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Mihails
Arhangelskis
^{a},
Athanassios D.
Katsenis
^{a},
Andrew J.
Morris
^{b} and
Tomislav
Friščić
*^{a}
^{a}Department of Chemistry, McGill University, 801 Sherbrooke St. W. H3A 0B8 Montreal, Canada. E-mail: tomislav.friscic@mcgill.ca
^{b}School of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Received
23rd November 2017
, Accepted 27th February 2018

First published on 28th February 2018

Pentazolate is the ultimate all-nitrogen, inorganic member of the azolate series of aromatic 5-membered ring anions. As an azolate ligand, it has the potential to form open framework structures with metal ions, that would be inorganic analogues of azolate metal–organic frameworks formed by its congeners. However, while the low stability and elusive nature of the pentazolate ion have so far prevented the synthesis of such frameworks, computational studies have focused on pentazolate exclusively as a ligand that would form discrete metallocene structures. Encouraged by the recent first isolation and structural characterization of pentazolate salts and metal complexes stable at ambient conditions, we now explore the role of pentazolate as a framework-forming ligand. We report a computational periodic density-functional theory evaluation of the energetics and topological preferences of putative metal pentazolate frameworks, which also revealed a topologically novel framework structure.

Fig. 1 (a) Cyclic azolate anions; (b) fragment of the crystal structure of the first pentazolate compound stable under ambient conditions, reported by Zhang et al.^{4} |

We now report a computational investigation of the topological landscape and enthalpic stability of putative pentazolate frameworks Zn(**pnz**)_{2} and Cd(**pnz**)_{2}, including their potential as energetic materials.^{16} Compared to zeolites and related tetrahedral structures, for which computational structure prediction and modelling are well established,^{18–27} the use of theoretical calculations to evaluate or predict properties of metal–organic frameworks is very recent, with notable work focusing on thermodynamic stability,^{28–30} gas storage capacity,^{31,32} catalysis^{33} or organic linker flexibility.^{34,35} Our study was encouraged by the recent demonstration of the ability of periodic density-functional theory (DFT) calculations to provide a realistic assessment of topological preferences and enthalpic stability of imidazolate-based MAFs.^{36} Importantly, whereas earlier theoretical work has focused on **pnz ^{−}** as a ligand that should form discrete molecular complexes of the metallocene type,

Due to the challenges of applying ab initio crystal structure prediction (CSP) techniques,^{39–41} to 3D-covalent structures that have so far prevented their application to coordination frameworks, we have based our study on an extensive survey of the Cambridge Structural Database (CSD) for framework structures composed of divalent metal ions bridged by azolate linkers in the respective stoichiometric ratio 1:2. The **pnz ^{−}** anion contains five nitrogen atoms potentially available for interacting with metal ions, indicating that metal-binding geometries accomplished through all types of azolates, i.e. imidazolates, pyrazolates, triazolates and tetrazolates, should be relevant to our study. We focused on zinc and cadmium as metal nodes, as they are highly popular in the synthesis of MAFs, and also exhibit the d

Throughout our study we have used PBE exchange-correlation functional combined with Grimme-D2 (ref. 46) dispersion correction. In this scheme the dispersion energy is evaluated as a sum of interatomic pairwise contributions, based on a pre-parameterized set of C_{6} coefficients for elements H–Xe. In order to evaluate the accuracy of PBE-D2 calculations, we have performed additional calculations with Tkatchenko–Scheffler (TS)^{55} and many body dispersion (MBD*)^{56,60,61} correction schemes. The TS approach derives pairwise C_{6} dispersion coefficients from the DFT-calculated electron density, as opposed to parameterization used in the D2 scheme. The MBD* adds many body terms to the TS pairwise dispersion energy. As the CASTEP implementation of MBD* method is currently in development, the full geometry optimization using the PBE + MBD* method was not possible. However, similarity of calculated geometries permitted single point calculations using the geometries obtained from PBE + D2 and PBE + TS calculations. In order to evaluate the importance of dispersion corrections on the final energy ranking of **pnz** frameworks, energies were also calculated for a subset of structures using uncorrected PBE^{44} and LDA^{62} functionals.

The plane-wave cut-off was set to 750 eV and the norm-conserving pseudopotentials^{63} were used. The Brillouin zone was sampled with a Monkhorst–Pack^{64}k-point grid of 0.03 Å^{−1} spacing. The following convergence criteria were used: maximum energy change 10^{−5} eV per atom, maximum force on atom 0.03 eV Å^{−1}, maximum atom displacement 0.001 Å and residual stress 0.05 GPa.

