Pressure-induced formation of hydrogen bonds in KNH₂ studied by first principles

Abstract

Using particle swarm optimization technique implemented in the CALYPSO code, we have performed systematic research for the structures of KNH₂ at pressures up to 20 GPa. Here, phase transition from the ground-state α-KNH₂ (monoclinic P2₁/m) to β-KNH₂ (monoclinic P2₁) occurs at 4 GPa; then, with pressure increasing up to 6.8 GPa, β-KNH₂ transforms into γ-KNH₂ (monoclinic Pc). By analyzing the partial density of states and charge density, ionic bonding nature between K⁺ and [NH₂]⁻ is revealed and there exists a strong covalent bonding between N and H atoms in NH₂ groups in the three structures. Moreover, N–H⋯N hydrogen bonding between neighboring NH₂ groups is suggested in β- and γ-KNH₂ by investigating the structural details and charge density, which could be favorable for accelerating dehydrogenation behavior of complex metal hydrides.

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1. Introduction

Great effort has been devoted to developing safe, efficient, and reversible hydrogen storage materials such as boronhydrides M(BH₄)_n,^1,2 alanates M(AlH₄)_n,^3,4 and amides M(NH₂)_n.^5,6 These complex metal hydrides have been considered the promising materials for hydrogen storage due to their innately high hydrogen content. However, many fundamental scientific and technological challenges still remain, such as hydrogen desorption under near-ambient conditions.^7–10 Due to strong metal–hydrogen bonding (B–H, Al–H, and N–H) in the anion subunits (i.e., BH₄⁻, AlH₄⁻, and NH₂⁻), these metal hydrides are so stable that releasing hydrogen can only be achieved at elevated temperatures. Therefore, accelerating the dehydrogenation behavior of the light complex metal hydrides has great scientific and practical significance in this field. Doping with Ti in NaAlH₄ has been considered as reversible with respect to hydrogen absorption/desorption.¹¹ Otherwise, improvement of the hydrogen reversibility of NaAlH₄ has been also achieved by ball milling experiments.¹² Recently, Vajeeston et al.⁴ have performed a theoretical study of NaAlH₄, which indicates high pressure could accelerate dehydrogenation kinetics accompanied with the structural changes. Thus, exploring high pressure structures is necessary for complex metal hydrides.

Alkali amides have become the scientific focus as hydrogen storage materials. LiNH₂ has been considered a potential complex hydride proposed by Chen et al.^7,13–16 The ambient structure of α-LiNH₂ phase with I4̄ symmetry initially transforms into a monoclinic β-LiNH₂ phase with P2₁ symmetry confirmed by experimental works.¹⁷ Meanwhile, the structure of γ-LiNH₂ phase with hydrogen bonding between the neighboring NH₂ groups has been predicted by theoretical and experimental studies under high pressures.¹⁸ Recently, sodium amide (NaNH₂) has also attracted considerable attention, although its theoretical hydrogen capacity is only ∼5.1 wt%.¹⁹ Under ambient conditions, α-NaNH₂ crystallizes in an orthorhombic lattice with the space group Fddd.²⁰ With the pressure increasing, α-NaNH₂ transforms to β-NaNH₂ (space group P2₁2₁2) phase at 2.2 GPa and then to γ-NaNH₂ (space group C2/c) phase at 9.4 GPa.^21,22 As the same as γ-LiNH₂ phase, existence of hydrogen bond has been conformed in the high pressure phases of NaNH₂.²² As for potassium amide (KNH₂), the ambient structure has a monoclinic phase (hereafter, α-KNH₂, space group P2₁/m).²³ However, the crystal structures of high pressure phases have not been observed. Besides, it is still an unknown question whether the high pressure phases of KNH₂ have more favorable properties than ambient structure such as the existence of hydrogen bond. Hydrogen bond is expected to weaken the N–H polar covalent bonds in amides ions and can accelerate dehydrogenation behavior, which prompts the candidate promising as hydrogen storage materials for complex metal hydrides.

