Uncommon structural and bonding properties in Ag16B4O10

Ag16B4O10 has been obtained as a coarse crystalline material via hydrothermal synthesis, and was characterized by X-ray single crystal and powder diffraction, conductivity and magnetic susceptibility measurements, as well as by DFT based theoretical analyses. Neither composition nor crystal structure nor valence electron counts can be fully rationalized by applying known bonding schemes. While the rare cage anion (B4O10)8− is electron precise, and reflects standard bonding properties, the silver ion substructure necessarily has to accommodate eight excess electrons per formula unit, (Ag+)16(B3+)4(O2−)10 × 8e−, rendering the compound sub-valent with respect to silver. However, the phenomena commonly associated with sub-valence metal (partial) structures are not perceptible in this case. Experimentally, the compound has been found to be semiconducting and diamagnetic, ruling out the presence of itinerant electrons; hence the excess electrons have to localize pairwise. However, no pairwise contractions of silver atoms are realized in the structure, thus excluding formation of 2e–2c bonds. Rather, cluster-like aggregates of an approximately tetrahedral shape exist where the Ag–Ag separations are significantly smaller than in elemental silver. The number of these subunits per formula is four, thus matching the required number of sites for pairwise nesting of eight excess electrons. This scenario has been corroborated by computational analyses of the densities of states and electron localization function (ELF), which clearly indicate the presence of an attractor within the shrunken tetrahedral voids in the silver substructure. However, one bonding electron pair of s and p type skeleton electrons per cluster unit is extremely low, and the significant propensity to form and the thermal stability of the title compound suggest d10–d10 bonding interactions to strengthen the inter-cluster bonding in a synergistic fashion. With the present state of knowledge, such a particular bonding pattern appears to be a singular feature of the oxide chemistry of silver; however, as indicated by analogous findings in related silver oxides, it is evolving as a general one.


Introduction
Employing advanced techniques in chemical synthesis constitutes an effective approach to realizing unconventional compounds, sometimes opening access even to new classes of materials featuring, e.g., novel bonding principles. One such example concerns multinary silver oxides, which are thermally notoriously labile. Using specially designed Bridgeman-type autoclaves made of distinctly scaling-resistant steel, 1 enduring conditions applied of up to 7 Â 10 8 Pa pressure of oxygen and up to 973 K temperature enables suppression of the thermal degradation of Ag 2 O and thus reaction of this oxide in all-solid state reactions with any other binary oxide in the periodic table. In a preconceived view, one would expect the oxides attainable this way, Ag x M y O z (M ¼ nonmetal or metal), to represent analogues of respective alkali metal oxides. However, systematic exploration of such systems has revealed that singular early observations of conspicuously short Ag + -Ag + separations in oxides are not strange exceptions, but manifestations of a general feature of the chemistry of silver. [2][3][4] Primarily in oxides with high silver contents, silver(I) ions tend to aggregate forming partial structures that are topologically reminiscent of elemental silver. Furthermore, such structural motifs are associated with specic physical properties. [5][6][7] From these ndings we concluded thus: "The substructures thereby formed have empty s and p conduction bands, which can easily accommodate further electrons on reduction". 3 As a consequence, one would expect oxides to exist that contain silver in oxidation states between 0 and +1, i.e. sub-valent silver. Indeed, a few candidates fullling such an expectation were communicated, e.g. Ag 3 O 8 and Ag 5 GeO 4 . [9][10][11] Here we report on a new compound, Ag 16 B 4 O 10 , a rather exotic oxide containing nominally Ag 0.5+ , or 8 excess electrons when assigning standard oxidation states according to (Ag + ) 16 (B 3+ ) 4 (O 2À ) 10 Â 8e À . Interestingly, the cation substructure Ag 16 B 4 corresponds to the ccp arrangement of metallic silver, where out of every 20 silver atoms four adjacent ones, forming a tetrahedron, are replaced by boron atoms. In turn, the latter are coordinated by four oxygen atoms each, resulting in the rare adamantane related cage anion B 4