Energy minimization of putative crystal structures provided energy landscapes for topologically distinct Zn(**pnz**)_{2} and Cd(**pnz**)_{2} frameworks (Table 1). The structure optimization sometimes led to structures of identical topologies, but of different energies due to differences in symmetry. An example of this would be Zn(2-methylimidazolate)_{2} (CSD code OFERUN01, space group P2_{1}/c)^{65} and Zn(5-methyltetrazolate)_{2} (CSD code HOKMUR, space group Pc),^{66} which share the same diamondoid (dia) topology, yet have significantly different unit cell parameters and different space group symmetries. These structural differences result in crystallographically distinct structures for both Zn(**pnz**)_{2} and Cd(**pnz**)_{2} frameworks. While such hypothetical structures, in principle, represent isoreticular polymorphs, their detailed description and comparison would not be justified considering the accuracy of the herein used approach. Consequently, in our analysis we focused on lowest energy calculated structure for each topology, with a complete set of minimized structures provided in the ESI.†

CSD code |
E
_{rel} (kJ mol^{−1}) |
Topology | CN | PC |
---|---|---|---|---|

WAQQUB | 0.000 | crs | 6 | 0.454 |

LIHQUP | 12.989 | Interpenetrated dia | 4 | 0.662 |

IMIDZB01 | 20.887 | zni | 4 | 0.555 |

IMIDZB07 | 23.044 | coi | 4 | 0.548 |

ONATUT | 25.249 | sql | 4 | 0.615 |

GUPBOJ | 30.472 | yqt1 | 4 | 0.519 |

CUIMDZ03 | 37.404 | mog | 4 | 0.532 |

GUPBOJ01 | 37.730 | ict | 4 | 0.437 |

HIFWAV | 39.188 | nog | 4 | 0.369 |

GITTEJ | 40.612 | crb | 4 | 0.397 |

To evaluate the thermodynamic feasibility of Zn(**pnz**)_{2} and Cd(**pnz**)_{2} in comparison to the reported mixed pentazolate salt,^{4} as well as their energies of combustion, we have also calculated energies for elements in their standard states, namely zinc and cadmium metals, O_{2}, N_{2}, H_{2}, Cl_{2}, and H_{2}O (all in gas phase), as well as energies of zinc and cadmium oxides, which are expected to be principal combustion products.

Finally, phonon and electronic density of states (DOS) calculations were performed for a selection of lowest-energy structures of Zn(**pnz**)_{2} and Cd(**pnz**)_{2}. The DOS and projected density of states (PDOS) were evaluated using the program OptaDOS.^{67,68} The purpose of phonon calculations was to verify the absence of imaginary frequencies in the putative metal pentazolate framework structures, while the DOS calculations were used to investigate the optical properties of these materials. Details of these periodic DFT calculations are given in the ESI.†

Fig. 2 Structure of crs-Zn(pnz)_{2}: (a) the pentanuclear Zn_{5}(pnz)_{6} SBU with (b) the tetrahedral orientation of the peripheral Zn^{2+} ions highlighted; (c) view of the crs-Zn(pnz)_{2} framework along the crystallographic c-direction and (d) view of the crs-Zn(pnz)_{2} framework along the crystallographic c-direction, displaying the contact surface area calculated for a spherical probe of 1.2 Å radius.^{74} |

The structure is best described through vertex-sharing tetrahedra in the crs-topology (Fig. 2c), although it can also be described as a 3,6,6T1-net with each **pnz ^{−}** as a 3-c node and zinc atoms as 6-c nodes. Importantly, the structure of crs-Zn(

The second lowest-energy framework topology for Zn(**pnz**)_{2} resulted from optimizing structures with CSD codes LIHQUP (zinc triazolate) and WAQRAI (zinc tetrazolate). Optimization led to almost identical singly-interpenetrated dia-topology structures that were 13.0 kJ mol^{−1} and 14.5 kJ mol^{−1} higher than crs-Zn(**pnz**)_{2}, respectively. Each zinc atom in dia-Zn(**pnz**)_{2} adopts a tetrahedral geometry, with Zn–N distances in the range of 1.98–2.01 Å, and each **pnz ^{−}** links two metal nodes through 1,3-nitrogen atoms (Fig. 3a). The third lowest-energy Zn(

Relative energy (E_{rel}) ordering of topologies for Zn(**pnz**)_{2} is very different compared to popular imidazolate MAFs (Table 1): the non-interpenetrated dia-, qtz- or zni-topologies, prominent as lowest-energy structures for imidazolates, are all 20 kJ mol^{−1} or more higher in energy than crs-Zn(**pnz**)_{2}.

