English

• 0.   Introduction

  As a result of CO₂ emissions and fossil fuel depletion, a sustainable and renewable energy resource is urgently needed for transportation and industrial use to replace coal and oil^[1]. Hydrogen energy has attracted worldwide attention due to its abundance, zero-polluting nature, renewability, and higher energy density compared to gasoline^[2-3]. However, the implementation of H₂ in transportation has faced challenges, primarily due to the absence of efficient hydrogen storage materials^[4-5]. Traditionally, hydrogen gas is stored through low-temperature liquefaction and high-pressure compression^[6-7]. However, these storage methods are not cost-effective because the processes of liquefaction and compression of H₂ consume a substantial amount of energy. Furthermore, the installation of liquid and compressed gas hydrogen tanks on vehicles presents significant challenges due to their cumbersome nature and the difficulties associated with securing them properly.

  An optimal H₂ storage medium must satisfy several criteria, including but not limited to high gravimetric density, recyclability, and cost-effectiveness^[8-10]. As requested, the U.S. Department of Energy (US-DOE) has set specific targets for optimal materials intended for practical H₂ storage applications. These targets include a H₂ storage density of 5.5% for onboard vehicle H₂ storage systems by the year 2025, as well as operational conditions ranging from 1 to 100 MPa and temperatures between 233 and 358 K for vehicles in operation^[11]. Given all this, solid-state H₂ storage media have emerged as a crucial research area due to their cost-effectiveness, resulting in the development of various forms like chemical hydrides^[12-14], covalent organic frameworks (COFs)^[15-16], metal-organic frameworks (MOFs)^[17-19], and carbon nanostructures^[20-21].

  In chemical hydrides, dehydrogenation is slow and requires high temperatures because H₂ molecules dissociate into atoms, forming covalent bonds with the host material. For example, although magnesium hydride (MgH₂) has a H₂ mass ratio of 7.6%, its slow reaction kinetics hinder H₂ desorption at ambient temperature^[22-23]. In contrast, COFs, MOFs, and pure carbon materials exhibit low adsorption enthalpies, rendering them chemically inert and thus impractical for effective H₂ storage under ambient conditions. To address the issue, previous studies indicated that MOFs^[24-25], COFs^[26-29], and carbon-based materials, including fullerene^[30-34], nanotubes^[35-38], and graphene^[39-41], exhibit a substantial enhancement in hydrogen storage capacity when decorated with transition metal (TM) atoms. In all these cases, H₂ adsorption occurs around the TM through orbital hybridization or polarization mechanisms. Consequently, a relatively strong interaction was established between the metal and hydrogen, resulting in an increased storage capacity and elevated desorption temperature. For example, Wei et al.^[27] showed that in the modified COF-1 structure, each Sc atom can tightly adsorb four H₂ molecules, achieving a H₂ uptake of 6.78%. Yildirim et al.^[30] employed the first-principles calculation to demonstrate that light TM-decorated C₆₀ had significant H₂ storage capability. Han et al.^[37] reported that the nickel-decorated carbon nanotubes demonstrated a significant H₂ uptake capacity of 0.87% at 298 K and 100 MPa, representing an enhancement factor of 2.5 compared to the untreated carbon nanotubes. However, the aggregation of TM atoms has been identified as a significant obstacle, mainly due to their extremely high binding energy, which in turn leads to a significant decrease in H₂ storage capacity^[42]. To address the aggregation problem, some researchers turned their attention from carbon-based materials to boron-based ones. Meng et al.^[43] observed that, in contrast to their behavior on carbon nanostructures, titanium atoms on boron nanotubes tend to remain isolated from one another. After this, various TM-decorated boron-based materials, such as boron fullerene^[44-49], boron nanotubes^[50], borane^[51-53], and boron clusters^[54-58], have been the subjects of extensive research in the context of H₂ storage. For example, Tang et al. have explored scandium-doped all-boron cages, specifically B₄₀^[44] and B₂₈^[45], as promising candidates for H₂ storage materials. Additionally, Dong et al.^[46] reported that a Ti-doped B₄₀ cluster (Ti₆B₄₀) can adsorb up to 34 H₂ molecules, achieving a maximum weight density of 8.70%. Sun et al.^[49] employed DFT methods to evaluate the H₂ storage potential of the highly stable La₃B₁₈ cluster, in which each lanthanum (La) atom could bind up to 6 H₂ molecules, thereby achieving a 5.6% weight density. Zhao et al.^[50] identified a low-energy single-walled scandium triboride (ScB₃) nanotube that is capable of adsorbing approximately 6.1% H₂, with a binding energy ranging from 22 to 26 kJ·mol^-1. The Chattaraj group reported that B₆H₆Sc, B₆H₆Ti, and B₆H₆V complexes could adsorb up to 4 H₂ molecules, achieving gravimetric H₂ uptakes of 6.51%, 6.36%, and 6.21%, respectively^[52].

  Most recently, the smallest perfect cubic metallo-borospherenes TM₈B₆ (TM=Pd, Ni) have been identified as superatoms, adhering to the 18-electron rule and exhibiting spherical aromaticity and enhanced stability^[59]. As far as we know, the H₂ storage capacities of TM₈B₆ have not been studied. As previously discussed, boron-based complexes often exhibit exceptional H₂ storage capabilities. Consequently, in the present study, the H₂ storage performances of TM₈B₆ clusters were systematically investigated.

