manner, we could also benchmark the reliability of various quantum chemical approaches. For DFT calculations we have tested three exchange functionals that are relevant for long-range weak interactions. These are B3LYP with empirical Grimme D3 dispersion correction,28 B97-D29 and M06-2X.30 On the ab initio side, geometries were optimized at the MP2 level of theory and the final energies were evaluated from single point calculations with spin-componentscaled MP2 (SCS-MP2)31 and CCSD(T) when possible. DFT calculations were carried out with Gaussian0932 and post-HF calculations were obtained from Molpro33 packages. One important test of this quantum chemical arsenal is the controversial N5-. This ion has been observed in solution15,16 and it has a pentagonal cyclic structure represented in Fig. 3(d). In an earlier calculation,10 it was reported that there was only a single minimum energy configuration having this cyclic conformation. The authors also reported that optimizations often produced N3- and N2 fragments, although it is unclear whether separate fragments were found or a weakly bound cluster recognized as unstable. For comparison with N2N3-, the cyclic structure was also optimized. All the DFT and ab initio methods find the cyclic (N5-) and parallel (N2N3-) structures as true minima with no negative Hessian eigenvalues, and no further minima could be identified from our search. In particular, the two geometries predicted by the polarizable and nonpolarizable versions of the potential are both much higher in energy and correspond to higher order stationary points. All our calculations concur to show that the parallel form in which a N3- chromophore is present is significantly more stable. The results are summarized in Table 1.

Table 1. Relative energies (in meV) for various isomers of N5-, as labelled in Fig. 3 and for various levels of theory. (a) (C2V)

(b) (C2V)

( c) (C2V)

(d) (D5h)

aug-cc-pVDZ

0

+46

+73

+953

aug-cc-pVTZ

0

+36

+69

+929

aug-cc-pVDZ

0

+14

+29

+569

aug-cc-pVTZ

0

+7

+26

+617

MP2

CCSD(T)

Including the zero-point-correction, the parallel structure is even more stable compared to the cyclic one by an additional 135 meV. These two structures are actually connected via a transition state which is still in the form of pentagon without the D5h symmetry and lies 1.1 eV above the cyclic structure. In all cases, the isomers based on the azide+nitrogen motif N2N3- are all more stable than the cyclic conformer N5-.


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To assist with the possible experimental assignment of N5-, we have calculated the absorption spectra of its parallel and cyclic isomers in both the infrared and ultraviolet ranges and using the M06-2X/augcc-pVDZ method. Owing to its higher symmetry, the cyclic isomer has fewer active modes in each of these spectral ranges. The IR spectra were obtained in the harmonic approximation, scaling all frequencies by 0.955 which is the appropriate factor for this correlation functional. 34 They are shown in Fig. 4(a) and exhibit strong differences, with highly active vibrational modes above 2000 cm-1 that are similar to those in the bare azide anion whose spectrum is superimposed on the same figure, while the highest frequency mode of the cyclic isomer is below 1500 cm-1 and is only marginally active. The electronic spectra in the UV range, determined using the same method, are shown in Fig. 4(b). The spectra of the two conformers of N5- are again very different, the cyclic isomer showing bands near 7.5 and 8.5 eV while the parallel isomer displays a series of active modes all below 7 eV, notably with a broader band near 4–6 eV. The UV spectrum for the azide ion also lies below 6 eV, with two degenerate excitations near 4.6 eV. The greater similarity with the spectrum of the parallel conformer indicates that the nearby nitrogen molecule has a minor role, whereas all atoms contribute collectively in the excited bands of the cyclic conformer. This is confirmed by looking at the electronic density associated with the HOMO and LUMO for the two conformations, which differ qualitatively (results not shown).

Fig. 4. Spectroscopic properties of N5- in the parallel (N2N3-) and cyclic configurations, as obtained from static quantum chemical calculations. (a) Harmonic infrared spectra; (b) Optical spectra in the UV range. The static spectra shown as bars are convoluted by Lorentzians with widths of 5 cm-1 and 50 meV in the IR and UV ranges, respectively. A scaling factor of 0.955 was used for the IR spectra.