Notably, crs-Zn(**pnz**)_{2} is the lowest-energy structure in our screen despite exhibiting a potentially microporous structure, with a packing coefficient lower than a number of other herein considered structures. However, such higher density structures are based on four-coordinated zinc atoms, compared to the octahedral coordination found in crs-Zn(**pnz**)_{2}. This indicates that forming additional Zn–N bonds, which is more likely for **pnz ^{−}** than for other azolates, can contribute more to stabilizing Zn(

The lowest-energy structure for hypothetical Cd(**pnz**)_{2} was obtained by optimization of the zinc tetrazolate structure with CSD code WAQRAI. The optimization led to a tri-nodal 3-D network with a novel topology with net point symbol {4.6^{2}}_{2}{4^{2}.6^{9}.8^{4}}, herein named arhangelskite (arh) (Table 2). The novelty of the arh topology was confirmed with the aid of ToposPro software and a new entry has been added to the TOPOS Topological Database (TTD).^{69,78}

CSD code |
E
_{rel} (kJ mol^{−1}) |
Topology | CN | PC |
---|---|---|---|---|

WAQRAI | 0.000 | arh | 6 | 0.647 |

WAQQUB | 9.905 | crs | 6 | 0.396 |

AXIVAF | 16.654 | bcu | 6 | 0.587 |

LIHQUP | 17.783 | Interpenetrated dia | 4 | 0.431 |

CUIMDZ02 | 30.317 | 4,4L37 | 4 | 0.692 |

ONATUT | 30.739 | seh-3,5-Pbca | 5 | 0.54 |

BOJXAZ | 31.159 | sql | 4 | 0.588 |

CUIMDZ03 | 39.198 | {4.6^{2}}_{2}{4.6^{9}}_{2}{6^{6}} |
4, 5 | 0.547 |

IMIDZB01 | 39.921 | zni | 4 | 0.558 |

IMIDZB07 | 33.756 | coi | 5 | 0.506 |

The arh-Cd(**pnz**)_{2} topology results from additional Cd–N bonds formed between components of two interpenetrated dia-nets in the original structure. This transforms the initially tetrahedral metal nodes to distorted octahedral ones, with Cd–N bonds ranging from 2.33 Å to 2.44 Å, with each **pnz ^{−}** ligand acting as a 3-c node with 1,2,4-coordination (Fig. 4). The arh-Cd(

The third lowest-energy framework is bcu-Cd(**pnz**)_{2}, based on the structure with the CSD code AXIVAF (Fig. 5, for detailed description of the geometry optimization see ESI†). In this structure, **pnz ^{−}** ligands adopt the 1,2,4 coordination mode and form dinuclear units with the formula Cd

Variation in packing coefficient of the lowest-energy hypothetical structures for Zn(**pnz**)_{2} and Cd(**pnz**)_{2} shows that changes in the coordination number of the metal ion are a significant factor in deciding the energies of pentazolate frameworks. The energy landscapes of Zn(**pnz**)_{2} and Cd(**pnz**)_{2} show different preferences for the metal coordination environment: the landscape for Zn(**pnz**)_{2} contains one 6-coordinate structure, the rest being based on 4-coordinate, almost exclusively tetrahedral metal nodes (Fig. 6a).

Fig. 6 Comparison of relative lattice energies (E_{rel}) and packing coefficients for putative: (a) Zn(pnz)_{2} and (b) Cd(pnz)_{2} framework structures. |

In contrast, Cd(**pnz**)_{2} shows a stronger preference for higher coordination number, explained by the larger size of the cadmium atom (Fig. 6b). In terms of intermolecular interactions, analysis using Olex2 (ref. 77) suggests that π⋯π stacking is not a significant factor in stabilizing Cd(**pnz**)_{2} structures: close π⋯π contacts of **pnz ^{−}** rings were only observed in higher energy structures with 4,4L37- and {4.6

Phonon calculations were also conducted for selected putative low-energy structures of Zn(**pnz**)_{2} and Cd(**pnz**)_{2}, confirming the absence of imaginary frequencies (see ESI, Tables S21–25†).

