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Chemically driven negative linear compressibility in sodium amidoborane, Na(NH2BH3)

Over the past few years we have been witnessing a surge of scientific interest to materials exhibiting a rare mechanical effect such as negative linear compressibility (NLC). Here we report on strong NLC found in an ionic molecular crystal of sodium amidoborane (NaAB) – easily-accessible, optically transparent material. In situ Raman measurements revealed abnormal elongation of B-N and N-H bonds of NaAB at pressure about 3 GPa. Ab initio calculations indicate the observed spectroscopic changes are due to an isostructural phase transition accompanied by a stepwise expansion of the crystal along c axis. Analysis of calculated charge density distribution and geometry of molecular species (NH2BH3) univocally points to a chemically driven mechanism of NLC – pressure-induced formation of hydrogen bonds. The new H-bond acts as a “pivot screw” coupling N-H covalent bonds of neighbor molecular species – a system resembling a two-lever “jack device” on a molecular scale. A mechanism based on formation of new bonds stands in apparent contrast to mechanisms so far reported in majority of NLC materials where no significant alteration of chemical bonding was observed. The finding therefore suggests a qualitatively new direction in exploration the field towards rational design of incompressible materials.

derivatives obtained by substitution of a hydrogen proton in the NH 3 group for a metal cation. Amidoboranes of alkali metals (Li, Na, K) release ca. 10 wt.%, 6 wt.% and 4 wt.% of molecular hydrogen respectively, and in contrast to pure AB, hydrogen is released in a quasi one-step process, at temperatures below 100 °C. This significantly improved dehydrogenation profile indicates substantial difference in decomposition mechanisms of AB and its metallated derivatives, most probably, as a result of different bonding. Applying hydrostatic pressure may induce substantial alteration of interatomic distances therefore providing convenient tool for probing intra-and intermolecular interactions. As an example, in our recent work on potassium amidoborane we found that weak intermolecular interactions experienced significant enhancement under pressure 14 . It is in this context we have choosen to study sodium amidoborane using diamond anvil cell technique coupled with Raman spectroscopy for in situ probing vibrational properties under pressure.

Results and Discussion
Freshly synthesized samples of NaAB were used for our spectroscopic study. Details of synthesis procedure and variable pressure Raman measurements are described in Methods. Here we will focus on changes observed in the spectral range of B-N (skeletal) as well as N-H stretching modes. One should note, the signal from B-N skeletal stretching vibrations is represented by a doublet due to natural occurence of two isotopes of boron. Typically as interatomic distances get reduced upon increasing pressure frequencies of measured Raman signals are expected to get higher their values demonstrating a 'blue' shift in a measured spectrum. Collected spectra of NaAB, however, revealed an unusual response of B-N and N-H stretching modes to external pressure. While at pressure range from ambient to ~2.1 GPa as well as higher pressure (P > 3 GPa), mode frequencies demonstrated typical behavior -a gradual shift to higher values, a sharp drop in frequency value, ca. 12 and 50 cm −1 for B-N and N-H modes respectively, was detected at pressure ~3 GPa ( Fig. 1a-d). A shift to a lower frequency (lower energy), known also as a 'red' one, is usually a consequence of bond elongation therefore a corresponding mode in vibrational spectrum is called a 'soft' one. 'Soft' mode behavior of bonds involving hydrogen atoms often points to the enhanced character of dispersive interactions which may lead to formation of either conventional hydrogen or dihydrogen bonds. The observed alternate 'blue -red -blue' shift behaviour of N-H modes in the compressed NaAB presents an individual case among metal amidoboranes and pristine ammonia borane. Lithium amidoborane (LiNH 2 BH 3 , LiAB), isostructural with sodium amidoborane, was shown to exhibit a continuous positive pressure dependence ('blue' shift) of both symmetric and asymmetric N-H stretching modes up to ~19 GPa. This finding suggests the absence of considerable enhancement of dispersive interactions in the material 15 . In the case of potassium amidoborane (KNH 2 BH 3 , KAB) the crystal structure is similar to that of LiAB and NaAB, however, in addition to molecular fragments [NH 2 BH 3 ] − angled at ~45° to c axis there is a layer with molecular anions aligned perpendicular to c axis. Our recent high-pressure study revealed a spectacular 'soft' mode behavior for the one of N-H stretching vibrations indicating formation and continuous enhancement of conventional hydrogen bonding between molecular fragments of different layers 14 . At the same time in pristine ammonia borane the observed 'soft' behaviour of all N-H stretching vibrations under pressure is accounted for by the enhancement of dihydrogen bonding, (N-H δ+ ---δ− H-B) 16,17 . While substantial elongation of N-H bonds resulting from enhancement of dispersive interactions has been observed in KAB and AB, we found no report on possible reason for elongation of skeletal B-N bonds under pressure. We thus undertook an extensive study of high-pressure behaviour of NaAB within ab initio theoretical approach with particular attention to bonding properties. Such an approach has been recently shown to yield results consistent with experimental data and proved useful for unveiling complex interplay of bonding in KAB 14 .