Returning to structural features, the most stable parallel conformer found for N5- suggests a growth scheme for larger clusters N2n+3- in which additional nitrogen molecules remain parallel to the azide chromophore and surround it progressively. For N7- we have thus considered cases where two nitrogen molecules parallel to each other and located symmetrically with respect to the azide chromophore [Fig. 5(a)]; inspired by the predicted geometry for the nonpolarizable potential with perpendicular nitrogen molecules in a centrally symmetric arrangement around the azide [Fig. 5(b)], and finally a nonplanar structure where two nitrogen molecules are parallel [Fig. 5(c)].



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Fig. 5. Five possible geometries for N7-. (a-c) Azide anion with two nitrogen molecules; (d) Nitrogen interacting with N5- chromophore; (e) N7- chain.

Among these three possibilities, structure (b) with D2h symmetry has 3 or 4 negative eigenvalues depending on the method used. However, structures (a) and (c) are true minima with (c) of C2v symmetry being always lowest in energy, although the energy difference between these structures is in the order of 30–40 meV only. In a previous study of N7- structures,13 it was found that the global minimum was in the form of a pentagonal N5- cycle with N2 lying above it [Fig. 5(d)]. Finally, structure of the [N3-N-N3]- type as suggested by Li and Zhao12 [Fig.5(e)] was tested and found to lie 6 eV higher than that of Fig.5(c). The relative energies of these structures are in Table 2. The C2v structure as in Fig. 5(c) corresponds to the global minimum. None of the afore mentioned structures from the earlier literature appears competitive with any of those reported in Fig. 5. Table 2. Relative energies of five isomers of N7-, as labelled in Fig. 5. Energies are in meV. Isomer

MP2/aug-cc-pVDZ

MP2/aug-cc-pVTZ

(a) D2h

40

32

(b) D2h

117

91

(c) C2v

0

0

(d) Cs

1001

981

(e) C2v

2086

2278

These calculations confirm the idea that odd-sized anionic nitrogen clusters are more stable as an azide chromophore surrounded by nitrogen molecules, as experimentally suggested by Weinberger et al.22 As the size of the cluster increases, geometry optimization becomes very difficult due to the very weak interaction between molecules and the computational cost associated with additional electrons. Many local optimizations typically converge to higher order stationary points. In order to come up with an economically feasible optimization scheme, we used M06-2x with aug-cc-pVDZ basis and started with a large number of initial structures inspired from the growth scheme 8 ACS Paragon Plus Environment

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identified at previous sizes. Once a minimum was found, it was tested with dispersion corrected B3LYP-D3 and B97-D functionals and then optimized again with MP2 using now the aug-cc-pVDZ basis set. For small systems CCSD(T) energies with aug-cc-pVTZ basis set were evaluated as well. A summary of these benchmark calculations for the most stable structure of N7- with the three parallel molecules, [Fig 5(c)] is given in Table 3. The binding energies are calculated as the energy to separate cluster into an azide anion and a hollow cluster of nitrogen molecules. These values are corrected for the basis set superposition error and they include N2-N2 interactions. This definition decribes the stability of clusters nicely as N2-N2 interactions are much weaker compared to azide anion –nitrogen interaction. Table 3. Binding energy between N3- and (N2)2 in the lowest energy parallel configuration shown in Fig. 5(c). Energies are given in meV and corrected for basis-set superposition error. Basis set for Geometry optimization aug-cc-pVDZ aug-cc-pVDZ aug-cc-pVTZ

Basis set for Single Point Energy aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVTZ

MP2

SCS-MP2 -316 -365 -344

-206 -248 -235

CCSD(T) -202 -249 -242

For noncovalent interactions, it has been shown previously35 that a proper scaling of the parallel- and anti-parallel spin components produces results comparable to those of more expensive CCSD(T) quality. Here we also notice that the differences between SCS-MP2 and CCSD(T) results are very small and that the optimized geometries with the small basis set of aug-cc-pVDZ are sufficiently good. Hence we proceed by using SCS-MP2 single energies for comparing different structural arrangements in larger clusters. Using the arguments for constructing N7-, we propose for N9- a structure in which 3 nitrogen molecules are wrapped around the azide chromophore in a cylindrical fashion. Here we considered symmetric structures with the molecules being arranged with 3π/2 rotations [D3h point group, shown in Fig. 6(a)] or packed closer to each other, and obeying C2v symmetry [Fig. 6(b)].

