What are some guidelines for metadynamic calculations

Nitrogen backbone oligomers


  • Chemical physics
  • Condensed Matter Physics


We found that nitrogen and hydrogen react directly to form chains of singly bonded nitrogen atoms at room temperature and pressures of ~ 35 GPa, with the rest of the bonds being terminated with hydrogen atoms - as demonstrated by IR absorption, Raman, X-ray diffraction experiments, and theoretical calculations. If pressures below ~ 10 GPa are released, the product converts to hydrazine. Our results could open a way for the practical synthesis of these extremely high-energy materials, since the calculations suggest that the formation of nitrogen-hydrogen compounds is favorable even at pressures above 2 GPa.


Nitrogen is a unique element in terms of its enormous difference in bond energy between nitrogen atoms bound by single (or double) bonds versus the very strong, short triple bond N≡N. This latter bond (−477 kJ mol −1 ) is one of the strongest known chemical bonds, while the NN bond is much weaker (−80 kJ mol −1 ) 1 . Because of this, many nitrogen compounds are high energy density materials (HEDM) that when decomposed potentially explosively into the most stable species - nitrous molecules 2 - release a large amount of energy. Full nitrogen crystal, the so-called "polymer nitrogen", became a three-dimensional crystal at very high pressures 1, 3 or as a disordered network of simply bound nitrogen atoms 4 formed . Chains of nitrogen atoms were also using 5, 6, 7 predicted. Polymeric nitrogen is considered to be a material that can ultimately store a large amount of chemical energy. Unfortunately, megabar pressures (100 GPa) are required to synthesize all nitrogen polymers. This excludes any practical application that should be in the pressure range of ~ 1 GPa or ideally ~ 0.1 GPa - the synthesis range of ammonia in the Haber-Bosch process.

Another route for high energy density nitrogen materials is to form nitrogen-hydrogen bonds. However, the weak single and double bonds prevent the easy formation of large molecules or polymers. Recent work has discovered molecules with a larger number of nitrogen atoms in a row: N5 8, N8 9 and N10 10 ; However, these compounds are either ionic or stabilized by carbon. Larger metastable polynitrogen molecules were predicted 11, but not yet found experimentally.

The use of very high pressures changes the chemistry of nitrogen dramatically, with a simple covalent bond being preferred. In the present work we investigated a synthesis of singly bound nitrogen-hydrogen compounds under high pressure with the idea that the addition of hydrogen could reduce the pressure required for the synthesis of new energetic materials and make them more stable compared to purely nitrogen-containing polymers. The nitrogen polymer was recently identified by ab initio evolutionary calculations 12 predicted: At pressures> 36 GPa, NH chains were formed from the ammonium azide precursor. Experimentally, these calculations do not seem to be supported, as ammonium azide works at pressures of at least ~ 55 GPa at room temperature 13 is stable, even a higher pressure is probably required for the polymerization. In principle, diimide (NH) 2, in which nitrogen atoms are double bonded, serve as a monomer, but it is very unstable and difficult to handle. Finally, hydrazine does not polymerize because we could not observe any qualitative changes in the IR and Raman spectra by increasing the pressure to 60 GPa and then releasing the pressure (Fig. S1).

Due to the apparent lack of nitrogen-hydrogen precursors, we investigated a direct reaction using molecular nitrogen and hydrogen as starting materials. Only a few studies are available on hydrogen-nitrogen mixtures under pressure. Changes in the Raman spectrum indicate that hydrogen is built into the nitrogen lattice and with the neighboring nitrogen atoms 14, 15, 16 interacts. An inclusion compound (N. 2 ) 12 D. 2 became from a 1: 9 D. 2 : N 2 -Mixture 16 observed . Ciezak et al. 15 examined a 1: 2 H. 2 : N 2 Mixture at room temperature and found evidence of chemical conversion when new bands appeared in Raman spectra assigned to bending and stretching of NN. On the other hand, molecular nitrogen and hydrogen vibrons were observed even at the highest pressures of 85 GPa, so that no clear conclusion could be drawn about the behavior of this mixture 15 . Recently, Spalding et al. 17 reported an amorphous nitrous network that ionizes ammonia at 50 GPa and room temperature in a 1: 1, 17 N 2 : H 2 -Mixture contained. Recent theoretical work on the N 2 / NH 3 -Mixture 18 have however demonstrated that the polymeric N 2 H can be stable above 33 GPa.

