Theoretical Insights on the High Pressure Behavior of Pentazolate Anion Complex [Co(H2O)4(N5)2]·4H2O

Periodic dispersion corrected density functional theory (DFT) calculations were carried out to examine the Hirshfeld surface, two dimensional (2D) fingerprint plots, crystal structure, molecular structure and density of state of all-nitrogen pentazolate anion complex [Co(H2O)4(N5)2]·4H2O under hydrostatic pressure from 0 to 20 GPa. The GGA/PW91-OBS method was applied in the present study. The intercontacts in [Co(H2O)4(N5)2]·4H2O were analyzed by Hirshfeld surfaces and 2D fingerprint plots. With ascending pressure, the lattice constants, compression rates, bond lengths, bond angles, and density of states change irregularly. Under 11.5, 13.0 and 15.8 GPa, covalent interaction competition is obvious between Co−N and Co−O bonds. It is possible to achieve orderly modification and regulation of the internal structure of [Co(H2O)4(N5)2]·4H2O by applied pressure. This is in accordance with the results from density of states analysis. The external compression causes the nonuniformity of electron density and the differential covalent interaction between pentazolate anion, coordinated water and atom Co. It is of great significance to interpret inter/intramolecular interaction and structural stability of [Co(H2O)4(N5)2]·4H2O and provide theoretical guidance for the design of metal complexes of all-nitrogen pentazolate anion.

www.nature.com/scientificreports www.nature.com/scientificreports/ Despite several studies have reported the synthesis and characterization of cyclo-N 5 − complexes, the underlying and practical problems of metal complexes of cyclo-N 5 − are still unclear due to the complex chemical behavior. For example, various behavioral studies have not yet been involved under different pressures. It is crucial to investigate the internal structure within a range of pressures, particularly under high pressure. The reason is that the shockwave with large velocity can produce up to 50 GPa of pressure during detonation process 19,20 . Explosives undergo phase transition and decomposition under these extreme conditions. Therefore, the investigation of metal complexes of cyclo-N 5 − under high pressure is significant for the understanding of inter/intramolecular interaction and structural stability. In addition, it also provides better theoretical guidance and early paving for the design and development of metal complexes of cyclo-N 5 It is a challenging work to study the microscopic properties of metal complexes of cyclo-N 5 − . Compared with the experimental work, theoretical calculation is a powerful tool to analyze inter/intramolecular interaction and structural stability in physical and chemical fields under high pressure 21,22 . The effect of high pressure on the geometrical and electronic structures of cocrystal NTO/TZTN has been explored by us under hydrostatic pressure of 0-80 GPa 21 . Based on the application of density functional theory (DFT) method with pseudopotentials  (Materials Studio 6.0, https:// www.3dsbiovia.com/products/collaborative-science/biovia-materials-studio/). and a planewave of basis set, the investigation of the relationship between structure and stability was favorably achieved under high pressures. In this study, under the external pressures of 0−20 GPa, the periodic DFT investigation of pressure effect was performed on Hirshfeld surface, two dimensional (2D) fingerprint plots, density of state, crystal and molecular structures of [Co(H 2 O) 4 (N 5 ) 2 ]·4H 2 O.