  1.   Computational methods

  The structures of isolated and hydrogenated TM₈B₆ were optimized without symmetry constraints using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional^[60-61], in conjunction with Grimme′s empirical dispersion correction (D3)^[62]. In comparison to the other functionals, the PBE method demonstrates greater suitability for investigating hydrogen adsorption in TM compounds^{[33, 63-64]}. In computational simulations, Pd was represented using the Stuttgart-Dresden double-ζ (SDD) basis set, whereas other atoms were modeled with the 6-311G(d, p) basis set. In the calculation of harmonic frequencies, there are no imaginary frequencies, thereby confirming the minimum energy structures. The average adsorption energy (ΔE_a) and continuous adsorption energy (ΔE_s) per H₂ molecule were calculated to evaluate the adsorption capability and the reversibility of hydrogen storage of TM₈B₆ clusters, respectively. They are defined as follows:

  $ \Delta {E}_{{\rm{a}}}=\left({E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}}+n{E}_{{{\rm{H}}}_{2}}-{E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n}}\right)/n $

  (1)

  $ \Delta {E}_{{\rm{s}}}=\left({E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n-8}}+8{E}_{{{\rm{H}}}_{2}}-{E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n}}\right)/8 $

  (2)

  where $ {E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}} $, $ {E}_{{{\rm{H}}}_{2}} $, $ {E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n}} $, $ {E}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n-8}} $ are the total energies of TM₈B₆, H₂, TM₈B₆(H₂)_n, and TM₈B₆(H₂)_n-8, respectively. Of particular note is that if ΔE_s > 0, H₂ can be continuously adsorbed. Conversely, ΔE_s < 0 inhibits further adsorption. The full counterpoise method was employed to correct for basis set superposition error (BSSE) in the calculation of adsorption energy^[65]. To assess the reliability of the employed method, we have recalculated certain adsorption energies utilizing the ωB97XD density functional in conjunction with the same basis set. The ωB97XD functional, known for accurately predicting non-covalent interactions, was used to calculate adsorption energies with long-range interactions considered^[66]. Comparable results were obtained at both computational levels; therefore, unless otherwise specified, the subsequent discussion will focus on the PBE(D3) level.

  To further investigate the interaction mechanisms between atoms in the isolated and hydrogenated TM₈B₆, the quantum theory of atoms in molecules (QTAIM)^[67] was applied. The molecular electrostatic potential (ESP) and atomic dipole-corrected Hirshfeld atomic charge (ADCH)^[68] distributions were carried out to analyze the electronic structures of the free and hydrogen-adsorbed TM₈B₆. Localized orbital locator (LOL)^[69], electron localization function (ELF) analyses_,^[70-72] and projected density of states (PDOS) analyses were performed to reveal the bonding nature. All calculations were facilitated by the Multiwfn software^[73]. Additionally, the study employed the independent gradient model (IGM) based on the Hirshfeld partition of molecular density (IGMH)^[74] to elucidate the bonding characteristics of the hydrogenated TM₈B₆ clusters. The thermodynamic stabilities of TM₈B₆ compounds were examined using Born-Oppenheimer molecular dynamics (BOMD) simulations. Hydrogen adsorption and desorption cycles were analyzed for reversibility using atom-centered density matrix propagation (ADMP)^[75], which can offer comparable insights to BOMD while requiring fewer computational resources.

  All the DFT calculations mentioned were implemented using the Gaussian 09 code^[76].

  2.   Results and discussion

  2.1   Geometrical structures of metallo-borospherene TM₈B₆

  The most stable configurations of TM₈B₆ clusters have a low-lying O_h geometry, as illustrated in Fig.1a. All the bond distances of isolated and hydrogenated Ni₈B₆ and are Pd₈B₆ listed in Table 1 and 2, respectively. The calculated TM—B bond lengths for Ni₈B₆ and Pd₈B₆ are 0.189 and 0.209 nm as reported (0.191 and 0.207 nm) by Ao et al.^[59], respectively. Furthermore, the thermodynamic stabilities of TM₈B₆ were evaluated through BOMD simulations conducted at 1 000 K, employing the PBE/6-31G(d) level of theory. The original structures utilized for the simulations are based on the optimized configurations at the PBE(D3)/6-311G(d, p) level of theory. A simulation duration of 3 ps is implemented with a trajectory time step of 0.5 fs. As illustrated in Fig.S1 (Supporting information), the relative potential energies of Ni₈B₆ and Pd₈B₆ exhibit minor oscillation around a consistent value throughout the simulation period. Analysis of the extractive snapshots (inset in Fig.S1) of TM₈B₆ at various simulation intervals (0, 1 500, and 3 000 fs) reveal that TM₈B₆ can consistently retain its respective cage-like structure, indicating a high degree of dynamic stability. The notable stabilities of the TM₈B₆ configurations can be ascribed to their unique structural and bonding characteristics. Take Ni₈B₆ as an example, the filled highest occupied molecular orbital (HOMO)-14 (1S²), triply degenerate HOMO-9 ($ {P}_{x}^{2} $, $ {P}_{y}^{2} $, and $ {P}_{z}^{2} $), doubly degenerate HOMO-1 (e_g) ($ {D}_{{x}^{2}-{y}^{2}}^{2} $and $ {D}_{{z}^{2}}^{2} $) and triply degenerate HOMO (t_2g) ($ {D}_{xz}^{2} $, $ {D}_{yz}^{2} $, and $ {D}_{xy}^{2} $) depicted in Fig.S2 correspond to the electronic configuration (1S²1P⁶1D¹⁰), indicating that Ni₈B₆ can be regarded as a superatom in accordance with the 18-electron rule, a classification that aligns well with prior research findings^[59]. As shown in Fig.S3, an analogous analysis indicat that Pd₈B₆ can be considered a superatom according to the 18-electron rule. To further elucidate the nature of the high stability of TM₈B₆, QTAIM analyses were conducted. Fig.1b illustrates the molecular graphs of TM₈B₆ featuring bond critical points (BCPs), ring critical points (RCPs), and cage critical points (CCPs).

  Figure 1

  

  Figure 1.  (a) Optimized structures with ADCH charge of Ni₈B₆ (left) and Pd₈B₆ (right); (b) Molecular graphs of Ni₈B₆ (left) and Pd₈B₆ (right)

  Pink, cyan, tan, orange, yellow, and green balls are B, Ni, Pd, BCP, RCP, and CCP, respectively.

