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Crystal Structure of Silver Pentazolates AgN5 and AgN6

Silver pentazolate, a high energy density compound containing cyclo-N5- anion, has recently been synthesized at ambient conditions. However, due to high sensitivity to irradiation, its crystal structure has not been determined. In this work, silver-nitrogen crystalline compounds at ambient conditions and high pressures, up to 100 GPa, are predicted and characterized by performing first-principles evolutionary crystal structure searching with variable stoichiometry. It is found that newly discovered AgN5 and AgN6 are the only thermodynamically stable silver-nitrogen compounds at pressures between 42 and 80 GPa. In contrast to AgN5, pentazolate AgN6 compound contains N2 diatomic molecules in addition to cyclo-N5-. These AgN5 and AgN6 crystals are metastable at ambient conditions with positive formation enthalpies of 54.95 kJ/mol and 46.24 kJ/mol, respectively. The underlying cause of the stability of cyclo-N5- silver pentazolates is the enhanced aromaticity enabled by the charge transfer from silver atoms to nitrogen rings. To aid in experimental identification of these materials, calculated Raman spectra are reported at ambient pressure: the frequencies of N5- vibrational modes of AgN5 are in good agreement with those measured in experiment.


Introduction
Polynitrogen high energy density materials are in the focus of intense experimental and theoretical investigations 1,2 due to their promise of delivering high explosive power upon decomposition of single and double bonded nitrogen atoms to triply bonded N 2 3,4 . Although pure nitrogen extended solids such as cubic gauche (cg) and layered polymeric nitrogen have been predicted 5 and subsequently synthesized at high pressures 6,7 , their recovery at ambient conditions is challenging 8 .
Most of metal pentazolates discovered so far are the crystals with alkali cations Li + 18,21,23,24 , Na + 10,25 , K + 19 , and Rb + 13 with 1:5 metal/nitrogen stoichiometry. They are just the one of several M x N y materials featuring isolated nitrogen atoms/ions, finite and infinite chains, 2D layers and other polynitrogen complexes. Such rich chemistry is due to the ease of alkali atoms to donate electrons to nitrogen species, resulting in plethora of M x N y chemical compositions.
Silver, being one of the coinage elements (Cu, Ag, and Au), is "noble", i.e. almost unreactive, compared to reactive alkali metals. This is because the outer valence electrons are more tightly bound than those of alkali atoms due to poor screening of the nuclear charge by the d-sub-shells compared to much stronger screening by filled s/p shells of alkali atoms.
Therefore, less variety is expected among stoichiometries of Ag x N y compounds; it is highly probable that 1:5 stoichiometry would be the only one that displays negative formation enthalpies at high pressures. In fact, even the existence of AgN 5 was questioned more than a century ago when it was purportedly synthesized by Lifschitz 26  It is known that application of pressure imparts a substantial thermomechanical energy of compression to precursor materials 34 , which may promote unusual chemistry of resulting compounds. Therefore, the investigation of AgN 5 as well as other Ag-N materials with different stoichiometries (if they exist) at high pressures is of great importance for elucidating bonding and structure of silver-nitrogen compounds.
The goal of this research is to answer these outstanding questions by performing crystal structure searching of new silver-nitrogen crystalline compounds, including AgN 5 , at ambient conditions and high pressures up to 100 GPa using variable composition first-principles evolutionary crystal structure prediction method. Once the new compounds are uncovered their stability, bonding and structure as well as electronic and vibrational properties are analyzed. Chemical pathways for synthesis of discovered thermodynamically stable compounds are proposed and Raman spectra of the resultant compounds are calculated to aid in experimental detection of these materials at ambient pressure.