X-ray powder diffraction
Laboratory powder X-ray diffraction (PXRD) data ( Fig. 1) were collected at room temperature on a Bruker D8 diffractometer with germanium monochromatized Cu-Ka1 radiation (l ¼ 1.5406Å), in steps of 0.01 over a 2q range of 10-90 degrees. A Rietveld prole t was carried out with the TOPAS-4.2.0.2 (AXS) program. 16 The rened parameters were scale factor, sample displacement (mm), background as a Chebyshev polynomial of 5th degree, 1/x function, crystallite size, micro-strain (Stephens broaden model 17 ) and cell constants. In addition, temperature dependent PXRD data were collected in the temperature range from room temperature to 773 K, in intervals of 50-100 K, as shown in the ESI, Fig. S1. †

X-ray single-crystal diffraction
A crystal suitable for single-crystal X-ray diffraction was selected in a drybox (M. Braun, Garching, Germany) under an argon atmosphere (<0.1 ppm O 2 , H 2 O) and mounted in a sealed glass capillary. Diffraction data were collected at room temperature (298 K) with a SMART APEX-I CCD X-ray diffractometer (Bruker AXS, Karlsruhe, Germany), using Mo-Ka radiation. The intensities of the Bragg reections were integrated with the SAINT subprogram in the Bruker Suite soware. 18 A multi-scan absorption correction was applied using SADABS. 19 The crystal structures were solved by direct methods and rened by fullmatrix least-square tting with the SHELXTL soware package. 20,21 Experimental details and crystallographic data are given in Tables S1-S3. †

Resistivity and magnetic susceptibility measurement
Magnetic properties were studied using a Quantum Design MPMS SQUID Magnetometer. Zero-eld-cooled (ZFC) and eldcooled (FC) magnetic susceptibility data were recorded in a 10 000 Oe eld while warming the sample from 5 to 300 K. Resistivities of polycrystalline bars (approximate dimensions 3 Â 3 Â 10 mm 3 ) of Ag 16 B 4 O 10 were recorded using a standard four-probe dc technique on a Quantum Design physical property measurement system.

Computational methods
Density functional (DFT) calculations, based on the experimental structure of Ag 16 B 4 O 10 , were performed using the CRYSTAL17 program package. 22 The bands in the semi-core and valence space, considering 19 valence electrons of each silver atom, 6 for O and 3 for B, are expanded in terms of local Gaussian basis functions. The core electrons are represented by scalar relativistic pseudopotentials. Details on the exponents and contractions are given in the ESI. † The integration in reciprocal space was based on 242 k-points in the irreducible part of the Brillouin zone. The results presented here are obtained with the short-range-separated hybrid functional HSEsol 23 for the exchange and correlation terms in the Kohn-Sham equations. Atomic charges were evaluated by analyzing the electron density topologically according to the QTAIM approach. 24 A search of the atomic basins was performed with the critic2 (ref. 25 and 26) program on the basis of a 321 Â 321 Â 201 grid of data points of the valence electron density, augmented by core densities. Within the basins, the valence density was integrated in order to get the net charges. Data grids of the electron localization function 27,28 (ELF) were computed with TOPOND, 29 integrated in CRYSTAL17. Structural data and volumetric data were visualized with the VESTA code. 30