For ab initio calculations, we used crystal structure parameters obtained by the Rietveld refinement of experimental powder XRD data collected at ambient pressure (See section "Sample characterization" of Supplementary Information). The optimized equilibrium lattice constants and internal atomic positions for initial phase are listed in Table S1 of Supplementary Information. Theoretical lattice parameters for α -NaAB (ambient pressure phase) are in good agreement with the experimental values obtained in our measurements and data reported in the literature 13 . Next the geometry optimization of α -NaAB structure was performed with 1 GPa step in the pressure range up to 20 GPa. It was found the optimized structures at each particular pressure were described within Pbca space group. Analysis of the variation of the individual lattice parameters as well as cell volume with pressure, shown in Fig. 2, reveals one of the major findings of this work. Irregular changes of lattice parameters and unit cell volume indicate isosymmetric phase transition at 10 GPa to a new phase, which hereinafter will be called α / -NaAB. Moreover an abnormal expansion of unit cell is found along the c axis indicating negative linear compressibility (NLC). The magnitude of NLC can be compared by means of isothermal compressibilities K NLC = (∂ lnl/∂ p) T , defined in terms of the relative rate of change of length 'l' with respect to pressure. Further on our calculations demonstrate this material exhibits strong NLC with the magnitude K NLC = − 7.9(5) TPa −1 which is almost twice as much as values reported for the majority of materials with NLC 1-3 . Abnormal compressibility of NaAB is quite unexpected as its crystal structure reveal no characteristic feature, e.g., tilting/rotating polyhedra networks, helices, specific framework topologies -typically shared by known materials with NLC. We therefore proceeded with detailed analysis of the theoretically optimized structures in order to understand the mechanism of the phase transition calculated at 10 GPa and find out whether the predicted phase transition was of relevance to the changes experimentally observed in Raman spectra.
In At the same time, the length of N A ---H contacts became clearly shorter 2.5 Å suggesting possible commencement of stronger dispersive interactions. Pressure-induced changes of bond lengths should have direct implications for vibrational properties of material. We therefore perform comparative analysis for Raman spectra calculated for low-and high-pressure phases of NaAB. Calculated frequencies of Raman modes revealed a clear 'red' shift (frequency decrease) in the spectrum at pressure 10 GPa in comparison to those calculated at 9 GPa for both B-N and N-H stretching vibrations. Furthermore spectrum at 10 GPa features higher anisotropy of N-H bonds, where at least three signals from N-H stretching modes can be resolved instead of two calculated at 9 GPa (details of mode assignments for calculated spectra are presented in Figure S3 of Supplementary Information).