Computational Details
The silver-nitrogen compounds Ag x N y of variable stoichiometry are searched using firstprinciples evolutionary structure prediction method implemented in Universal Structure Predictor: Evolutionary Xtallography code (USPEX) [35][36][37] . The variable composition searches are performed at several pressures using unit cells containing varying amounts of silver and nitrogen atoms between 8 to 16 atoms in the cell. In total, about 100 different Ag x N y stoichiometries are sampled. Once the variable composition search at a given pressure is complete, fixed composition or molecular searches using larger unit cell sizes up to 48 atoms are performed at stoichiometries corresponding to the thermodynamically stable compounds at the vertices of the convex hull and the metastable compounds up to 20 meV above the convex hull.
The process of structure prediction begins by generating structures based on all space groups and random lattice parameters in the first generation. The obtained structures are then optimized to a target pressure. Their normalized formation enthalpy is determined as follows: where H AgxNy , H Ag and H N are enthalpy of the compounds and best structures of pure elements, respectively. Based on the normalized formation enthalpy, the convex hull at each pressure is constructed using the lowest formation enthalpy structures. For each subsequent generation, a small subset of the lowest enthalpy structures is kept while a new generation is built by adding more random crystals and by applying variation operators to the best "parent" structures. The process is repeated until the best kept structures do not change for ten consecutive generations.
Once combined variable and fixed stoichiometry searches are completed at several pressures, all the resulting crystal structures are combined in one single database, which is then used for high precision geometry optimization and construction of the final convex hull at every pressure of our interest, from 0 to 100 GPa. Such combined method was shown to be successful in overcoming computational limitations of the variable composition search. For example, during variable composition search at 50 GPa only one thermodynamically stable stoichiometry, AgN 5 , was found. However, a second thermodynamically stable stoichiometry AgN 6 was uncovered in subsequent fixed stoichiometry molecular search using twice larger unit cell containing four silver atoms and twenty-four nitrogen atoms.
The USPEX method and similar structure search methods 38,39 have already been successful in prediction of experimentally known crystal structures of pure elements. To speed up the search, the known lowest enthalpy reference structures of pure elements were taken: fcc Ag-Fm-3m for Ag across the entire pressure range, and α-N 2 at 0 GPa, ε-N 2 at 50 GPa, and cg-N above 50 GPa for reference structures of nitrogen. If a compound lies on the convex hull it is considered thermodynamically stable meaning it will not decompose into either the pure elements or into a mixture of other Ag x N y compounds 40 . Compounds that lie above the convex hull must be dynamically stable, i.e. no negative phonon frequencies, to be considered metastable.
Perdew cies. 43 The intensities are determined by calculating the macroscopic dielectric polarizability tensors for each normal mode eigenvector. 44 The atomic charges and bond orders are calculated using density derived electrostatic and chemical charges (DDEC) method implemented in VASP. 45 Results and discussion  and S2 in the supplementary information.
The N 2 dimer of AgN 6 -P2 1 2 1 2 is almost electroneutral, as the atomic charges on N atoms  It is important to note that 0 K data are the lowest pressure estimates. The transition pressures at high temperatures are determined by a complex interplay of thermodynamics and kinetics of solid-state reactions. 49 On the one hand, temperature helps to activate kinetics, thus potentially lowering transition pressure. 50 On the other hand, temperature might thermodynamically stabilize the molecular precursors compared to solid reactants due to entropic -TS contribution to the Gibbs free energy, thus increasing transition pressure upon increase of temperature. 49,51 Due to extreme complexity of the phenomena involved a meaningful predictions of finite temperature effects seem to be impractical to make within the scope of the current work.

Conclusions
Using first-principles evolutionary structure prediction calculations, we discovered two novel silver pentazolate compounds: AgN 5 -P2 1 /c and AgN 6 -P2 1 2 1 2, which are predicted to be thermodynamically stable at pressures 41.5 Pa and 41.7 GPa, respectively. These structures are proved to be dynamically stable at 0 GPa. In contrast to AgN 5 novel pentazolate AgN 6 compound contains N 2 diatomic molecules in addition to cyclo-N − 5 . Synthesis of AgN 5 -P2 1 /c may be possible by compressing mixture of N 2 and AgN 3 to pressures above 21.42 GPa at which point AgN 5 -P2 1 /c is becoming thermodynamically favorable. Synthesis of AgN 6 -P2 1 2 1 2 may be possible at pressures above 25.58 GPa via the same route. The Raman spectra of both AgN 5 -P2 1 /c and AgN 6 -P2 1 2 1 2 are presented. We report agreement between calculated Raman spectrum of and experimental data from Sun et al. 17 and is therefore strong evidence that this structure was synthesize in experiment.