In order to confirm the accuracy of our predictions on metal pentazolate framework energies and topology predictions, as well as to verify that the observed trends are general and independent of the choice of computational method, we have performed additional calculation on a subset of topologically-distinct structures of Zn(**pnz**)_{2} and Cd(**pnz**)_{2} (Tables 1 and 2) using Tkatchenko–Scheffler (TS)^{55} and many body dispersion (MBD*) correction schemes. The results were also compared to those obtained using PBE and LDA functionals without dispersion corrections. The energy rankings of Zn(**pnz**)_{2} structures produced by three dispersion-corrected methods were generally consistent, the notable exception being the crs-Zn(**pnz**)_{2} structure (Fig. 7, also ESI Table S6†). Under the PBE-D2 method this structure is the global energy minimum, separated by 13.0 kJ mol^{−1} from the second lowest structure with interpenetrated dia-topology. The ranking of these two structures was reversed using the PBE-TS method, with interpenetrated dia-Zn(**pnz**)_{2} now becoming the energy minimum at a separation of 5.0 kJ mol^{−1} from crs-Zn(**pnz**)_{2}. Finally, with PBE-MBD* method the crs-Zn(**pnz**)_{2} structure again becomes the global energy minimum, separated by 5.3 kJ mol^{−1} from the second-ranked dia-Zn(**pnz**)_{2} structure. Therefore, the many-body dispersion terms appear to stabilize the crs-structure more, relative to pairwise-only TS dispersion approach.

Fig. 7 (Left) Energy ranking of selected Zn(pnz)_{2} structures using dispersion-corrected PBE functional as well as uncorrected PBE and LDA. For the D2 and TS corrections full geometry optimisation was performed. For the development version of MBD*, it was not possible to perform dispersion correction geometry optimization and, therefore, single point calculations were performed for structures optimized with PBE + D2 and PBE + TS methods. (Right) Number of short (3.0–3.1 Å) N⋯N contacts found in each structure using Olex2.^{77} All three dispersion corrections provide consistent energy rankings with the exception of crs-WAQQUB structure, which is found at the global minimum with D2 and MBD* methods, and is ranked second with TS dispersion correction. The anomalous behaviour of WAQQUB is correlated with the number of short N⋯N contacts present in the structure. The energy rankings produced by uncorrected PBE are entirely different from dispersion-corrected calculations, whereas the LDA-derived energy rankings are in good agreement with those obtained from dispersion-corrected PBE. |

The crs-structure is the only Zn(**pnz**)_{2} structure containing an octahedrally coordinated metal ion, and also has the highest number of very short (3.0–3.1 Å) N⋯N contacts (Fig. 7). The behavior of crs-Zn(**pnz**)_{2} upon switching between D2, TS and MBD* dispersion correction schemes suggests that TS penalizes short-range interactions more heavily than D2 or MBD*. This observation is buttressed by the analogous behavior of higher energy sql- and mog-Zn(**pnz**)_{2} structures. These two structures also exhibit a significant number of short intermolecular N⋯N contacts and undergo similar, but less pronounced, variation in calculated energy between TS, D2 and MBD* dispersion correction schemes.

For Cd(**pnz**)_{2}, all three dispersion correction approaches showed consistency in the lowest two energy structures with arh- and crs-topologies. The energy rankings of the third- and fourth-ranked structures of bcu-Cd(**pnz**)_{2} and dia-Cd(**pnz**)_{2} were reversed under PBE + TS and PBE + MBD* schemes. The result is not surprising, as the energy separation of these structures under the PBE-D2 method was only 1.1 kJ mol^{−1} under PBE-D2 method.

In general, all three dispersion correction schemes provide consistent energy rankings and unit cell volumes for Zn(**pnz**)_{2} and Cd(**pnz**)_{2}. While some reranking is observed, it generally occurs for the structures separated by less than 5 kJ mol^{−1}, the only exception being the crs-Zn(**pnz**)_{2} structure. In contrast, the uncorrected PBE functional produces energy ranking entirely different from dispersion-corrected PBE. As an example, a low-density structure crb-Zn(**pnz**)_{2} fell from rank 10 under PBE-D2 (+40.6 kJ mol^{−1}) to rank 4 for uncorrected PBE (+8.5 kJ mol^{−1}). Evidently, accounting for dispersion forces is crucial for the accurate evaluation of relative enthalpic stability of topologically distinct polymorphs of metal pentazolate frameworks.