Results and Discussion
Hirshfeld surface and 2D fingerprint plots. Hirshfeld surface analysis and 2D fingerprint plots describe the types and regions of intercontacts in crystal stacking, which can explore explicit inter/intramolecular atomatom close contacts and provide a measurable value to the fraction of a special close contact 23,24 . The structure a from experimental crystal [Co(H 2 O) 4 (N 5 ) 2 ]·4H 2 O serves as the input file. The relative contributions to Hirshfeld surface for the close contacts are illustrated by Fig. 2. It is obvious that the fractions of H···H (22.0%), H···N (27.2%), O···O (15.1%), N···H (13.9%), and O···H (9.2%) contacts are more than those of other contacts. The H···N, N···H, and O···H contacts display the spike features in Fig. 2, considering to hydrogen bond interactions 23 , which play an important role in the stability of the whole system. The shortest distance of H···N and O···H are 3.00 Å and 2.15 Å, belonged to weak and medium hydrogen bond, respectively 23,25 . The O··O contact is not conducive to the stability of system, which lead to the increasing repulsion. Therefore, for crystal design, avoiding or reducing O··O contact is helpful to reduce the total energy of system. Figure 3 exhibits the Hirshfeld surfaces of structure a under 0, 10, and 20 GPa. At 0 GPa, the blue regions predominate on Hirshfeld surfaces. As the pressure increases to 20 GPa, the blue area decreases and the red area increases, which indicated that the relative contributions to Hirshfeld surface for the closer contacts increase with ascending pressure. Actually, with ascending pressure, the molecules are getting closer and closer to achieve the reduction of structural spaces, increasing the intermolecular interactions, which demonstrate that a theoretical insight to investigate the structural response is obtained by Hirshfeld surface analysis under an applied pressure.
To elaborate information on the Hirshfeld surface in detail, the corresponding contributions of close contacts under 0, 10, and 20 GPa are pictured in Fig. 4. The relative contributions of H···N and N···H contacts increase from 22.8% to 28.6% and from 9.3% to 14.1%, respectively, under the whole pressures. In contrast, the contributions of H···O and O···H contacts decrease to 1.7% and 10.3%, respectively. These observations indicate that hydrogen bonds are the main interactions between N, O and H atoms. The existence of hydrogen bonds O−H···N ensure the planarity and conjugation of pentazolate anion rings. In addition, the hydrogen bonds O−H···O further achieve the maximum bonding between constitution water and coordinated water to ensure the minimum energy, which is in line with the results from experimental results 8 .
External pressure is essential to the formation of hydrogen bond interaction. From the above analysis, it can be seen that pressure is more conducive to the formation of O−H···N hydrogen bonds between pentazolate anion and constitution water. The reason is that the larger space, the easier compress, which match well with the reduction of blue area on Hirshfeld surfaces. Another obvious change is that O···O contacts are almost negligible under external pressure, thus avoiding space repulsion to a large extent. At 0 GPa, the H···N and O···H contacts are 2.26 and 1.78 Å, respectively, while those are 1.87 and 1.51 Å, respectively, at 20 GPa indicating that the hydrogen bonds shorten, but the O···H contacts is less compressible than H···N contacts under the pressure ranging from 0 to 20 GPa.   The reason is that as the bond length of Co1−O1 decreases, the distance between two oxygen atoms becomes closer and closer, and the repulsion increases. Besides the covalent interaction competition between Co−N and Co−O bonds, the repulsion between oxygen atoms also has a great influence on the stability of system. In the whole pressure range, the pentazolate anion rings and Co atoms maintain favorable planarity and conjugation, which contribute greatly to the stability of system, but with the increase of pressure, steric hindrance increases. The hydrogen bond interactions of N2···H1 and O5···H9 increase generally from 0 to 20 GPa. The change of other N···H and O···H hydrogen bonds is consistent with those of N2···H1 and O5···H9, respectively. This is mainly due to the increasing closeness between pentazolate anion, coordinated water and constitution water under external pressure.
Density of state. The total density of state (DOS) and partial density of state (PDOS) were investigated for a detailed explain on the electronic structure of [Co(H 2 O) 4 (N 5 ) 2 ]·4H 2 O under various pressures 29 . Figure 6 displays the calculated total DOS and PDOS for Co atoms, pentazolate anion and coordinated water. From Fig. 6, the higher the pressure, the wider peak of DOS curve, which illustrates that the electrons move freely between valence and conduction bands. The crystal compression causes the better mobility of electrons and stronger delocalization of system. Under the applied pressure, the conduction bands shift to the lower energy, which reduces the band gap and increases the possibility of electron excitation. From −25 to −2.5 eV, the DOS is mainly composed of pentazolate anion and coordinated water. In contrast, from −2.5 to 2.5 eV, Co atom and pentazolate anion contribute to the DOS. It is indicated that the delocalization of pentazolate anion results in the appearance of electrons in the whole energy bands.
From 11.0 to 11.5 GPa, at the Fermi energy level, the PDOS peaks of pentazolate anion and coordinated water increase 0.017 and 0.790 electrons·eV −1 , respectively, meaning that the change of electron density between atoms Co and O is higher than that between atoms Co and N. This is consistent with the result that the Co−O covalent interaction predominates in the competition between Co−N and Co−O bonds. When the pressure reaches 13.0 GPa, at the Fermi energy level, it is noticeable that the PDOS peaks of pentazolate anion and coordinated water increase 0.246 and 0.124 electrons·eV −1 , respectively. The electron density between atoms Co and N varies greatly. Under hydrostatic pressure from 13.0 to 15.8 GPa, at the Fermi energy level, the PDOS peaks of Computational details. The first-principle computations were carried out based on the application of density functional theory (DFT) method with the Vanderbilt-type ultrasoft pseudopotential 30,31 implemented in Materials Studio's CASTEP module 32,33 . The cutoff energy of plane waves and k-point grid were set to 500 eV and 2 × 2 × 3, respectively. The total energy, residual force, displacement of atoms, and residual bulk stress were converged less than 1.0 × 10 −5 eV, 0.03 eV·Å −1 , 0.001 Å, and 0.05 GPa, respectively. The experimental crystal was taken from Lu et al. (CCDC 1527750) 8 . The [Co(H 2 O) 4 (N 5 ) 2 ]·4H 2 O crystallize in orthorhombic space group Fmmm (Fig. 1).
Hirshfeld surface and two dimensional (2D) fingerprint plots were presented and analyzed by Crystal where d i and d e mean the distances from the surface to the nearest atom inside and outside the surface, respectively; r i vdw and r e vdw mean the van der Waals (vdW) radius of two atoms inside and outside the surface, respectively. The d norm was mapped on Hirshfeld surface with colors range from −0.461 Å (red) to 1.526 Å (blue). The 2D fingerprint plots were generated through Hirshfeld surfaces, which displayed the dimensional summary of intermolecular interactions for the close contacts.

Data availability
The data that support the findings of this study are available from the corresponding authors on request.