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  Table 1

  

  Table 1.  Average bond lengths, ΔE_s, and ΔE_a of Ni₈B₆(H₂)_n

  下载: 导出CSV

  n	PBE(D3)				ωB97XD			PBE(D3)
  	dTM—B / nm	dTM—H / nm	dH—H / nm		ΔEs / eV	ΔEa / eV		ΔEs / eV	ΔEa / eV
  0	0.189	—	—		—	—		—	—
  8	0.191	0.165	0.084 8		0.680	0.680		0.569	0.569
  16	0.192	0.215	0.080 1		0.298	0.489		0.159	0.364
  24	0.192	0.239	0.078 3		0.025 0	0.335		0.140	0.289
  32	0.192	0.262	0.077 4		0.015 0	0.255		0.122	0.248
  40	0.192	0.288	0.077 0		0.013 0	0.206		0.046 0	0.207

  Table 2

  

  Table 2.  Average bond lengths, ΔE_s, and ΔE_a of Pd₈B₆(H₂)_n

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  n	PBE(D3)				ωB97XD			PBE(D3)
  	dTM—B / nm	dTM—H / nm	dH—H / nm		ΔEs / eV	ΔEa / eV		ΔEs / eV	ΔEa / eV
  0	0.209	—	—		—	—		—	—
  8	0.209	0.197	0.079 5		0.258	0.258		0.210	0.210
  16	0.209	0.264	0.077 4		0.057 0	0.157		0.064 0	0.137
  24	0.209	0.287	0.076 7		0.059 0	0.125		0.069 0	0.114
  32	0.209	0.297	0.076 4		0.064 0	0.110		0.072 0	0.103

  Table 3 presents the key to the pological parameters at BCPs for TM₈B₆, including electron density (ρ(r)), Laplacian of electron density (∇²ρ(r)), and total energy density (H(r)). In the TM₈B₆ clusters, BCPs are observed for TM—B interactions, while bond paths and BCPs between TM atoms are not present, indicating that TM atoms do not aggregate. Based on topological criteria, the interaction with ρ(r) at BCPs greater than 0.2 a.u., and H(r) less than 0 a.u. is typically considered a covalent bond^[77]. As demonstrated in Table 3, Ni—B and Pd—B interactions, characterized by low ρ(r) (0.119 and 0.097 0 a.u., respectively) and negative H(r) values, predominantly exhibit covalent characters. For comparison, we additionally computed the ELF and LOL values at BCPs. If ELF and LOL values are greater than 0.5, it signifies regions of localized electrons, including both non-bonding and bonding electrons, while ELF and LOL values below 0.5 denote regions of delocalized electrons^[66]. As presented in Table 2, the values of ELF and LOL exhibit a high degree of consistency. More importantly, the bond characteristics of TM—B, as calculated by ELF and LOL, exhibites strong concordance with the findings from the topological analyses. The interactions were further examined by analyzing the PDOS shown in Fig.2. The notable hybridization of Nid and Pdd orbitals with Bp orbitals, spanning from -15 to -4 eV and -12 to -4 eV, respectively, indicates that the presence of strong covalent bonds between TM and B atoms. As illustrated in Fig.1a, the ADCH charge analysis reveals that B and Ni atoms in Ni₈B₆ possess charges of approximately -0.545|e| and 0.408|e|, respectively. Similarly, B and Pd atoms in Pd₈B₆ carried about -0.471|e| and 0.353|e|, respectively. These observations indicate substantial electron transfer from TM atoms to the adjacent B atoms. Consequently, the TM atoms are induced into a cationic state, suggesting the potential for H₂ adsorption is via a polarization mechanism. Furthermore, an ESP examination of the Ni₈B₆/Pd₈B₆ cluster is depicted in Fig.3a and Fig.S5a. The corresponding color scales are provided at the bottom of the figures. It is clearly shown that Ni/Pd atoms exhibit positive potentials (indicated in blue), while B atoms display negative potentials (indicated in red). These distributions of ESP accord with the ADCH analysis, suggesting that H₂ molecules are more likely to be preferentially adsorbed onto the Ni/Pd atoms.

  Table 3

  

  Table 3.  Principal topological data of the bare TM₈B₆ and the TM₈B₆(H₂)_n complexes

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  Sample	Bond	ρ(r) / a.u.	∇2ρ(r) / a.u.	H(r) / a.u.	ELF	LOL
  Ni8B6	B—Ni	0.119	-0.018 0	-0.075 0	0.575	0.538
  Ni8B6(H2)40	B—Ni	0.111	-0.006 00	-0.063 0	0.562	0.531
  	Ni—H	0.092 0a	0.357a	-0.022 0a	0.189a	0.326a
  		0.008 00b	0.018 0b	0.001 00b	0.052 0b	0.190b
  	B—H	0.008 00	0.150	0.000	0.071 0	0.217
  	H—H	0.217a	-0.704a	-0.194a	0.994a	0.971a
  		0.254b	-0.100b	-0.251b	1.000b	0.996b
  Pd8B6	B—Pd	0.097 0	0.010 0	0.048 0	0.601	0.551
  Pd8B6(H2)32	B—Pd	0.096 0	0.010 0	-0.046 0	0.586	0.543
  	Pd—H	0.060 0a	0.223a	-0.007 00a	0.150a	0.296a
  		0.005 00b	0.010 0b	0.000b	0.030 0b	0.149b
  	B—H	0.005 00	0.010 0	0.000	0.034 0	0.159
  	H—H	0.231a	-0.831a	-0.251a	0.999a	0.971a
  		0.254b	-0.101b	-0.251b	1.000b	0.999b
  a The hydrogen atom is the closest to the host structure; b The hydrogen atom is the farthest from the host structure.

  Figure 2

  

  Figure 2.  PDOS of (a) Ni₈B₆ and (b) Pd₈B₆

  Dashed lines represent HOMO levels; Inset: the corresponding HOMO and LUMO.