Results and discussion
A new compound, Ag 16 B 4 O 10 , has been obtained as a coarse crystalline material via solid state synthesis. The shiny black crystallites are insensitive to humid air and start decomposing thermally at $623 K with silver metal and amorphous B 2 O 3 resulting in the nal solid residues, see Fig. S1. † The title compound can be prepared from various starting materials in the required molar ratios, as there are boron(III) oxide, boronic acid, silver oxide and nally elemental silver as an essential component, while adding varying amounts of water as a mineralizing agent. At rst glance it appears unintuitive that for the synthesis of such a considerably reduced material applying moderately elevated oxygen pressures of 2 Â 10 7 to 5 Â 10 7 Pa is an indispensable requirement. However, running the experiments at ambient pressure results in the decomposition of silver oxide to the metal, while a too high oxygen pressure would end up in the formation of silver(I) borates. So, the synthesis of the title compound is a delicate balancing act, and even for the optimized synthesis conditions, given above in detail, one or the other synthesis run may fail in yielding single phase products. Fig. 1 displays a Rietveld prole t of an X-ray powder diffractogram of a sample obtained using the optimized synthesis procedure; a three-phase renement has revealed that only traces of Ag (2.1%) and Ag 2 O (2.3%) are present. The atomic parameters obtained are given in Table S4. † The constitution has been conrmed unambiguously by single crystal X-ray structure determination. As illustrated in Fig. 2, the general structural organization of Ag 16 B 4 O 10 derives straight forwardly from a ccp pattern of elemental silver: out of every twenty silver atoms four adjacent ones are replaced by boron. Since boron atoms are of considerably smaller size compared to silver, the substitution generates some empty space tolerating the insertion of oxygen atoms to form the polyoxoanion B 4 O 10 8À . From this picture it is immediately obvious that the title compound ideally matches the notion of classifying crystal structures of extended inorganic solids rather based on the packing of the cations 31 than on that of anions. Even beyond, it lends strong support to the further reaching concept according to which certain oxides may be regarded as alloys being stuffed with oxygen. 32,33 This particular structural interrelation is underpinned by Fig. 3     In more detail, all silver atoms are engaged in octahedral homoatomic building units, which are linked by sharing edges and vertices to form a 3D framework. Every silver atom is coordinated by either one or two oxygen atoms at a distance typical of this pair of atoms d(Ag-O) ¼ 2.20-2.35Å (see Table  S3 †).
The rare complex anion B 4 O 10 8À has been observed here as an "isolated", i.e. unbridged, entity for the rst time. 12 Two previous reports present this building block as part of an extended framework. Moreover, in both cases the structural analyses performed suffer from disorder, where occupation factors of 1/2 for the intra-cage bridging oxygen atoms even question the connectivity, i.e. the presence of such an integral anion, at all, 13 or from rening split atom positions for the anion in two orientations, impairing the accuracy of the data obtained. 14 The molecular anion, see Fig. 5, is isostructural and (valence) isoelectronic to P 4 O 10 . The bond lengths are in the expected range, see Tables 1 and S3, † and the variations reect the position of the oxygen atoms, terminal or bridging within the adamantane type of cage. Drawing the chemical bonds of the cage anion in terms of the Lewis concept requires placing a formal negative charge on both, the boron and the terminal oxygen atoms. Although a formalism, this tells that the bonding situation is special and suggests looking for the respective structural distinguishing features by comparing with the     10 Â 8e À have to be accommodated by the silver substructure. As a consequence, one would expect itinerant electrons being present, giving rise to metallic conductivity. Surprisingly, the compound is a small band gap semiconductor, and diamagnetic, as shown in Fig. 6. By tting the resistivities in the high temperature range above 150 K to the Arrhenius equation (Fig. 6 inset), an experimental band gap of 4.71(1) meV was obtained. This value is essentially identical to the calculated one, see below. The diamagnetic susceptibilities are estimated to be À1147 Â 10 À6 cm 3 mol À1 , based on an analysis of the magnetic susceptibilities applying a Curie-Weiss, Pauli and diamagnetic term. The upturn tail below 30 K is dominated by an unknown paramagnetic impurity (about 0.2% with S ¼ 1/2). These results indicate the presence of localized and paired excess electrons. However, no particularly shortened individual Ag-Ag bondlength can be identied that would provide evidence for normal 2e-2c bonds, although the interatomic silver separations are on average smaller than those found for elemental silver. As can be seen from Fig. 4 (red circle) the 'empty' octahedral silver units appear to cluster, forming blocks consisting of ve edge sharing octahedra. Each such cluster entity features two tetrahedral voids, where three out of six edges formed by silver atoms are substantially shorter (2.80Å on average) than the separation in elemental silver (2.89Å). This gives a rst qualitative hint to the fact that these are the regions in real space where the excess electrons might be accommodated. Since these tetrahedral sites add up to four per formula unit, which in total may host four pairs of excess electrons, i.e. all of them, this view would comply with the experimentally found magnetic and transport properties. We exclude the possible presence of hydride anions, lling the contracted voids, for chemical reasons. Along any synthesis protocol yielding the title compound protons are essential constituents, and, moreover, applying an elevated oxygen pressure is an indispensable requirement. The pronouncedly basic and strongly reducing hydride ion cannot exist under such conditions. In order to back this explanation quantitatively, we performed a DFT based computational analysis on the density of states (DOS), electron densities and localizations. DOS as well as the projections onto the atoms (PDOS) is shown in Fig. 7a. Over the whole energy range, which is shied relative to the Fermi level (E F ¼ 0 eV), oxygen basis functions contribute to the DOS. Below À7 eV, the silver PDOS is low. Bands are at and can be associated with the B-O bonds in the B 4 O 10 8À unit. The low contribution of boron to these bands points to the ionic character of the B-O bonds. The DOS between À7 eV and À3.2 eV is dominated by the 4d states of the silver atoms, however, it  shows two peculiarities. At lower energies within this range, Ag3 and Ag4 show a signicantly higher PDOS than Ag1 and Ag2, due to additional 5s-contributions. At À5.5 eV, the DOS shows a maximum. Here further at bands attributed to B-O bonds can be assigned within the manifold of silver d-states, in this case, however, with a higher Ag 4d ratio. In the range between À3.2 eV and À1.4 eV the PDOS of silver and oxygen atoms contribute at nearly equal weight to the total DOS. These bands are related to the interaction between the oxygen lone pairs and the silver 4d-shells. From À1.44 eV up to the Fermi level bands with higher dispersion are located. The respective atomic contributions can be visualized by drawing isosurfaces of the electron density computed from these bands (Fig. 7b). These bands are delocalized over the whole crystal. Note, for clarity reasons, only a cut-out of the isosurface is shown in Fig. 7b. The bands are lled and the system is not metallic. There is a distinct band gap in most parts of the Brillouin zone. Only at k ¼ (1/2 1/2 1/6) it becomes as tiny as 15 meV (Fig. 7c). The highest valence band and the lowest conduction band exhibit a parabolic dispersion. Signicant effects of spin-orbit coupling are not expected, as the Ag 4d-shell is practically lled and the 5d-orbitals are only affected indirectly. Moreover, the projected densities of states show the same character in both bands. The band gap at k ¼ (1/ 2 1/2 1/6) can be seen only in calculations with hybrid functionals. When using gradient corrected (GGA) functionals without fractional Hartree-Fock exchange the band gap is underestimated and vanishes, although still a minimum of the DOS can be seen at E F . The projections of the DOS shown in Fig. 7a are based on a partitioning with respect to atomic basis functions. In the linear expansion of the bands, a certain basis function may contribute to a state which is attributed to a neighboring atom, and an interpretation in terms of chemical bonding may not be unique. Additional methods in position space give complementary information. The partitioning of space resulting from a topological analysis of the total electron density 24 gives atomic volumes and net charges, which are quite robust with respect to the choice of the basis set. The values computed for Ag 16   bonding. Besides the obvious ionic interactions between the anionic unit and the silver framework, no indications for covalent contributions have been identied in the ELF. We understand the large overlap of the projected DOS of silver and oxygen to reect dispersion interaction between the silver d 10shells and the oxygen lone pairs, both being highly polarizable, leading to a further stabilization of the compound.