In this thesis we investigate H experimentally and theoretically 2 / N 2 -Mixtures at high pressures to detect the formation of nitrogen chains and identify the compounds formed.

Experimental results

We systematically have N 2 / H 2 - Mixtures with a wide range of nitrogen concentration ratios (5%, 10%, 20%, 50% and 80%) as well as pure nitrogen and hydrogen at pressures up to 70 GPa were examined. For all mixtures we have obtained consistent results and will illustrate the results that are common for different N 2 / H 2 Compositions were obtained. For example, the Raman spectra give way for the 1: 9-N 2 / H 2 Mixture at pressures of only ~ 10 GPa of those of pure nitrogen and hydrogen: the nitrogen vibron peak split (Fig. 1a) and two strong satellites of the hydrogen vibron were formed (Fig. 1c), which indicates that hydrogen and nitrogen are mixed and strongly interact with each other. At these pressures, however, they remained in the molecular state because the vibron excitations in the Raman spectra persisted.

( a ) Raman vibron of nitrogen in the N 2 : H 2 1: 9 mixture. The spectra are shifted vertically for better comparison. Note that Raman signals at pressures of 47 and 52.3 GPa are very weak and therefore amplified three and ten times, respectively. Red lines are the spectra of pure nitrogen. ( b ) Pressure dependence of the Raman vibron on nitrogen in 1: 9 N 2 : H 2 -Mixtures compared to pure nitrogen (red dots and lines). ( c ) Development of hydrogen vibrons under pressure at 1: 9 N 2 : H 2 -Mixture. ( d ) Comparison of Raman vibrons by H. 2 in 1: 9 N. 2 : H 2 -Mixture (black circles and squares) with IR 24- Vibrons (red dashed line) and Raman vibrons (red squares) of pure H. 2 and IR vibrons (red stars) from H. 2 in 1: 4 N. 2 : H 2 -Mixture.

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Above ~ 35 GPa, one major change occurs: the intensity of H 2 - and N 2 Raman vibrons decreases sharply and then even disappears at ≅ 50 GPa (Fig. 1a - d, Fig. S2, S3). This transformation is accompanied by a strong reduction in volume, which is indicated by the automatic decrease in pressure over time at high pressure (Fig. S3b). The new phase is amorphous because the X-ray diffraction pattern disappears at pressures above ~ 50 GPa (Fig. S2c, d).

IR spectroscopy gave us several clues as to the nature of the new phase. First is the strong absorption band at 3300 cm −1 (Fig. 2a) characteristic of NH vibrational elongation modes, indicating that the high pressure conversion involves a chemical reaction between nitrogen and hydrogen. Second, when the pressure is released below ~ 10 GPa, the product converts strongly to hydrazine as it is clearly identified by the IR and Raman spectra (Fig. 2b and 3) 19 . This conversion indicates that the product is related to hydrazine. The lack of a torsion mode at ~ 600 cm −1 and a wobble mode at ~ 1300 cm −1 (Fig. S4), however, suggests that longer molecules than hydrazine may be synthesized. However, an exact identification of such a disordered chain-length material with spectroscopic and X-ray data alone is not possible, since the product is apparently a disordered mixture of different molecules, which leads to the broad IR and Raman spectra (Figs. 2 and 3). and the diffuse X-rays.

( a ) Infrared absorption spectra of N 2 : H 21 : 19 mixture with a pressure increase at 300 K. A broad absorption band around 3300 cm –1 appeared at 38 GPa (or 35 GPa in other runs with different mixtures). The oscillations in this spectrum are due to light interference between parallel diamond anvil spheres. The spectrum below (blue line) is the calculated total absorption of oligomers from N3 to N6 chains in the gas phase. The peaks are sharp and narrow because there are no broadening interactions with the bulk material. Gas phase spectra of individual molecules and details of the calculations are shown in Figures S9 - S16. ( b ) IR spectra of the 1:19 N 2 : H 2 Mixture at a release pressure after polymerization of 300 K. The spectra did not change qualitatively with a pressure of up to ~ 10 GPa. Below this pressure, the spectra are identical to those of hydrazine (Fig. S4) and according to Ref. 19 . It should be noted that the comparison of the spectra for the 1: 4 and 1: 1 N 2 : H 2 -Mixture with the spectra of pure hydrazine is shown in Fig. S4.