To further analyze the nature of chemical bonding we plot the variation of ∠ N D -H---N A angle with pressure (Fig. 4). Depending on hydrogen atom under consideration data for molecular fragments engaging H1 and H2 To probe the existence of hydrogen bonding in α / -NaAB, we calculated the charge density distribution (CDD) as well. Distribution of charge mapped within the plane parallel to a and b axes sliced across NH 2 groups for α -(at 9 GPa) and α / -NaAB (at 10 GPa) are displayed in Fig. 4. According to the calculated CDD dominating interaction between N and H atoms is a strong polarized covalent bond in both phases. At the same time, an increased charge density between the nearest N and H1 atoms belonging to neighboring NH 2 group indicates the possibility of the existence of hydrogen bonding in α / -NaAB, in contrast to low values of the electron density in interstices of the NH 2 groups found in α -NaAB.
Data presented in Figs 3 and 4 imply that the new phase, α / -NaAB, has rather strong N D -H---N A hydrogen bonds, engaging H1 type of hydrogen atoms, which account for the major changes in calculated Raman spectra. The formation of hydrogen bonds engaging H2 hydrogen atoms cannot be ruled out since the H---N A intermolecular distance (data set 2 in the Fig. 3(d)) reaches values < 2.5 Å at 10 GPa as well. However, gradual drop of ∠ N D -H---N A values (data set 2 in the Fig. 4(b)) indicates rather weakening of hydrogen bonds of this type with further pressure increase.
Following the spectroscopic changes observed both experimentally and computationally, the NLC mechanism of NaAB can be rationalized as follows. Hydrostatic compression leads to distance reduction (d NA---H ) between neighbour NH 2 groups which significantly enhance initially weak intermolecular interactions. At the pressure about 7 GPa the d NA---H distance approaches the critical value of 2.5 Å driving the formation of chains of weak hydrogen bonds. Compression to about 9 GPa leads to gradual evolution of weak hydrogen bonds to a moderate ones which is featured by both gradual increase of ∠ N D -H---N A angle values and gradual shortening of the d NA---H distance. Further enhancement of intermolecular hydrogen bonding is featured by an abrupt and substantial reduction of the d NA---H distance along with flattening of N D -H---N A fragments. Enhanced chemical attraction between neighbour molecular moieties results in elongation and thus weakening strength of B-N skeletal bonds which should be evidenced by the 'red' shift in Raman spectrum. Weaker B-N bonds facilitate rotation of NH 2 groups, corraborated by the steep increase of dihedral angle, in the plane perpendicular to N D -H---N A bond line which gives rise to negative linear compressibility of crystal along c axis (Fig. 5).
Similar character of observed changes in experimental Raman spectra, namely, the "redshift" of B-N and N-H stretching modes as well as the higher anisotropy of N-H stretching vibrations, strongly suggests the experimentally found phase transition at about 3 GPa is of the same origin with the computed one at 10 GPa. The discrepancy in the value of the phase transition pressure might stem from the fact that total-energy calculations were performed at zero temperature. The measured magnitude of the "redshift": ~14 and 45 cm −1 , is lower than the calculated one: 25 and 74 cm −1 for B-N and N-H stretching modes respectively. The magnitude of the N-H "redshift" is a measure of hydrogen bond strength. Assuming there is a linear dependence of the expansion rate along c axis on the magnitude of the N-H "redshift" the material exhibit one of the strongest NLC reported in the literature.
As a matter of speculation, the observed high-pressure behaviour of NaAB may have implications suitable for practical uses. Due to elongation of interatomic distance the strength of N-H bonds in α / -NaAB is expected to be lower than in α-NaAB. Therefore the weakening of N-H bonds may facilitate the hydrogen release from α / -NaAB. Considering the low pressure of αto α / -NaAB phase transition one may attempt recovering of α / -NaAB to ambient pressure through additional modification of chemical composition, i.e., either substitution or doping, like it has been demonstrated for materials based on cyanide framework 18,19 . Considering the narrow pressure range of the phase transition, perhaps, the most immediate application of NaAB, beside hydrogen storage, would be a pressure sensitive switchable component of a device using NLC. Similarly one can speculate certain modification of chemical composition may have beneficial effect on the magnitude of NLC through tuning subtle interactions in NaAB.
