Hydrogen storage of Li4&B36 cluster.

The Saturn-like charge-transfer complex Li4&B36, which was recently predicted with extensive first-principles theory calculations, were studied as a candidate for hydrogen storage material in the present work. The bonding characters of Li-B, B-B and Li-H2 bonds were revealed by the quantum theory of atoms in molecules (QTAIM). Each Li atom in Li4&B36 cluster can bind six H2 molecules at most, which results into the gravimetric density of 10.4%. The adsorption energies of H2 molecules on Li4&B36 cluster are predicted in the range of 0.08-0.14 eV at the wB97x level of theory.

Introduction

The hydrogen storage is an important issue not being solved up to now. Hydrogen can be adsorbed on a material through three different manners[1,2]. For chemisorption, the materials bind the dissociated hydrogen atoms with high binding energy of 2-4 eV, like metal hydrides and light complex hydrides[3,4]. The desorption occurs at high temperatures for the case of chemisorption. On the other hand, the materials, like nanostructured carbon[5,6], attached hydrogen molecules weakly with a binding energy in the meV range, which was regarded as physisorption. The strength of third form of binding is in the 0.1–0.8 eV range, and is intermediate between physisorption and chemisorption. Metal-decorated carbon-based nanomaterials and even their derivates[7-13], in which the metal atoms bind hydrogen in molecular form with intermediate binding energy, belong to the third form of binding. For example, the Li12C60 cluster was theoretically predicted to bind 60H2 at most, resulting in high gravimetric density[14], and Yoon et al.[15] have indicated that Ca can functionalize carbon fullerenes into high hydrogen storage capacity with a gravimetric density >8.4 wt%. In experiments, a lithium-doped fullerene with a Li:C60 mole ratio of 6:1 can reversibly desorb up to 5 wt % H2 with an onset temperature of ~270 °C[16]. Deuteration of Li12C60 was determined in experiment[17], and the results indicated that up to 9.5 wt % deuterium (D2) are absorbed in Li12C60.

Highly stable clusters were generally designed in theory for the hydrogen storage[18-20]. For example, Ba Tai et al.[19] have found that the B6Li8 cluster is a promising candidate for hydrogen storage media, which corresponds to a hydrogen uptake of 24% and adsorption energy of 0.099 eV estimated at the DFT level. Our previous work[21] indicated that the CTi72+cluster can bind 20 H2 molecules at most with adsorption energy of 0.24 eV, which can result into the gravimetric density of 19%. However, an ideal system is yet to be synthesized in experiment.

Boron fullerenes are also seen as efficient hydrogen storage media due to the light weight and capability to bind with metal adatoms. Many works reported the hydrogen storage of doped cage-like B80 with alkli-metal[22], alkaline-earth metal[23,24] and transitional metal[25]. In fact, B80 favors a core-shell (stuffed fullerene) structure in energy, not a cage-like configuration[26,27]. Therefore, the applications of B80 as hydrogen storage materials may be unrealistic. Recently, a combined experimental and theoretical study[28] observed the first borospherenes (B40) with a cube-like cage structure, which brings the development of borospherene chemistry. Bai et al.[29] have investigated the hydrogen storage of the lithium-decorated borospherene B40, and found the potential utilization of Li-B40 complexes as a novel nanomaterial for hydrogen storage. The Ti-decorated borospherene[30] also theoretically studied as a promising hydrogen storage material, and the evaluated reversible storage capacity is 6.1 wt% for Ti-B40 complexes.

A high-symmetry C6v quasi-planar structure with dual π aromaticity was predicted as the ground state of B36[31]. Nevertheless, by introducing four Li+ counterions into the B364− system, the neutral Saturn-like charge-transfer Li4&B36 complex with D2h symmetry can be highly stabilized[32]. In the present work, we will pay attention to the hydrogen storage capability of Li4&B36 system.