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( a ) Raman spectra of a 1: 4 N 2 : H 2 -Mixture at the pressure generated after the reaction. At the highest pressures, the Raman spectra only show broad bands around 3200 cm −1 and 4200 cm −1 . At pressures below ~ 10 GPa, these bands developed into sharp peaks known as hydrazine 19 and hydrogen 24 have been identified. The increase in the intensity of the hydrazine peaks is accompanied by a decrease in the intensity of the hydrogen vibrons, as shown in ( b ) for the mixture N 2 : H 2 1:19 is shown in detail. Hydrazine decomposes to produce hydrogen and ammonia by lowering the pressure below 2 GPa before opening the cell, as can be seen from the sharp characteristic spectra.

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Theoretical calculations

In order to gain further insights into the possible nature of the amorphous high-pressure phase formed in the hydrogen-nitrogen mixture, we carried out theoretical calculations based on two different approaches: Metadynamic calculations 20, 21 to simulate structural changes in the mixture and quantum chemical calculations to investigate the energetics and the spectrum of hydrogen-nitrogen molecules.

Metadynamics simulations were performed at 300 K for a 1: 4 ratio of N. 2 : H 2 performed in an initial mixed molecular arrangement (4a). At 30 GPa, no apparent structural changes or reactions were observed after 100 metastases, which is typically long enough to model phase transitions in good agreement with our experimental results. When compressed to 60 GPa, a reaction between nitrogen and hydrogen was found to stabilize four types of hydrogen nitrogen compounds: H. 2 N-NH 2 (Hydrazine), H. 2 N-NH-NH-NH 2 (N4-II), H. 2 NN = NNH 2 (marked with N4-I) and H. 2 NNH-N (NH 2 ) -NH-NH 2 (N6) in a ratio of 7: 3: 1: 1. Its formation is associated with a large gain in enthalpy, about –298 kJ mol –1 per N 2 H 8 -Formula unit (corresponding to the 1: 4 N 2 : H 2 Mixture) compared to the reference value N 2 (R

c structure) and H 2 (P 6 3 / m) (Fig. 4c). The formation of nitrogen-hydrogen compounds is favorable even at pressures above 2 GPa. However, there is a large kinetic barrier to polymerization while it is quite difficult to gauge its value. We have calculated the electronic band structure and density of states of NH compounds at 60 GPa. The results showed that the formed NH compounds with a band gap of ~ 3.7 eV (Fig. S5) are insulating and not a metal that was predicted for a chain, just made up of nitrogen atoms 5, 6, 7 consists . Higher temperatures favor polymerisation: at 500 K, longer chains are formed in larger quantities (Fig. S6).

The initial ( a ) and predicted ( b ) Structures of N 36 H 144 at 60 GPa and 300 K are displayed. Large and small spheres denote nitrogen and hydrogen atoms, respectively. ( c ) Calculated enthalpy of formation of the NH compound in relation to the elemental decomposition into solid hydrogen (P6 3 / m) and nitrogen (R-3c) at 0 K and high pressures. ( d ) Ball-and-stick representation of N 10 H 12 to Illustration of the low energy spiral backbone structure.

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Our quantum chemical calculations are based on the theoretical level M06-2X / aug-cc-pVDZ (see methods and the complete description in the SI). We note that the azanes, the systematic class of the N n H n + 2 Compounds analogous to the carbon-based alkanes, in qualitative agreement with the above ab initio calculations, are energetically stable compounds even at zero pressure (Fig. 4). They have precisely defined minima on the potential energy surface and can therefore exist as separate compounds, even if their thermal life is currently unknown. This is also true with references to the literature 22 match. Linear, unbranched polymer chains, NH 2 - (NH) n -NH 2, have been studied for up to N10. In contrast to hydrocarbons with a linear backbone, the most stable conformer of the azanes is a spiral-shaped nitrogen backbone due to the interactions between the lone pair of electrons and the bonds on the nitrogen atoms (Fig. 4). Your enthalpy of formation, based on N 2 and H 2, increases with each additional NH monomer by about 84 kJ mol −1which makes azanes high-energy materials with an energy density comparable to polymeric nitrogen.