In conclusion, a comprehensive high-pressure study of structural properties of sodium amidoborane (NaNH 2 BH 3 , NaAB) was performed using in situ Raman spectroscopy measurements and density functional theory calculations. Particular attention was drawn to understanding the role of dispersive interactions in structural stability of NaAB. In our calculations the isosymmetric phase transition to α / -NaAB phase was found at 10 GPa. Experimental proofs of the transition were found at pressure about 3 GPa. The phase transition is accompanied by a strong negative linear compressibility (NLC) along crystal c axis. The first of its kind the mechanism of the observed NLC is controlled by the pressure-induced enhancement of dispersive interactions which leads to formation of hydrogen bonds. This work uncovers an example of intricate interplay between chemical interactions and mechanical response which opens up an exciting new direction for tailoring materials with rare functionality. Methods Sample preparation. We used the highest purity available substrates: NH 3 BH 3 (98%, JSC Aviabor), NaH (95%, Sigma Aldrich) and THF (99.9%, Sigma Aldrich). We synthesized sodium amidoborane (NaAB) in a direct reaction of ammonia borane with sodium hydride in solid state via a dry mechanochemical way described in the literature 13,20,21 , using tungsten carbide disk milling vessel together with a high energy mill from Testchem. All operations were carried out under argon atmosphere with no contact with atmospheric air, according to the reaction equations: NaNH BH H single 3 minutes milling In an alternative way we synthesized NaAB in a direct reaction of sodium hydride with THF solution of ammonia borane. We used dry THF as a solvent under argon atmosphere with no contact with atmospheric air, according to the reaction equations: NaNH BH  H   3  3  2  3  2 After the reaction the solvent was desorbed at room temperature under argon atmosphere.
Variable-pressure in situ Raman scattering measurements. Diamond anvil cell (DAC) with type-I diamonds of 500 μ m culet size was used for the high-pressure experiments. A stainless steel gasket was preindented to ~ 35 μ m thicknesses and then a hole of ~155 μ m in diameter was drilled in the center as a sample chamber. Polycrystaline sample, powder of NaAB, along with some ruby crystals (in form of sphere) for in situ pressure measurement, was loaded in the sample chamber inside the glovebox. Pressure was calibrated from the shift of Ruby fluorescence. Several series of measurements upon pressure loading and unloading course were performed. Except one run, no pressure medium was used in the sample chamber, because sample material is fairly soft. For comparison, one run of measurements was performed with mineral oil as a pressure medium. The results showed no noticeable difference in the high-pressure behavior of NaAB. Raman spectra of NaAB loaded in DAC were collected in backscattered geometry using custom disigned setup for micro-Raman measurements based on monochromator Jobin Yvon THR1000 (focal length 1000 mm) equipped with a single grating (with 1200 grooves mm −1 ) giving a resolution of ~1 cm −1 , notch filters (Keiser Optical Systems) and thermoelectrically cooled (− 75 °C) (Peltier effect) CCD (Horiba Synapse) detection. He-Ne laser (Melles-Griot) line 632.8 nm was used for sample excitation.

Details of ab initio calculations. The underlying ab initio structural relaxations and electronic calculations
have been carried out using density functional theory within the Perdew− Burke− Ernzerhof (PBE) exchange correlation as implemented in the CASTEP code 22 . Lattice parameters and atomic positions were optimized by seeking a total minimum energy based on density-functional theory and the plane-wave pseudopotential method. In order to perform the geometry optimization, the following thresholds were applied for a convergence window of two successive self-consistent steps: total energy change smaller than 5 × 10 −6 eV/atom, maximum force per atom below 0.01 eV/Å, pressure smaller than 0.02 GPa, and maximum atomic displacement not exceeding 5 × 10 −4 Å. The BFGS minimizer was employed to carry out the unit cell optimization. The quality of this basis set was kept fixed as the unit cell volume varied during geometry optimization. The cutoff energy of 770.0 eV for the expansion of the wave function into plane waves and fine Monkhorst− Pack k meshes have been chosen to ensure that all the energy calculations are well converged to required values.