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  Figure 3

  

  Figure 3.  ESP of (a) Ni₈B₆, (b) Ni₈B₆(H₂)₈, (c) Ni₈B₆(H₂)₁₆, (d) Ni₈B₆(H₂)₂₄, (e) Ni₈B₆(H₂)₃₂, and (f) Ni₈B₆(H₂)₄₀

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  2.2   H₂ adsorbed on TM₈B₆

  To survey the H₂ storage capacity of metallo-borospherene TM₈B₆, multiple H₂ molecules were incrementally introduced, followed by optimization of the host structures. This process was iteratively conducted until ΔE_a decreased to below 0.10 eV, which ensured that H₂ molecules were physisorbed, making it appropriate for reversible adsorption under operational conditions. The resulting structures of Ni₈B₆(H₂)_n and Pd₈B₆(H₂)_n are shown in Fig.4 and 5, respectively. The Ni₈B₆ and Pd₈B₆ clusters can bind up to 40 and 32 H₂ molecules, respectively. The saturated complexes Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂ have maximum H₂ uptake densities of 13.134% and 6.562%, respectively, surpassing the US-DOE target of 5.5%. In Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂, the initial 8 H₂ molecules are adsorbed onto TM in a side-on configuration, with the H₂ axis perpendicular to the line connecting the TM atoms and the H₂ center. The axes of the subsequently adsorbed H₂ molecules are vertical to the host. Table 1 summarizes the typical bond distances of the hydrogenated TM₈B₆. The hydrogens are incorporated into Ni₈B₆ and Pd₈B₆ clusters molecularly with H—H bond lengths ranging from 0.077 0 to 0.848 nm and 0.076 4 to 0.795 nm, respectively. In TM₈B₆(H₂)₈, the TM—B bond lengths exhibit a slight increase relative to those in free TM₈B₆ due to TM-H₂ interactions. However, as additional H₂ molecules are adsorbed by TM₈B₆(H₂)₈, the TM—B bond lengths are almost unchanged. With each step of sequential adsorption, H₂ molecules are adsorbed farther from the TM sites due to steric hindrance. As presented in Table 1 and 2, the ΔE_s values of TM₈B₆(H₂)_n are in the range of 0.013 0 to 0.680 eV by two methods, indicating that up to 40 and 32 H₂ molecules can be effectively adsorbed onto Ni₈B₆ and Pd₈B₆, respectively. The predicted ΔE_a for Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂ is 0.207 and 0.103 eV at the PBE(D3) level, respectively, which are close to 0.206 and 0.110 eV calculated at the ωB97XD functional. Obviously, the TM₈B₆ clusters exhibit an adsorption strength between physisorption and chemisorption, making them potentially ideal for H₂ storage under ambient conditions. It is well known that a large energy gap (ΔE_gap) between HOMO and the lowest unoccupied molecular orbital (LUMO) can reflect the high chemical stability of a compound^[52-53]. As shown in Fig.S4, the values of ΔE_gap are calculated to analyze the stabilities of the isolated and hydrogenated TM₈B₆. The ΔE_gap is different between the two methods; however, the tendency is generally consistent. It can be found that the ΔE_gap values of the hydrogenated TM₈B₆ are larger than those of the corresponding bare cluster TM₈B₆. The analysis result shows that the cluster TM₈B₆ will be more stable after multiple H₂ molecules are adsorbed. Furthermore, the computed ESP for the hydrogenated Ni₈B₆ and Pd₈B₆ is presented in Fig.3 and S5. The areas surrounding Ni/Pd atoms transition from blue to light blue with successive H₂ adsorption, signifying the saturation of H₂ uptake after the addition of 40 or 32 H₂ molecules.

  Figure 4

  

  Figure 4.  View of Ni₈B₆ with (a) 8 H₂, (b) 16 H₂, (c) 24 H₂, (d) 32 H₂, and (e) 40 H₂

  The spheres colored gray, blue, and pink are H, Ni, and B atoms, respectively.

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  Figure 5

  

  Figure 5.  View of Pd₈B₆ with (a) 8 H₂, (b) 16 H₂, (c) 24 H₂, and (d) 32 H₂

  The spheres colored gray, tan, and pink are H, Pd, and B atoms, respectively.

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  In the onboard application, it is essential to consider the influence of temperature and pressure on the processes of H₂ adsorption and desorption. Consequently, we underscore the significance of applying Gibbs free energy corrections to achieve an accurate assessment of H₂ adsorption. The Gibbs free energy change (ΔG) for the reaction TM₈B₆+8nH₂→TM₈B₆(H₂)_8n (TM=Ni, n=1-5; TM=Pd, n=1-4) was examined to identify the favorable temperature range. The ΔG is defined as:

  $ \Delta G=\left({G}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n8}}-{G}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}}-8n{G}_{{{\rm{H}}}_{2}}\right)/\left(8n\right) $

  (3)

  where $ {G}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}({{\rm{H}}}_{2}{)}_{n8}} $, $ {G}_{{\rm{T}}{{\rm{M}}}_{8}{{\rm{B}}}_{6}} $ and $ {G}_{{{\rm{H}}}_{2}} $ is the Gibbs free energies of TM₈B₆(H₂)_8n, TM₈B₆ and H₂, respectively. According to the definition, ΔG < 0 suggests that the adsorption of H₂ on TM₈B₆ occurs spontaneously. In contrast, ΔG > 0 signifies that the adsorption of H₂ is energetically unfavorable. Fig.6a and 6b show the ΔG changes of Ni₈B₆(H₂)_8n and Pd₈B₆(H₂)_8n with temperature at 101.325 kPa, respectively. Obviously, ΔG exhibits a gradual increase as the temperature rises. For Ni₈B₆(H₂)_8n (n=1-5), all ΔG values are negative when the temperature is less than 169 K. Upon reaching 169 K, the adsorbed H₂ molecules begin to relax. As the temperature further increased to ambient conditions, 32 H₂ molecules are fully desorbed from Ni₈B₆(H₂)₄₀. It indicates that a H₂ addition and release of 10.790% can be readily achieved under 101.325 kPa. For Pd₈B₆(H₂)_8n (n=1-4), all adsorbed H₂ molecules start releasing from the host at 86 K and are completely desorbed by 173 K. This process allows for a 6.562% H₂ uptake and release at atmospheric pressure.