We have also explored the ranking of the structures Zn(**pnz**)_{2} and Cd(**pnz**)_{2} structures using the LDA functional. In comparison with GGA functionals, LDA shows over-binding, resulting in more attractive supramolecular interactions. Indeed, the energy rankings of **pnz** frameworks produced by LDA were very similar to those generated by dispersion-corrected PBE, hinting at its use as a “poor man's energy dispersion correction”. The unit cell volumes produced by LDA calculations were all found to be ca. 5–10% lower than the volumes obtained by PBE-D2 calculations for the corresponding structures (Tables S8 and S9†), which is interpreted as a manifestation of stronger supramolecular forces in LDA structures.

In order to provide a preliminary assessment whether zinc- or cadmium-based pentazolate frameworks are experimentally accessible, we evaluated their enthalpies of formation with respect to the elements, by subtracting the energies of the elements in their standard states (crystalline zinc and cadmium, N_{2} gas) from the calculated energies of crs-Zn(**pnz**)_{2} and arh-Cd(**pnz**)_{2} structures. Analogous calculation was also done for the reported structure of the mixed salt (H_{3}O)_{3}(NH_{4})_{4}(**pnz**)_{6}Cl. The formation enthalpies for the lowest-energy structures of Zn(**pnz**)_{2} and Cd(**pnz**)_{2} were found to be +221.6 kJ mol^{−1} and +266.2 kJ mol^{−1} respectively. The formation of the mixed **pnz ^{−}** salt, on the other hand, was found to be exothermic with an enthalpy of −59.0 kJ mol

While the positive enthalpies of formation suggest that metal pentazolate frameworks would be significantly less stable than (H_{3}O)_{3}(NH_{4})_{4}(**pnz**)_{6}Cl, this does not imply that Zn(**pnz**)_{2} and Cd(**pnz**) should not be feasible: enthalpies of formation for known solid energetic compounds readily exceed +240 kJ mol^{−1},^{79} as illustrated by hexahydro-1,3,5-trinitroso-1,3,5-triazine (TIT, +286 kJ mol^{−1}),^{80} hexanitroazobenzene (HNAB, +284 kJ mol^{−1})^{79} or ε-hexanitrohexaazaisowurtzitane (CL-20, +377 kJ mol^{−1}).^{81} Moreover, MAFs are typically obtained by solution crystallization, where reaction thermodynamics are strongly influenced by solvent–solute interactions, which might facilitate the formation of herein described structures. Indeed, complexation with Zn^{2+} ions was noted to stabilize **pnz ^{−}** in solution.

M(N_{5})_{2}(s) + 1/2O_{2}(g) → MO(s) + 5N_{2}(g), (M = Zn, Cd) | (1) |

Calculated enthalpies for reactants and products in their standard states were found to be −763 and −739 kJ mol^{−1} for crs-Zn(**pnz**)_{2} and arh-Cd(**pnz**)_{2}, respectively, corresponding to energy densities of 3.71 and 2.93 kJ g^{−1} that are close to that of 1,3,5-trinitrotoluene (TNT, 4.6 kJ g^{−1}).^{88}

The enthalpies of formation (ESI Tables S12 and S13†) and combustion (ESI Tables S16 and S17†) were also calculated using the LDA functional. However, the LDA calculations revealed a large deviation from the enthalpies calculated using PBE. A tentative explanation of this difference might be in the known tendency of the LDA functional to overestimate bond dissociation energies,^{89} with GGA methods showing higher accuracy. We verified this by calculating bond dissociation energies for O_{2} and N_{2} molecules as well as atomization enthalpies for **pnz** frameworks (ESI Tables S18–S20†). While LDA calculations predicted higher dissociation energies compared to PBE in all cases, the comparison with experimentally determined dissociation energies for O_{2} and N_{2} molecules confirms the higher accuracy of the PBE functional (ESI Table S20†).^{90}

Finally, we have also investigated the optical properties of pentazolate frameworks by calculating the electronic density of states (DOS) for the three lowest energy predicted structures of Zn(**pnz**)_{2} and Cd(**pnz**)_{2}. The band gaps for all materials were in the range of 4.5–5.1 eV but, as the PBE functional generally underestimates the band gaps, the true values are likely to be even higher. These results suggest that these putative materials should be colorless. In addition, PDOS analysis confirmed that HOCO and LUCO bands in these structures are entirely localized on the **pnz** ligand orbitals, consistent with the d^{10} electronic configurations of Zn^{2+} and Cd^{2+} ions.

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## Footnote |

† Electronic supplementary information (ESI) available: Details of database surveys, candidate structures, computational procedures, and topological analyses, in pdf format. Crystallographic data for theoretical Zn(pnz)_{2} and Cd(pnz)_{2} frameworks in CIF format. See DOI: 10.1039/c7sc05020h |

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