Fig. 6. Two possible isomers of N9- made by arranging nitrogen molecules parallel to the azide ion around it. (a) D3h point group; (b) C2v point group.

Structure (a) happens to be a high order stationary point with 2 negative Hessian eigenvalues while (b) is a true minimum with a SCS-MP2 energy 22 meV lower than that of (a). Based on the parallel growth scheme, we further propose for N11- and N13- structures obtained by surrounding the azide chromophore with additional nitrogen molecules. In case of N11-, distributing 9 ACS Paragon Plus Environment


the four nitrogen molecules symmetrically in a D4h orientation produces a high order stationary point and it is much more favorable to break the symmetry and bring the nitrogen molecules closer to one another as in the C2v structure shown in Fig. 7(a). In the case of N13-, placing the five nitrogen molecules aligned with the azide chromophore with perfect pentagonal symmetry (D5h point group) leads to a highly stable minimum shown in Fig. 7(b).

Fig. 7. Structures proposed for (a) N11- ; (b) N13- ; (c) N15- ; (d) N17- ;(e) N19- ; (f) N21- .

The bond lengths of N2 and N3- remain almost constant as cluster size increases. The distance between the central N atom in the azide ion and the centers of mass of nitrogen molecules (which is close to the radius of the cylinder) starts at 2.856 Å for N5- and increases almost linearly to reach 2.905 Å for N13-, as the result of the mild repulsion between nitrogen molecules when five of them are present around the azide anion. The highest, energetically favorable radial packing can be achieved by placing 5 molecules around the azide ion and in the case of N15- the additional molecule must be placed away from the cylinder in order to overcome the N2-N2 repulsion. The optimal location for an extra molecule away from the N15- core was found to be at diagonal positions [Fig.7(c)], leading to candidate minima depicted in Fig.7(d) for N17, Fig.7(e) for – N19- and Fig.7(f) for N21-. Actually all these structures are locally optimized relatively easily and correspond to true minima with no negative Hessian eigenvalue. For N17- we found that placing the two additional molecules over the existing N13- cluster either on opposite side of the azide axis or on the same side yields essentially similar energies.

3.3 Relative stability and dissociation energies The relative energetic stability of the different cluster sizes N2n+3- (n>0) was quantified by partitioning the total energy and determining the specific interaction energies of the n nitrogen molecules with the azide chromophore. The BSSE corrected binding energy of the azide and a hollow (N2)n cluster was calculated using DFT and SCS-MP2 methods, in order to provide a simple test for the stability of the corresponding cluster size. The results are given in Table 4.


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Table 4. Binding energies between the azide anion and n nitrogen molecules using different quantum chemical methods and the aug-cc-pVDZ basis. The values in parentheses are obtained using the aug-cc-pVTZ basis and, in the case of the SCS-MP2 method, correspond to single point calculations. All energies are in meV. n 1 2 3 4 5 6 7 8 9

M06-2x

-175(-159) -352(-322) -510(-468) -655(-601) -807(-743) -891(-820) -974(-896) -1063(-978) -1148(-1059)

B3LYP-D3

wB97xD

-175(-170) -331(-324) -468(-465) -601(-586) 743(-702) -820(-771) 896(-838) -902(-911) -965(-977)

-130(-115) -253(-226) -364(-326) -465(-419) -565(-511) -631(-575) -696(-640) -762 -828

SCS-MP2

-103(-124) -206(-248) -301(-359) -380(-454) -473(-559) -537(-629) -596(-696) -653(-759) -716