  Figure 6

  

  Figure 6.  ΔG changed with temperature for (a) Ni₈B₆(H₂)_8n (n=1-5) and (b) Pd₈B₆(H₂)_8n (n=1-4) at 101.325 kPa

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  To investigate the interactions between atoms within hydrogenated TM₈B₆ clusters, topological analyses were conducted on saturated hydrogen-adsorbed clusters. The molecular graphs and topological parameters of Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂ are detailed in Fig.7 and Table 3, respectively. The topological parameters associated with the B—TM bonds closely resemble those of the isolated TM₈B₆ motifs, suggesting that the structural integrities of the host clusters are preserved after the incorporation of H₂ molecules. Furthermore, it is found that ELF and LOF values at the BCPs of H₂ are approximately 1.000, suggesting that the absorbed H₂ molecules retain their molecular forms. Additionally, it is noted that BCPs are formed between TM/B atoms and the H₂ molecules. The B—H bonds are characterized as weak noncovalent interactions, as evidenced by low values of ρ(r), ELF, and LOF, along with positive ∇²ρ(r) and H(r) values. The interactions between TM and the initial 8 H₂ molecules exhibit partial covalent characteristics, as evidenced by slightly elevated values of ρ(r), ∇²ρ(r), electron ELF and LOF, along with negative H(r) at BCPs. In contrast, the other BCPs between TM/B and H₂ display low values of ρ(r), ∇²ρ(r), and H(r) approaching zero, indicating that these interactions are weak and noncovalent nature.

  Figure 7

  

  Figure 7.  (a) Molecular graphs of Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂; (b) Standard color scale and chemical explanation of sign(λ₂)ρ based on IGMH analysis^[74]

  a: Gray, pink, cyan, tan, orange, yellow, and green balls are H, B, Ni, Pd, BCP, RCP, and CCP, respectively; Inset: sign(λ₂)ρ with IGMH δg^inter=0.005 a.u. isosurface.

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  The interaction characteristics between H₂ and the host structures in Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂ were further investigated through IGMH analysis. The isosurface maps of sign(λ₂)ρ with IGMH δg^inter=0.005 a.u for Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂ are presented in Fig.7a. Fig.7b depicts the IGMH color scale, in which blue, green, and red represent strong attractive interactions, weak van der Waals attractions, and steric hindrance, respectively. As shown in Fig.7a, the isosurface with a blend of blue and green hues suggests that the interactions between TM and the initial 8 H₂ molecules exhibit an intermediate nature between van der Waals forces and strong attractive interactions.

  Conversely, the BCPs between the remaining H₂ molecules and the hosts are characterized predominantly by van der Waals interactions, as evidenced by the green isosurfaces. In prior research, exemplified by compounds Ti₆B₄₀^[46] and La₃B₁₈^[49], a single TM atom demonstrates the capacity to store up to 6 and 5 H₂ molecules through Kubas interactions, respectively. However, in the cases of Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂, each Ni or Pd atom binds only 1 H₂ molecule via Kubas interaction^[78], while the remaining H₂ molecules interact with the host structures through van der Waals forces.

  Fig. 8 presents the PDOS plots for the hydrogenated metallo-borospherene TM₈B₆. Fig. 8a illustrates that upon adsorption of an initial H₂ molecule by each Ni atom, the overlap between σ orbitals of H₂ molecules and the 3d orbitals of Ni occurs within the energy ranges of -13.00 to -11.37 eV, which are below the HOMO levels of Ni₈B₈(H₂)₈. Meanwhile, σ^* orbitals of H₂ molecules interact with the 3d orbitals of Ni. In brief, the interactions between H₂ and Ni₈B₆ follow the Kubas mechanism. This facilitates a minor electron transfer from the σ orbitals of H₂ to the 3d orbitals of Ni, accompanied by enhanced back-donation of electrons from the 3d orbitals of Ni to the σ^* orbitals of H₂. Consequently, the ADCH charge of each Ni atom increases from 0.408|e| to 0.472|e|. Furthermore, the bond lengths of the initially adsorbed H₂ molecules are elongated relative to the subsequent 32 H₂ molecules. As shown in Fig. 8b, when Ni₈B₈ reaches saturation adsorption, the overlap regions between σ orbitals of H₂ molecules and the d orbitals of Ni expand to the energy ranges of -13.30 to -10.16 eV. This expansion suggests a decrease in the adsorption strength of H₂ as more H₂ molecules are adsorbed, a trend corroborated by the ΔE_a values presented in Table 2. Likely, in Pd₈B₈(H₂)₈, σ orbitals of H₂ molecules exhibit overlap with the d orbital of Pd within the energy range of -12.64 to -11.50 eV. Consequently, the charge on each Pd atom decreases from 0.353|e| to 0.288|e|. In contrast, this orbital overlap in Pd₈B₈(H₂)₃₂ extends over a broader energy range of -12.20 to -10.13 eV, along with the decrease in adsorption strength of H₂.