The longer azanes were found to be less thermally stable than hydrazine. The thermal cracking of hydrazine requires more than 250 kJ mol −1 and forms two NH 2 -Radical. For larger chains> N4, only 125 kJ mol are required to break the internal NN bonds −1 required, resulting in more stable -N H radicals leads. This could indicate that longer azanes have a greater tendency to decompose into smaller compounds, although the predicted barrier at 300 K still offers long thermal lifetimes. The complete quantum chemical characterization of this chemistry would go beyond the scope of this work.


The combination of the experimental data with the theoretical predictions leads to further insights into the possible structure of the amorphous phase formed at high pressures. The metadynamic calculations show that longer NH chains than hydrazine can be formed. The quantum chemical calculations of the enthalpies of formation show that the enthalpies of formation per NH unit are very similar over longer azane chains. This suggests that if hydrazine can be formed, there is no undue energetic limitation on the formation of longer azanes. When the pressure is relieved, the weaker internal nitrogen-nitrogen bonds loosen more easily and enable a rearrangement in the direction of shorter chains. This process is terminated by the formation of hydrazine, which only has a stronger terminal H. 2 N-NH 2 -Binding contains. This decomposition hypothesis is supported experimentally: First, when the pressure is released from 50 GPa, the broadband spectra in the IR and Raman spectrum sharpen, which could indicate a gradual conversion of longer chains into shorter ones. In addition, hydrazine clearly dominates the IR and Raman spectra below 10 GPa (Fig. 2b and 3, Fig. S4, S7). Second shows the intensity of Raman-H 2 -Vibrons shows a decrease which is associated with the significant increase in the hydrazine lines in the Raman spectrum (Fig. 3b, Fig. S7).

We compare the theoretically predicted spectra for azane mixtures (Fig. 2, Fig. S9-S16) with the experimental data (Fig. 2a, Fig. S4) and find interesting similarities. First, the spectra say a band of NH stretching vibrations around 3500 cm –1 ahead. For hydrazine this peak is well structured, while in larger azanes this peak broadens due to the greater variety of NH units, with the positioning in the chain, the branching and the folding of the chains influencing the individual NH stretching modes. Compared to the high pressure spectra, the predicted peaks are neither as broad nor as intense, but this may be related to intermolecular interactions in the matrix. The same consideration applies to a band around 1650 cm −1that as NH 2 -Deformation mode is calculated. It was found that this peak is noticeable in the spectra of all azanes from N2 to N10 and, for more complex mixtures, broadens as a function of conformer folding, branching and chain length.Finally there are two broad peaks, 1500–700 cm −1 and under 700 cm −1which agree reasonably well with the observed spectrum. These modes cannot easily be assigned to specific movements, as they often contain larger skeletal vibrations. Also cyclic azanes, N n H n, were investigated. However, these lack the pronounced NH 2 - Deformation peak around 1650 cm −1 and they can therefore only make up a small proportion of the products.

It has been shown experimentally that the formation of singly bonded hydrogen-nitrogen compounds occurs at room temperature and pressures of about 35 GPa, which opens up new avenues for the synthesis of these high-energy materials. Compared to other high-energy materials such as polymeric nitrogen, where polymer formation occurred at 150 GPa, the pressures required for synthesis are significantly lower. The polymerization pressure could be further reduced dramatically, since the formation of the oligomer chains is energetically favorable at pressures of only 2 GPa (FIG. 4c) according to the ab initio calculations and even at zero pressure according to the quantum chemical calculations. Raising the temperature is one of the ways to overcome the kinetic barrier of the reaction. Instead of pressure like at room temperature, we changed the temperature at a certain pressure. The conversion was monitored based on the disappearance of the hydrogen vibron. Indeed, the pressure required to form the new phase decreases sharply with temperature (Fig. S8), as we did when examining a 1: 1 N 2 : H 2 - have detected the mixture. The IR absorption spectra were recorded after cooling to room temperature to verify the conversion. The pressure of the conversion decreases approximately linearly with the temperature. Due to the hydrogen diffusion from the sample through the metal seal, we were unable to reach higher temperatures. However, a problem associated with high temperatures is the formation of ammonia. Even at room temperature, in some cases we observed a small area of ​​ammonia on the edge of the steel gasket (which is a catalyst). The problem of separating the NH oligomers and ammonia and the search for suitable catalysts for the high temperatures has yet to be solved. We believe that another method - ultraviolet illumination - might be effective for the practical synthesis of the NH oligomers at room temperatures and atmospheric or low pressures. For example, UV radiation from an excimer laser with a wavelength of 193 nm (~ 6.4 eV) N 2 - and H 2 - Stimulate molecules to higher energy states through one or two photon absorption or break their bonds. The practical implementation of the synthesis appears to be feasible with a complexity that is comparable, for example, with the Haber-Bosch process for ammonia synthesis.