Overall, a qualitatively similar picture emerges for all methods tested, although DFT tends to overestimate the binding energies. For the present systems, only the B97-D functional gives results close to those of SCS-MP2; however, their frequency analysis shows that only up to n=5 they are true minima. Using the larger basis set aug-cc-pVTZ, the binding energies are generally improved towards the SCS-MP2 values, without changing the qualitative picture of stability. From SCS-MP2 calculations we extrapolate that each nitrogen molecule of the first 5-molecule shell has a binding energy of about 90 meV and that for subsequently placed molecules this value drops to about 60 meV. The significant difference between these binding energies confirm the greater stability of the 5-molecule cylindrical arrangement. A related quantity more relevant in mass spectrometry experiments is the dissociation energy ΔE(n) defined for a given cluster with n nitrogen molecules from its binding energy and that of its daughter at size n-1: ΔE(n)=E(N2n+3-)- E(N2)-E(N2n+1-) The values obtained for ΔE(n) from the absolute electronic energies are given in supporting information for the different quantum chemical methods and basis sets, and their variations with increasing size are depicted in Fig. 8 with the various methods and the aug-cc-pVDZ basis set. With the M06-2x geometries we also evaluated the influence of zero-point delocalization, using vibrational frequencies obtained in the harmonic approximation and without additional scaling. Both the table and the figure clearly show the effect of different shells on the stability of clusters. Once the second shell starts to form, dissociation costs much lower energies hence the clusters become less stable. A second dip at n=8 is still seen for the four methods, which confirms that it is favorable to build the second shell by placing the additional molecules at the side of the 6 parallel molecules and perpendicularly to them. Vibrational delocalization appears to be quite significant and reduce the dissociation energies by a factor ranging between 5% and 45%. With zero-point energy accounted for, size 8 no longer appears particularly stable, although the pentagonal cluster N13- remains prominent.



Fig. 8. Dissociation energy ΔE(n) of (N2)nN3- clusters obtained from different quantum chemical methods. For M06-2x structures, the results are shown also with harmonic zero-point energy (ZPE) correction accounted for. 3.4 Intermolecular charge transfer Insight into chemical bonding within (N2)nN3- clusters was further provided by determining the effective charge carried by the azide chromophore as more and more nitrogen molecules surround it. Consistently with our determination of the partial charges on isolated azide in Sec. 3.1, we have used the M06-2x/aug-cc-pVDZ method and the RESP charge analysis to evaluate how much of the additional electron remains upon microsolvation by N2, and how is the residual charge distributed on these supposedly neutral molecules. The results are given in Table 5.

Table 5. Effective charge on the azide chromophore in (N2)nN3- clusters, and average charge on individual nitrogen atoms from the surrounding N2 molecules, as obtained using a RESP charge analysis from M06-2x/aug-cc-pVDZ and HF/aug-cc-pVTZ (in parentheses) electronic structure calculations at the minimum geometries. All values are reported in units of electronic charge. n 1 2 3 4 5 6 7 8 9

Total charge on azide anion

Average charge on remaining nitrogen atoms

-0.921(-0.899) -0.814(-0.846) -0.801(-0.840) -0.714(-0.748) -0.794(-0.753) -0.666(-0.631) -0.596(-0.556) -0.689(-0.616) -0.535(-0.441)

-0.04(-0.05) -0.05(-0.04) -0.03(-0.03) -0.04(-0.03) -0.02(-0.03) -0.03(-0.04) -0.03(-0.04) -0.02(-0.04) -0.03(-0.04)


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Based on this analysis, the extra electron on the azide chromophore appears to significantly and steadily spill away onto the neighboring molecules, even above the completion of the first 5-molecule shell. This analysis indicates that the classification of the clusters as being formed of distinct nitrogen and azide subparts is questionable, although N3 and N2 fragments are clearly identified from the quantum chemical optimizations. This explains the difficulty in constructing non-reactive force fields (polarizable or not) for these systems, as the amount of intermolecular charge transferred to the nitrogen molecules exceeds what can be captured by simple polarization terms.

3.5 Photodetachment energies Following our above evaluation of vibrational and optical spectra for selected clusters, we have considered vertical photodetachment energies to possibly provide experimental connections in future investigations. Photoelectron spectroscopy is a particularly useful experimental technique for probing anionic clusters. While anionic nitrogen clusters have not yet been probed using this method, photoelectron spectra have been reported for the microhydrated azide system.36 Assuming that the cluster does not relax its geometry upon the loss of an electron, the vertical photodetachment energies (VDE) can be computed from energy differences between the neutral and anionic forms. We have computed these energies from both M06-2x for all clusters and MP2 and CCSD(T) calculations for small clusters (Table 6). Increasing the basis size do not affect the results significantly. MP2 as in binding, are overestimating the photodetachment energies and CCSD(T) reduces them again to the range of M06-2x results.