  Figure 8

  

  Figure 8.  PDOS of (a) Ni₈B₆(H₂)₈, (b) Ni₈B₆(H₂)₄₀, (c) Pd₈B₆(H₂)₈, and (d) Pd₈B₆(H₂)₃₂

  Dashed lines represent HOMO levels; Inset: partial occupied molecular orbitals of (a) Ni₈B₆(H₂)₈, (b) Ni₈B₆(H₂)₄₀, (c) Pd₈B₆(H₂)₈, and (d) Pd₈B₆(H₂)₃₂

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  2.3   H₂ adsorption and desorption dynamics

  Next, we conducted ADMP molecular dynamics simulations to investigate the stability, reversibility, and desorption kinetics of saturated hydrogen-adsorbed complexes at varying temperatures and 101.325 kPa. Temperature regulation was exclusively achieved through the velocity scaling method. Saturated hydrogen-adsorbed clusters are subjected to 100 and 300 K at a 101.325 kPa for 1 000 fs with a 0.2 fs time step. Fig.9 and 10 illustrate the temporal trajectories of relative potential energies and snapshots from the ADMP molecular dynamics simulations, respectively. The average molecular motion increases with rising temperature, leading to the desorption of H₂ molecules at shorter time intervals and at an accelerated rate. In the case of the Ni₈B₆(H₂)₄₀ cluster, 23 or 25 H₂ molecules are released from the host simultaneously within time frames of 500 or 1 000 fs at a temperature of 100 K, respectively. In contrast, only 9 or 8 H₂ molecules remain adsorbed during the same intervals at 300 K. For the Pd₈B₆(H₂)₃₂ clusters, 23 or 24 H₂ molecules are expelled from the host within 500 or 1 000 fs at 100 K, respectively. Conversely, only 6 or 8 H₂ molecules is adsorbed on the host during the same time intervals at 300 K. In short, the failure of the residual H₂ molecules to completely desorb from the parent body is due to their ΔE_a values being relatively high and approaching the range of chemical adsorption. This was consistent with the above calculation results. All the H₂ molecules may leave the hosts at higher temperatures.

  Figure 9

  

  Figure 9.  Variation of relative potential energy of (a) Ni₈B₆(H₂)₄₀ and (b) Pd₈B₆(H₂)₃₂ vs simulation times at 100 and 300 K

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  Figure 10

  

  Figure 10.  Extracted snapshots of (a) Ni₈B₆(H₂)₄₀ and (b) Pd₈B₆(H₂)₃₂ for the ADMP molecular dynamics simulations at 100 and 300 K

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  2.4   Thermodynamic under temperature and pressure

  For a material to be considered viable for H₂ storage, it must be capable of adsorbing a substantial quantity of H₂ molecules, while also allowing for their desorption under operational conditions. Consequently, a more pertinent parameter in the study of hydrogen storage may be the net difference between the number of H₂ molecules adsorbed and desorbed. Therefore, to achieve a quantitative assessment of hydrogen adsorption and desorption over a broad range of temperature and pressure, we calculated the practical number of H₂ molecules using thermodynamic analysis based on the grand canonical partition function^[79].

  $ Z=1+\sum\limits_{i=1}^{n}\exp\left(-\frac{\Delta {E}_{{\rm{a}}}^{i}-{\mu }_{{{\rm{H}}}_{2}}}{{k}_{{\rm{B}}}T}\right) $

  (4)

  where Z is the practical number of H₂ molecules, n is the theoretical number of absorbed H₂ molecules on the TM₈B₆, $ \Delta {E}_{{\rm{a}}}^{i} $ is the $ \Delta {E}_{{\rm{a}}} $ of the ith absorbed H₂ molecule on the TM₈B₆, k_B is the Boltzmann constant, and $ {\mu }_{{{\rm{H}}}_{2}} $ is the chemical potential of H₂ at a specific temperature (T) and pressure (p):

  $ {\mu }_{{{\rm{H}}}_{2}}= ΔH-TΔS+k_{{\rm{B}}}T \ln(p/p_{0}) $

  (5)

  where ΔH and ΔS denote the changes of enthalpy and entropy, respectively. The reference pressure (p₀) was set at 0.1 MPa. The values for ΔH and ΔS are derived from the experimental database as cited in reference^[80]. If N₀^* denotes the maximum number of adsorbed H₂ molecules at 0 K, then N_ave represents the average number of adsorbed H₂ molecules at T and p, calculated as follows:

  $ N_{{\rm{ave}}}=N_{0}*(Z-1)/Z(6) $

  (6)

  Based on equations 4-6, we present the N_ave-p-T diagram in Fig.11, which quantitatively characterizes the H₂ adsorption and desorption behavior of TM₈B₆ under p and T. Within the temperature range of 100-200 K and the pressure range of 0.5-1.2 MPa, Ni₈B₆ and Pd₈B₆ exhibit a maximum adsorption of 40 and 32 H₂ molecules, respectively. As the temperature increased to 250 K, H₂ molecules began to desorb from the host systems. Nevertheless, at 200 K within the pressure range of 0.5-1.2 MPa, the majority of H₂ molecules remains adsorbed on the parent structures, with only 2-3 and 3-5 H₂ molecules being released from Ni₈B₆ and Pd₈B₆, respectively. Upon further increasing the temperature to 500 K, complete desorption of H₂ molecules occurs from both metallo-borospherene systems. Typically, for the practical process, the adsorption conditions are 1.2 MPa and 233 K, while for desorption conditions, they are 0.5 MPa and 358 K^[11]. Table 4 presents the theoretical storage capacity (G_theor) at 0 K, the number (N_ads) of adsorbed H₂ molecules under adsorption conditions, the number (N_des) of adsorbed H₂ molecules under desorption conditions, the practically usable number (N_prac=N_ads-N_des), and the effective storage capacity (G_prac). At the maximum theoretical capacity (G_theor=13.134%) for Ni₈B₆, about 33 out of 40 H₂ molecules are practically utilizable. Consequently, the practical gravimetric density decreases to 11.344%. In contrast, at the G_theor=6.562% for Pd₈B₆, around 26 molecules can practically be useful out of 32 H₂ molecules, leading to a practical gravimetric density of 5.412%. Therefore, the calculated G_prac of Ni₈B₆ and Pd₈B₆ are 11.344% and 5.412%, respectively, within the pressure range of 0.5-1.2 MPa and temperature range of 233-358 K.