Results and Discussion

Structures and bonding characters of Li4&B36 cluster

In previous work, the extensive structural search has found that the most stable structure of Li4&B36 cluster is one high-symmetry Saturn-like geometry[32]. As shown in Fig. 1, our calculations also obtained a cage structure with point group (PG) symmetry of D2h, this structure corresponds to a closed-shell electronic state (ES) (1Ag). As Table 1 shows, the average Li-B and B-B bond lengths are 2.306 Å and 1.687 Å, respectively, predicted with wB97x functional[33] in conjunction with 6-31 g (d, p) basis set, and the calculated bond lengths are excellent in agreement with previous results[32]. Natural population analysis (NPA)[34] charge (shown in Table 1) indicate that each face-capping Li atom donating about one electron to the electron-deficient B36 core acts as electron donor, resulting into the (Li+)4B364− charge-transfer complex. From the electron configuration of Li atoms (CLi) in Li4&B36 cluster, one can find that the charge transfer from Li to B atoms result into the empty occupancy of 2 s valence shell. The sphere aromaticity of Li4&B36 is revealed by the huge negative nucleus-independent chemical shifts (NICS)[35] of -44.6 ppm at the cage centers. The lowest vibrational frequency is 203 cm−1 at the wB97x level of theory, which is sufficiently large to meet a stability criterion suggested by Hoffmann et al.[36]. The high binding energy of 4.09 eV per Li atom also confirms the high stability of Li4&B36 cluster.

Figure 1

Relaxed structure of Li4&B36 cluster (D2h), a) side view, b) top view.

Table 1

The calculated structural parameters, the lowest frequency, NICS, NPA charge (QLi) and electron configuration (CLi) of Li atoms and interaction energy (Eint) of bare Li4&B36 cluster.

Species		RLi-B(Å)	RB-B(Å)	ωL (cm−1)	NICS (0)	QLi (e)	C Li	Eint (eV)
Li4&B36	This worka	2.306	1.687	203	−44.6	0.86	1s22s02p0.1	4.09
	Theoryb	2.266	1.690	—	−42.8	0.83		3.27

aOur calculated values at the wB97x/6-31 G(d, p) level of theory.

aPredicted values at the PBE0/6-311 + G(d) level of theory from ref [32].

The bonding nature of Li4&B36 cluster will be revealed with QTAIM method[37], the molecular graphs and corresponding topological parameters are given in Fig. 2 and Table 2, respectively. Different (3, -1) bond critical points (BCPs) relative to B-B bonds and the bond critical points (BCPs) between Li atoms and two neighboring B atoms are found. For the traditional topological criterion, the covalent interaction corresponds to a negative Laplacian of electron density (∇2ρ(r) < 0) at the BCP. Another property, the total energy density H(r) (defined as the sum of local kinetic energy density G(r) and local potential energy density V(r)) proposed by Cremer and Krala[38] was proven to be very appropriate to characterize the degree of covalency of a bond. The negative H(r) is the indicator of a covalent bond. As Table 2 shows, all bond critical points relative to Li-B bonds correspond to positive Laplacian of electron density ∇2ρ(r) and H(r) value. This indicates that the Li-B bonds show typical closed-shell character corresponding to ionic bonds. On the other hand, the covalent bond nature of B-B bonds is revealed by their large electron density ρ(r), negative ∇2ρ(r) and H(r) values. This result is in excellent agreement with fuzzy bond order (FBO)[39] analyses, which predicts the bond order between Li and B atoms to be 0.23, suggesting the weak ionic bond nature of Li-B bonds. And the high fuzzy bond order (FBO) of B-B bonds reveal the strong covalent interaction between the bonding B atoms. The topological parameters of electron density shown in Table 2 indicate that all Li-B and B-B chemical bonds in Li4&B36 show typical ionic and covalent natures, respectively, which is also supported by the electron localization function (ELF)[40,41] shown in Table 2.

Figure 2

Molecular graph of Li4&B36 (a) and Li4&B36-H2 (b) complexes. The colour scheme identifying critical points is as follows: cyan ball for attractors, blue ball for bond critical points (BCP), red ball for ring critical points (RCP).

Table 2

Topological parameters of isolated H2 molecule and Li4&B36 cluster and H2-adsorbed Li4&B36-H2 complex.

Species	BCP	ρ	∇2ρ	H(r)	FBO	ELF
H2	H-H	0.270	−1.219	−0.305	1.00	1.00
Li4&B36	B-Li	0.026	0.113	0.001	0.23	0.05
	B-B	0.127 (0.151)a	−0.090 (−0.271)	−0.073 (−0.115)	0.56 (0.87)	0.69 (0.87)
Li4&B36-H2	B-Li	0.026	0.113	0.001	0.23	0.05
	B-B	0.127 (0.151)	−0.090 (−0.271)	−0.073 (−0.115)	0.56 (0.87)	0.69 (0.87)
	Li-H2	0.008	0.043	0.002	0.21	0.01
	H-H	0.267	−1.190	−0.299	0.76	1.00

aparameters for the shortest B-B bonds were shown in the parentheses.