In the present work, we perform the systematic research for high-pressure structures of KNH₂ by using particle swarm optimization technique implemented in the CALYPSO code and density functional theory (DFT). Here, we predict two new structures at different pressures that never reported, and discuss their structures, structural stability, electronic structures and chemical bonding.

2. Computational methods

The high-pressure structure searches for KNH₂ were explored by using the particle swarm optimization technique implemented in the CALYPSO code.^24,25 The simulation method has been successfully used to investigate the structures of a great variety of materials^26–29 at high pressures. In our calculations, ab initio structure relaxations were performed using density functional theory^30,31 within the Perdew–Burke–Ernzerhof (PBE) parameterization of the generalized gradient approximation (GGA),³² which is implemented in the Vienna ab initio simulation package (VASP).³³ The projector augmented wave potentials³⁴ were used to describe the ionic potentials with valence electrons of 3s²3p⁶4s¹, 2s²2p³ and 1s¹ for K, N and H atoms, respectively. The cutoff energy (1000 eV) for the expansion of the wave function into plane waves and a Monkhorst–Pack kmesh³⁵ of 0.03 × 2π Å⁻¹ were chosen to ensure that all the enthalpy calculations are well converged to better than 1 meV per atom. The convergence tests have been described elsewhere.^36–39 The elastic constants was calculated using density functional theory within the (PBE) parameterization of the (GGA)³² as implemented in the Vienna ab initio simulation package CASTEP code.⁴⁰ Vanderbilt ultrasoft pseudopotentials⁴¹ were generated for K, N, and H with the valence configuration of 3s²3p⁶4s, 2s²2p³ and 1s¹, respectively. Convergence tests concluded that suitable values would be a 1000 eV kinetic energy cutoff and a Monkhorst–Pack (MP) k-point mesh of 0.03 × 2π Å⁻¹ for the electronic Brillouin zone (BZ) integration. Phonon dispersion of the structures predicted was obtained using direct supercell method⁴² with the PHONOPY code.⁴³

3. Results and discussion

CALYPSO structure predictions are performed for simulation cells containing up to 4 unit cells at pressures range from 0 to 20 GPa. Besides, the earlier predicted structures of LiNH₂ and NaNH₂ are considered in our structural searching. The ground-state α-KNH₂ is successfully obtained at 0 GPa. Other five energetic competing structures are detected in our structure searches with different unit cells. They are, namely, orthorhombic Amm2, orthorhombic P2₁2₁2, monoclinic P2₁(1) (β-LiNH₂ structure), monoclinic P2₁(2) (2 f.u. per cell), and monoclinic Pc structures as depicted in Fig. 1. Except for monoclinic P2₁(1) (β-LiNH₂ structure), NH₂ amide group in all proposed structures are orientational order. In the Amm2 structure, the NH₂ groups arrange in the same orientation and a layer of K⁺ ions is inserted between two NH₂ layers. The ordered NH₂ groups in different orientations appear in P2₁2₁2, monoclinic P2₁(2), and Pc structures. Moreover, we can see that the orientations of two adjacent NH₂ molecules are opposite and K⁺ ions are surrounded by NH₂ molecules in the three structures.

Fig. 1 Crystal structures of competing KNH₂ phases: (a) orthorhombic Amm2, (b) orthorhombic P2₁2₁2, (c) monoclinic P2₁ β-LiNH₂-type, (d) monoclinic P2₁, (e) monoclinic Pc. The pink, blue and black spheres represent K, N and H, respectively.