Conclusions
The new compound Ag 16 10 Â 8e À , reveals an appreciable number of excess electrons to be accommodated in the silver sub-structure. Surprisingly, these excess electrons do not give rise to metallic conductivity, instead, small band gap semiconducting transport behavior was observed experimentally. Since moreover a diamagnetic response was recorded, the additional electrons have to be localized pairwise. Indeed, in the silver substructure, four signicantly contracted tetrahedral voids per formula unit have been identied, which are suited to exactly accommodate the four pairs of excess electrons. DFT based theoretical analyses conrm opening of a small band gap and a signicant ELF contour in the center of the contracted silver tetrahedra. In summary, our ndings reported here are suited to consolidate earlier sparse reports on subvalent ternary silver oxides featuring similar structural and physical properties, [9][10][11] characterized by compositions violating conventional rules of chemical valence with excess electrons localized in 2e-multicenter bonds in the silver substructure. The ndings appear to reect a singularity, so far only associated with silver, where in accordance with an early supposition 3 d 10 -d 10 bonding interactions provide extended Ag + partial structures in position space involving low lying empty s and p states in reciprocal space. By deliberately accommodating excess electrons in those local s and p states, low electron count silver clusters are formed, stabilized by synergistic interactions among the lled 4d 10 -shells and local 2e-multicenter bonding of 5s and 5p skeleton electrons.

Conflicts of interest
There are no conicts to declare.