  Figure 11

  

  Figure 11.  N_ave for (a) Ni₈B₆ and (b) Pd₈B₆ with change of temperature and pressure

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  Table 4

  

  Table 4.  Thermodynamical results of usable hydrogen capacity

  下载: 导出CSV

  Sample	Gtheor / %	Ntheor	Nads	Ndes	Nprac	Gprac / %
  Ni8B6	13.134	40	39.473	5.620	33.853	11.344
  Pd8B6	6.562	32	31.564	5.491	26.073	5.412

  2.5   Effects of TM₈B₆ oligomerization on H₂ storage

  Although the aforesaid results are promising for the isolated TM₈B₆ clusters, several critical issues remain to be addressed. For instance, is it feasible to synthesize the cluster-assembled materials composed of TM₈B₆ clusters as building blocks while preserving the structural integrity of the individual TM₈B₆ clusters? To address these questions, we examined the interactions between two TM₈B₆ clusters in the dimer configuration TM₁₆B₁₂. The results of geometric structure optimization indicate that the two TM₁₆B₁₂ (Fig.12a, 12b) clusters can connect to each other via two staggered and parallel TM₂B₂ rings. The dimerization processes of TM₁₆B₁₂ are exothermic. To investigate the adsorption capacity of dimers for H₂ molecules, we introduced 1 to 4 H₂ molecules incrementally onto the TM atoms of TM₁₆B₁₂. During the optimization of Ni₁₆B₁₂(H₂)₆₄ and Pd₁₆B₁₂(H₂)₆₄, we find that 9 and 6 H₂ molecules escape from the parent bodies, respectively. As illustrated in Fig.12c and 12d, the dimers Ni₁₆B₁₂ and Pd₁₆B₁₂ can accommodate a maximum of 55 and 58 H₂ molecules, respectively, resulting in hydrogen weight densities of 9.412% and 5.983%. Although the adsorption capacities of the dimers (TM₈B₆)₂ are slightly lower than those of the monomers (TM₈B₆), but they still surpass the set goal of 5.5%. Furthermore, the ΔE_a values of Ni₁₆B₁₂(H₂)₅₅ and Pd₁₆B₁₂(H₂)₅₈ are 0.163 and 0.141 eV, respectively, suggesting their suitability for reversible H₂ storage under ambient conditions.

  Figure 12

  

  Figure 12.  Optimized structures of (a) Ni₁₆B₁₂, (b) Pd₁₆B₁₂, (c) Ni₁₆B₁₂(H₂)₅₅, and (c) Pd₁₆B₁₂(H₂)₅₈

  The spheres colored gray, blue, tan, and pink are H, Ni, Pd, and B atoms, respectively.

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  3.   Conclusions

  The metallo-borospherenes TM₈B₆ were investigated as potential H₂ storage candidates by employing two DFT approaches. BOMD simulations reveal that these systems demonstrated excellent thermodynamic and dynamic stability at 1 000 K. The notable stabilities of TM₈B₆ can be attributed to the fact that they can be considered superatoms meeting the 18-electron rule. The analysis of PDOS reveal that the covalent interactions, arising from substantial overlaps between the TMd orbitals and the Bp orbitals, are predominant in TM₈B₆ clusters. Ni₈B₆ and Pd₈B₆ can at most attach 40 and 32 H₂ molecules with a hydrogen uptake density of 13.134% and 6.562%, respectively, exceeding the target set by US-DOE. The ΔE_a values for Ni₈B₆(H₂)₄₀/Pd₈B₆(H₂)₃₂ are 0.207/0.103 and 0.206/0.110 eV at the PBE(D3) and ωB97XD levels, respectively, satisfying the criteria for reversible H₂ adsorption and desorption cycles under ambient conditions. The analyses of QTAIM, ELF, LOL, PDOS, and IGMH were employed to elucidate the interactions between H₂ molecules and the parent structures, originating from electrostatic polarization and orbital hybridization. Thermos-chemistry calculations indicate that Ni₈B₆ and Pd₈B₆ have a H₂ uptake and release of 10.790% and 6.562% at atmospheric pressure, respectively. ADMP molecular dynamics simulations revealed that the vast majority of H₂ molecules in Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂ can completely detach from the parent compounds within the temperature range of 100 to 300 K. The obtained practical storage densities of Ni₈B₆ and Pd₈B₆ are 11.344% and 5.412% at 0.5-1.2 MPa and 233-358 K, respectively. Despite potential reductions in H₂ storage capacity, Ni₁₆B₁₂ and Pd₁₆B₁₂ dimers can effectively store 55 and 58 H₂ molecules with a gravimetric density of 9.412% and 5.983%, respectively. The ΔE_a values for Ni₁₆B₁₂(H₂)₅₅ and Pd₁₆B₁₂(H₂)₅₈ are determined to be 0.163 and 0.141 eV, respectively. These results indicate that the metallo-borospherenes TM₈B₆ exhibit potential as candidates for H₂ storage. However, further experimental validation is necessary to substantiate these findings.

  
  Acknowledgment: This work was supported by Applied Research Program of Yuncheng University (Grant No.YY-202513). Supporting information is available at http://www.wjhxxb.cn
  
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  Figure 1  (a) Optimized structures with ADCH charge of Ni₈B₆ (left) and Pd₈B₆ (right); (b) Molecular graphs of Ni₈B₆ (left) and Pd₈B₆ (right)

  Pink, cyan, tan, orange, yellow, and green balls are B, Ni, Pd, BCP, RCP, and CCP, respectively.

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  Figure 2  PDOS of (a) Ni₈B₆ and (b) Pd₈B₆

  Dashed lines represent HOMO levels; Inset: the corresponding HOMO and LUMO.

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  Figure 3  ESP of (a) Ni₈B₆, (b) Ni₈B₆(H₂)₈, (c) Ni₈B₆(H₂)₁₆, (d) Ni₈B₆(H₂)₂₄, (e) Ni₈B₆(H₂)₃₂, and (f) Ni₈B₆(H₂)₄₀

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  Figure 4  View of Ni₈B₆ with (a) 8 H₂, (b) 16 H₂, (c) 24 H₂, (d) 32 H₂, and (e) 40 H₂

  The spheres colored gray, blue, and pink are H, Ni, and B atoms, respectively.