For exploring the stability of the structures, the free energies of competing phases must be investigated. In our work, all total-energy calculations are performed at zero temperature. Therefore, the Gibbs free energy becomes equal to the enthalpy, H = E₀ + PV, where E₀ is the internal energy of the system. Fig. 2 displays the calculated enthalpy difference (ΔH) relative to α-KNH₂ as a function of pressure. Below 4 GPa, α-KNH₂ is the most stable structure. With the pressure increasing, the first phase transition from α-KNH₂ to P2₁(2) (hereafter, β-KNH₂) occurs at 4 GPa. Above 6.8 GPa, the Pc phase (hereafter, γ-KNH₂) becomes the most stable until 20 GPa. Our results show that two phase transformations occurs at 4 GPa and 6.8 GPa, respectively, in which the zero point energy (ZPE) has not been included. It is known that the effect of ZPE plays a non-negligible role in the total energy of the hydrogen rich materials, but the relative ordering of the structures is not influenced by the ZPE in our calculations. As shown above, we can see that a decrease in symmetry of KNH₂ with pressure, which is very similar to the high-pressure behavior of the related compounds LiNH₂ (I4̄ → Fddd → P2₁2₁2) and NaNH₂ (Fddd → P2₁2₁2 → C2/c). The pressure–volume relation of KNH₂ is derived by fitting the third-order Birth–Murnaghan equation of state⁴⁴ as shown in Fig. 3. The α → β and β → γ phase transformations for KNH₂ are accompanied by large volume shrinkages of 5.0% and 3.8%, respectively. Volume discontinuous under high pressures indicates the two phase transformations for KNH₂ are both the first-order phase transition.

Fig. 2 Calculated enthalpies relative to α-KNH₂ as a function of pressure for various structures.

Fig. 3 Calculated volume–pressure relationship for α-KNH₂, β-KNH₂ and γ-KNH₂.

It is importance of calculating the phonon spectra of a crystal for further confirming the dynamical stability of the structures predicted. Fig. 4 lists the phonon dispersion curves for β-KNH₂ and γ-KNH₂ at 5 GPa and 8 GPa, respectively. No imaginary phonon frequencies are observed, which indicates the β-KNH₂ and γ-KNH₂ is dynamically stable. The calculations of the elastic constants are essential, which can help to provide valuable information for the mechanical stability of a structure. The well-known mechanical stability criteria⁴⁵ for monoclinic system is:

C₁₁ > 0, C₂₂ > 0, C₃₃ > 0, C₄₄ > 0, C₅₅ > 0, C₆₆ > 0,

[C₁₁ + C₂₂ + C₃₃ + 2(C₁₂ + C₁₃ + C₂₃)] > 0,

(C₃₃C₅₅ − C₃₅²) > 0, (C₄₄C₆₆ − C₄₆²) > 0, (C₂₂ + C₃₃ − 2C₂₃) > 0

Fig. 4 Calculated phonon dispersion curves for high-pressure phases: (a) β-KNH₂ at 5 GPa, (b) γ-KNH₂ at 8 GPa.

The independent elastic stiffness constants of the β-KNH₂ and γ-KNH₂ are shown in Table 1, which indicates the mechanical stability of the two phases.

Table 1 Elastic constants C_ij (GPa) for β-KNH₂ at 5 GPa and γ-KNH₂ at 8 GPa

	C11	C22	C33	C44	C55	C66	C12	C13	C15	C23	C25	C35	C46
β-KNH2	48.1	59.7	53.9	16.9	16.4	23.1	32.8	25.3	6.3	30.8	−0.9	−3.7	1.3
γ-KNH2	93.6	94.2	93.0	20.1	21.8	35.2	39.3	24.7	−0.1	23.1	−0.1	0.5	−3.6