Table 6. Vertical photodetachment energies from M06-2x. All values reported are in eV. n 1 2 3 4 5 6 7 8 9

M062x(aug-cc-pVDZ) 2.86 3.04 3.18 3.31 3.43 3.50 3.57 3.64 3.71

M062x(aug-cc-pVTZ) 2.94 3.11 3.24 3.37 3.49 3.56 3.63 3.70 3.76

The results obtained for the bare azide anion are in good agreement with the experimental measurements from the Wang group,36 and as in the case of hydrated azide the VDE increases steadily with increasing number of surrounding molecules although more slowly. This result is interesting, because the solvation patterns of nitrogen and water around of the azide ion are very different from one another, the anion being hydrophobic.

4. Concluding remarks



Anionic nitrogen clusters have been shown to exhibit some degree of polymorphism, the excess charge being possibly carried by a variable subset of atoms. Our structural exploration of Nm- clusters for odd size m using a variety of computational methods clearly indicates that they consist of an azide chromophore N3- surrounded by nitrogen molecules and could thus be referred to as N2n+3-. The growth proceeds stepwise, with the initial molecules placing themselves parallel to the chromophore and, once 5 molecules have been added, further away from the anion and in a more diagonal orientation. The dissociation energies are consistent with the structural pattern identified in our calculations, and confirm different stabilities of the two types of molecules from the different shells, dissociation energies dropping above n=5, or for N15-. Experimentally22 the abundances drop at N13-, which suggests a discrepancy with the present calculations. It is of course possible that we missed competing structures, although we believe the basic growth scheme with nitrogen molecules parallel to the azide chromophore should remain at small sizes. Systematic (fully unbiased) global optimization using e.g. basin-hopping or genetic algorithms with an explicit description of electronic structure could be attempted in small systems, although some bonding hypotheses might be needed to speed up convergence. Because the experiments of Weinberger and coworkers were conducted under the cryogenic environment of helium nanodroplets,22 we can rule out finite temperature and entropic effects as the cause of discrepancy. However, vibrational delocalization could act similarly as finite temperature, the extension of the vibrational wavefunction of the peripheral nitrogen molecules possibly explaining why the optimal packing seen in the mass abundances is at four molecules instead of 5 as our static calculations. This hypothesis is supported by the very comparable binding energies of nitrogen to the azide chromophore found in the linear minimum and after rotating nitrogen to the perpendicular plane. The present incorporation of zero-point energy corrections in the harmonic approximation already suggested such an importance, although it is too primitive to be conclusive. In a recent paper 37 we showed that anharmonic nuclear quantum effects were responsible for the observed magic numbers in anionic hydrogen clusters, producing highly symmetric structures owing to the effectively lower density of outer molecules. If the nitrogen molecules around the azide anion were indeed allowed to rotate, it might become difficult to accommodate five of them. To support this speculative interpretation, a proper account of vibrational delocalization is needed, which unfortunately cannot be achieved at the present level of electronic structure method used to describe the clusters on a static level. The azide anion significantly spills its extra electron onto the neighboring nitrogen molecules. Intermolecular charge transfer explains the inability of the force fields that we tried to use to generate candidate structures. Constructing a reactive force field for the present purely nitrogenic compounds seems a difficult objective, because standard approaches that go beyond fixed charges such as those based on the charge equilibration method38 will likely not work here. Ab initio molecular dynamics simulations of the nitrogen anion cluster anions could shed light on the extent to which the charge on the various molecules further depends on geometry in addition to size itself. The successful (but hypothetical) implementation of such a reactive force field would pave the way to the inclusion of nuclear quantum effects that could be important in explaining the discrepancy of one molecule found experimentally in the completion of the first solvation shell of N3-.

5. Supporting Information


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Cartesian coordinates of clusters from M062x/aug-cc-pVTZ and MP2/aug-cc-pVDZ optimized calculations, Energies of optimized clusters with M062x and SCS-MP2 (S1); Dissociation energies with M062x, B3LYP-D3, wB97xD and SCS-MP2; (S2).

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A Quantum Chemical View on the Growth Mechanisms of Odd-Sized

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