We filled the diamond anvil cell with nitrogen-hydrogen mixtures using a gas charger at pressures of ~ 1500 bar. Typically we used a T301 steel seal. We checked whether this material, which contains ~ 70% Fe, 17% Cr and 7% Ni, acts as a catalyst for the N. 2 : H 2 -Mixture can act. For this we used an insert made of NaCl and cleaned the surface of diamonds from the rest of the sealing material. We got the same results as with the metal gasket at room temperature.

We used synthetic type IIa diamonds for IR examinations and type Ia diamonds with low luminescence for Raman examinations. The Raman spectrometer was equipped with a nitrogen-cooled CCD, blocking filters and edge filters. The 632.8 nm line from a He-Ne laser and the 647.1 nm and 676.4 nm lines from a krypton laser were used to excite the Raman spectra. Low temperature measurements were carried out in an optical cryostat. IR measurements were made using a Bruker IFS-66 V FTIR spectrometer equipped with a KBr beam splitter and a global mid-infrared source. X-ray diffraction measurements were collected in the European Synchrotron Radiation Facility (ESRF, Beamlines ID27) and the Extreme Conditions Beamline at PETRA III in DESY (Germany). The pressure was determined from the shift in the high frequency edge of the Raman spectrum caused by the cocked tip of the diamond anvil 23 or with a ruby ​​knife 24 was recorded. The diamond anvil cell was heated with the aid of an external heater; The monitored pressure did not change significantly.

Quantum chemical calculations were made at the theoretical DFT level using the M06-2X functional 25 carried out in conjunction with the aug-cc-pVDZ basic set. This theoretical level is expected to be sufficiently accurate to analyze trends in properties over chain length. Sampling calculations were performed for hydrazine at a higher level, which found that the differences were not significant for our current purpose. All calculations were carried out with the Gaussian 09 program suite.

In the present study, the metadynamics method 20, 21 with the projector augmented plane wave method (PAW method 26 ) as they are in the Vienna ab initio Simulation Package (VASP) code 27 is implemented. A PAW potential with a Perdew-Burke-Ernzerhof 28- Exchange correlation functional was assumed. The simulation cells were constructed using 18 nitrogen and 72 hydrogen molecules, and the Brillouin zone was scanned with a Γ point approximation. The canonical (NVT) ensemble was used for molecular dynamic runs. Each metastages of the metadynamics simulation comprised 600 time steps of 1.0 fs. Extensive metadynamic simulations with typically 100 metastages for each simulation were carried out at pressures and temperatures of 30–60 GPa and 300–500 K, respectively. The width and height of the Gaussian bias potentials were δ = 30 (kbar Å 3 ) 1/2 or W = 900 kbar Å 3 . The metadynamic method 20, 21 is able to overcome barriers and thus investigate a wide range of candidate structures at finite temperatures. Successful applications of the method include several examples of reconstructive structure transitions 29, 30, 31 .

For the underlying structural relaxations from the beginning, a limit value for plane wave energy of 600 eV was used. The k-point scan of 4 × 3 × 4 for N 2 H 8, 7 × 7 × 7 for N 2 (R -3 c) or 9 × 9 × 10 for H 2 (P 6 3 / m) were used to ensure that all enthalpy calculations converge well.

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