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Table 2 summarize the optimized equilibrium crystal structural details for α-(0 GPa), β-(5 GPa) and γ-KNH₂ (8 GPa). The characteristic geometries of amide ions in α-(0 GPa), β-(5 GPa) and γ-KNH₂ (8 GPa) are shown in Fig. 5. In α-KNH₂, each N–H bond length is 1.032 Å and H–N–H bond (∠_H–N–H) angle is 143.1° in NH₂ molecular. Two adjacent NH₂ molecules are parallel to each other and the intermolecular N⋯H distance is 3.112 Å, which is larger than the sum of the van der Waals radii of N and H (2.75 Å).⁴⁶ Therefore, hydrogen bond is difficult to be observed in α-KNH₂. Fig. 5(b) shows that each N–H bond length is 1.028 Å and ∠_H–N–H angle is 101.8° in NH₂ molecular. The neighboring NH₂ groups are perpendicular to each other, and each N–H bond is connected almost linearly with the N atom in its neighboring NH₂ group. The calculated N–H⋯N bond (∠_H–N⋯H) angle and length are 171.6° and 2.286 Å at 5 GPa, respectively, which can easily form the hydrogen bond. The neighboring NH₂ groups for γ-KNH₂ are shown in Fig. 5(c). In each NH₂ group, each N–H bond length and ∠_H–N–H angle can reach 1.035 Å and 99.8° at 8 GPa, respectively. The four neighboring NH₂ groups lie in two different planes and the NH₂ groups in each plane are parallel to each other. Each N–H bond is aligned almost linearly with the N atom in its neighboring NH₂ group. The obtained ∠_H–N⋯H angle and N–H⋯N bond length are 169.9° and 2.162 Å at 8 GPa in each plane. Besides, the ∠_H–N⋯H angle and N–H⋯N bond length between the neighboring planes can reach 174.8° and 2.266 Å. As a result, the formation of hydrogen bond can be observed in β-KNH₂ and γ-KNH₂, which can also be understood from our latter analysis of electronic structure.

Table 2 Predicted lattice constants and atomic coordinates for α-KNH₂, β-KNH₂, and γ-KNH₂ at 8 GPa at the selected pressures

Pressure (GPa)	Space group	Lattice parameter (Å)	Atomic coordinates (fractional)
0	P21/m	a = 4.635, b = 3.835	K 2e (0.2189, 0.25, 0.3121)
		c = 6.334, β = 96.3°	N 2e (0.2804, 0.25, 0.7575)
		a = 2.870, c = 2.409	H 4f (0.3089, 0.0435, 0.8622)
5	P21	a = 3.698, b = 4.622	K 2a (0.0609, 0.1460, 0.2523)
		c = 5.112, β = 82.4°	N 2a (0.6208, 0.6561, 0.2683)
			H1 2a (0.5931, 0.1673, 0.8407)
			H2 2a (0.5224, 0.5117, 0.4149)
8	Pc	a = 5.976, b = 4.982	K 2a (0.7153, 0.2031, 0.8437)
		c = 4.915, β = 147.9°	N 2a (0.2409, 0.7207, 0.3731)
			H1 2a (0.9213, 0.2829, 0.5781)
			H2 2a (0.2610, 0.5831, 0.2366)

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Fig. 5 Geometries of amide ions in (a) α-KNH₂ at 0 GPa, (b) β-KNH₂ at 5 GPa, and (c) γ-KNH₂ at 8 GPa.

To further understand the nature of chemical bonding in KNH₂, we calculate the partial DOS (PDOS) of α, β, and γ phases at different pressures as depicted in Fig. 6. The three phases have the insulator character due to the finite energy band gap (E_g) between the valence band (VB) and conduction band (CB). The calculated E_g can reach 2.1 eV (α-KNH₂) at 0 GPa, 3.7 eV (β-KNH₂) at 5 GPa, and 4.1 eV (γ-KNH₂) at 8 GPa, respectively. The results show that N 2p and H 1s contribute mostly to the VBs. However, the contributions to the VBs from K are very little for the three phases. Therefore, we conclude that the interaction between K⁺ cations and [NH₂]⁻ anions is ionic. Otherwise, energetically degenerate between N 2p and H 1s in the VB region can be observed, which indicates the hybridization between N and H atoms is very remarkable and there exists strong covalent bond between N and H atoms in the [NH₂]⁻ anions. Fig. 6 shows that VBs for the three phases are split into three separate regions in the range from −8 to 0 eV. With increasing pressure, from α- to β-, to γ-KNH₂ there is a little difference in peak profiles and the PDOS peaks for β-KNH₂ and γ-KNH₂ become broader, which indicates that electronic delocalization in KNH₂ increases under the influence of pressure.

Fig. 6 Calculated total and partial density of states for α-(at 0 GPa), β-(at 5 GPa), and γ-KNH₂ (at 8 GPa). Fermi levels are set to zero energy and marked by dotted vertical lines; s, p and d states are red, green, and blue lines, respectively.