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  Figure 5  View of Pd₈B₆ with (a) 8 H₂, (b) 16 H₂, (c) 24 H₂, and (d) 32 H₂

  The spheres colored gray, tan, and pink are H, Pd, and B atoms, respectively.

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  Figure 6  ΔG changed with temperature for (a) Ni₈B₆(H₂)_8n (n=1-5) and (b) Pd₈B₆(H₂)_8n (n=1-4) at 101.325 kPa

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  Figure 7  (a) Molecular graphs of Ni₈B₆(H₂)₄₀ and Pd₈B₆(H₂)₃₂; (b) Standard color scale and chemical explanation of sign(λ₂)ρ based on IGMH analysis^[74]

  a: Gray, pink, cyan, tan, orange, yellow, and green balls are H, B, Ni, Pd, BCP, RCP, and CCP, respectively; Inset: sign(λ₂)ρ with IGMH δg^inter=0.005 a.u. isosurface.

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  Figure 8  PDOS of (a) Ni₈B₆(H₂)₈, (b) Ni₈B₆(H₂)₄₀, (c) Pd₈B₆(H₂)₈, and (d) Pd₈B₆(H₂)₃₂

  Dashed lines represent HOMO levels; Inset: partial occupied molecular orbitals of (a) Ni₈B₆(H₂)₈, (b) Ni₈B₆(H₂)₄₀, (c) Pd₈B₆(H₂)₈, and (d) Pd₈B₆(H₂)₃₂

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  Figure 9  Variation of relative potential energy of (a) Ni₈B₆(H₂)₄₀ and (b) Pd₈B₆(H₂)₃₂ vs simulation times at 100 and 300 K

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  Figure 10  Extracted snapshots of (a) Ni₈B₆(H₂)₄₀ and (b) Pd₈B₆(H₂)₃₂ for the ADMP molecular dynamics simulations at 100 and 300 K

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  Figure 11  N_ave for (a) Ni₈B₆ and (b) Pd₈B₆ with change of temperature and pressure

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  Figure 12  Optimized structures of (a) Ni₁₆B₁₂, (b) Pd₁₆B₁₂, (c) Ni₁₆B₁₂(H₂)₅₅, and (c) Pd₁₆B₁₂(H₂)₅₈

  The spheres colored gray, blue, tan, and pink are H, Ni, Pd, and B atoms, respectively.

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  Table 1.  Average bond lengths, ΔE_s, and ΔE_a of Ni₈B₆(H₂)_n

  n	PBE(D3)				ωB97XD			PBE(D3)
  	dTM—B / nm	dTM—H / nm	dH—H / nm		ΔEs / eV	ΔEa / eV		ΔEs / eV	ΔEa / eV
  0	0.189	—	—		—	—		—	—
  8	0.191	0.165	0.084 8		0.680	0.680		0.569	0.569
  16	0.192	0.215	0.080 1		0.298	0.489		0.159	0.364
  24	0.192	0.239	0.078 3		0.025 0	0.335		0.140	0.289
  32	0.192	0.262	0.077 4		0.015 0	0.255		0.122	0.248
  40	0.192	0.288	0.077 0		0.013 0	0.206		0.046 0	0.207

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  Table 2.  Average bond lengths, ΔE_s, and ΔE_a of Pd₈B₆(H₂)_n

  n	PBE(D3)				ωB97XD			PBE(D3)
  	dTM—B / nm	dTM—H / nm	dH—H / nm		ΔEs / eV	ΔEa / eV		ΔEs / eV	ΔEa / eV
  0	0.209	—	—		—	—		—	—
  8	0.209	0.197	0.079 5		0.258	0.258		0.210	0.210
  16	0.209	0.264	0.077 4		0.057 0	0.157		0.064 0	0.137
  24	0.209	0.287	0.076 7		0.059 0	0.125		0.069 0	0.114
  32	0.209	0.297	0.076 4		0.064 0	0.110		0.072 0	0.103

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  Table 3.  Principal topological data of the bare TM₈B₆ and the TM₈B₆(H₂)_n complexes

  Sample	Bond	ρ(r) / a.u.	∇2ρ(r) / a.u.	H(r) / a.u.	ELF	LOL
  Ni8B6	B—Ni	0.119	-0.018 0	-0.075 0	0.575	0.538
  Ni8B6(H2)40	B—Ni	0.111	-0.006 00	-0.063 0	0.562	0.531
  	Ni—H	0.092 0a	0.357a	-0.022 0a	0.189a	0.326a
  		0.008 00b	0.018 0b	0.001 00b	0.052 0b	0.190b
  	B—H	0.008 00	0.150	0.000	0.071 0	0.217
  	H—H	0.217a	-0.704a	-0.194a	0.994a	0.971a
  		0.254b	-0.100b	-0.251b	1.000b	0.996b
  Pd8B6	B—Pd	0.097 0	0.010 0	0.048 0	0.601	0.551
  Pd8B6(H2)32	B—Pd	0.096 0	0.010 0	-0.046 0	0.586	0.543
  	Pd—H	0.060 0a	0.223a	-0.007 00a	0.150a	0.296a
  		0.005 00b	0.010 0b	0.000b	0.030 0b	0.149b
  	B—H	0.005 00	0.010 0	0.000	0.034 0	0.159
  	H—H	0.231a	-0.831a	-0.251a	0.999a	0.971a
  		0.254b	-0.101b	-0.251b	1.000b	0.999b
  a The hydrogen atom is the closest to the host structure; b The hydrogen atom is the farthest from the host structure.

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  Table 4.  Thermodynamical results of usable hydrogen capacity

  Sample	Gtheor / %	Ntheor	Nads	Ndes	Nprac	Gprac / %
  Ni8B6	13.134	40	39.473	5.620	33.853	11.344
  Pd8B6	6.562	32	31.564	5.491	26.073	5.412

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