In complex metal hydrides, hydrogen bond is advantageous for accelerating dehydrogenation behavior. For further probing the existence of hydrogen bond, we calculate the charge density for the three phases. The calculated charge densities for some selected planes across the NH₂ group for α-(0 GPa), β-(5 GPa), and γ-KNH₂ (8 GPa) are displayed in Fig. 7(a–c). We can see that there is a strong covalent bonding between N and H atoms in NH₂ groups. Additionally, hydrogen bond between the neighboring NH₂ groups can be confirmed by investigating the charge density (ρ) at the bond critical point (bcp).⁴⁷ Scheiner et al. have proposed that existence of hydrogen bond can be achieved if the electron density (ρ_bcp) at the bond critical point is in the range from 0.01 to 0.03 e Å⁻³. In α-KNH₂, the ρ_bcp in the N–H⋯N bond is 0.001 e Å⁻³ as depicted in Fig. 7(a), which indicates there is no hydrogen bond in this phase. Fig. 7(b) shows that the ρ_bcp is 0.017 e Å⁻³ in β-KNH₂, meanwhile we can see that the ρ_bcp can reach 0.017 e Å⁻³ in the same plane and 0.018 e Å⁻³ in the N–H⋯N bond between the neighboring NH₂ groups for γ-KNH₂ as shown in Fig. 7(b and c), respectively, which indicates the hydrogen bond can be formed in high pressure phases for KNH₂. Our results are similar to those of NaNH₂ (ref. 22) under high pressures.

Fig. 7 Charge density distribution of KNH₂ within the scale of 0 to 0.01 e Å⁻³: (a) the slice across the NH₂ group for α-KNH₂ at 0 GPa, (b) the slice across the neighboring NH₂ group for β-KNH₂ at 5 GPa, and (c) the slice across the neighboring NH₂ groups for γ-KNH₂ at 8 GPa. The hydrogen bond paths are denoted by the dotted lines.

4. Conclusions

We have performed the predictions of new high-pressure structures of KNH₂ by using particle swarm optimization technique implemented in the CALYPSO code and density functional theory (DFT). Five energetically competing structures have been selected as the candidates in our structural predictions. The calculations of enthalpy difference relative to α-KNH₂ have suggested two pressure-induced structural phase transformations occur with increasing pressure. The ground-state α-KNH₂ transforms into a monoclinic β-KNH₂ with space group P2₁ at 4 GPa and then into a monoclinic γ-KNH₂ with space group Pc at 6.8 GPa. Moreover, these phase transformations are companied with volume reductions of 5.0% and 3.8%, respectively, which reveals the nature of the first-order structural phase transition. The predicted structural sequence (P2₁/m → P2₁ → Pc) of KNH₂ is very similar to the high-pressure behavior of the related compounds LiNH₂ (I4̄ → Fddd → P2₁2₁2) and NaNH₂ (Fddd → P2₁2₁2 → C2/c), which further verify that the trend of lowering symmetry induced by high pressure may be common in alkali metal amides. The results of phonon dispersion curves and elastic constants indicate the new predicted high-pressure structures are stable dynamically and mechanically. By analyzing partial density of states and charge density, we can see that there exists a strong covalent bonding between N and H atoms in NH₂ groups in the three structures. Meanwhile, N–H⋯N hydrogen bonding between neighboring NH₂ groups have been proposed in β- and γ-KNH₂ by investigating the structural details and charge density. The existence of hydrogen bonding can weak the covalent bonding between N and H atoms in NH₂ groups, which could be favorable for accelerating dehydrogenation behavior of complex metal hydrides.

Acknowledgements

This work was supported by Open Project of State Key Laboratory of Superhard Materials (Jilin University), the National Natural Science Foundation of China (No. 11104019, 2011CB808200), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), and National Found for Fostering Talents of basic Science (No. J1103202). Parts of calculations were performed in the Scientific Computation and Numerical Simulation Center of Changchun University of Science and Technology.

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