H2 adsorption on Li4&B36 cluster

In this section, we will pay attention to the hydrogen storage stability of Li4&B36 cluster. The bond length of free H2 molecule is predicted as 0.744 Å at the wB97x/6-31 g (d, p) level of theory, and is in agreement with the experimental value of 0.741 Å[42]. The free and adsorbed H2 molecules in Li4&B36 show almost the same topological parameter as shown in Table 2. This indicates that the hydrogen is attached by the cluster in molecule form. The geometry of Li4&B36 cluster is maintained after H2 being attached comparing with isolated one. The molecular graph of Li4&B36-H2 is also shown in Fig. 2, from which one can find that one bond critical point between Li atom and H2 molecule is localized. The corresponding electron density, and other topological parameters (∇2ρ, H(r)) of Li-H2 BCP suggest that the Li-H2 interaction shows weak noncovalent characteristic. In addition, we note that the topological parameter of bond critical points relative to Li-B and B-B bonds in H2-adsorbed species are almost the same to those of isolated Li4&B36 cluster. This further demonstrates that the structure of host cluster was not distorted after H2 being attached.

The nH2-adsorbed configurations were extensively optimized to probe into the hydrogen storage stability. Vibrational frequency calculations confirmed that all the relaxed nH2-adsorbed structures are to be local stable, and the Cartesian coordinates of these species are listed in Table S1 of supporting information. The relaxed configurations are depicted in Fig. 3. Our calculations indicate that each Li atom in Li4&B36 cluster can attach six H2 molecules at most. The average Li-B and B-B bond lengths of nH2-adsorbed species are collected in Table 3, from which one can see that the B-B bond lengths in adsorbed species are not changed relative to the isolated cluster. On the other hand, the Li-B bonds are gradually elongated as the numbers of adsorbed H2 molecules increase due to the increased interaction between Li atoms and H2 molecules. The largest elongation of 0.025 Å is found for (Li-6H2)4&B36 species. Therefore, the H2 adsorptions do not result into the high structure distortion of Li4&B36 cluster. The bond lengths of adsorbed H2 molecules are elongated by only 0.7% relative to the isolate H2 molecule (0.774 Å). It is obvious that the H-H bonds are not broken after being adsorbed on Li4&B36 cluster. The Li–H2 distances are in a rather wide range from 2.207 Å to 3.080 Å as shown in Table 3. It is observable that there is an abrupt increase in the Li–H2 bond lengths from Li4&B36-4H2 to Li4&B36-5H2, so that the first four H2 molecules are closer to the Li site than the next one. By comparing Li4&B36-4H2 and (Li-H2)4&B36, one can find that the Li-B bonds are more elongated in Li4&B36-4H2 (4 H2 coadsorption on one Li atom) than those in (Li-H2)4&B36 which corresponds to uniform adsorption on 4 Li atoms. Moreover, the adsorption energy of (Li-H2)4&B36 is significantly larger than that of Li4&B36-4H2. This indicates that the hydrogen molecules tend to uniformly be attached by 4 Li atoms.

Figure 3

Optimized structure of H2 molecules adsorbed Li4&B36 cluster.

Table 3

Calculated structural parameters, NPA charge (QLi) and electron configuration (CLi) of Li atom, adsorption energy (Eads) and consecutive adsorption energy (Er) of H2-adsorbed Li4&B36 species.

Species	RLi-B(Å)	RB-B(Å)	RH-H(Å)	RLi-H(Å)	QLi(e)	C Li	Eads (eV)	Er (eV)
Li4&B36-H2	2.306	1.687	0.748	2.207	0.74	1s22 s02p0.20	0.14	0.14
Li4&B36-2H2	2.309	1.687	0.749	2.257	0.60	1s22s02p0.30	0.13	0.12
Li4&B36-3H2	2.311	1.687	0.749	2.407	0.54	1s22s02p0.36	0.11	0.07
Li4&B36-4H2	2.314	1.687	0.748	2.645	0.52	1s22s02p0.37	0.10	0.07
Li4&B36-5H2	2.314	1.687	0.748	2.914	0.52	1s22s02p0.37	0.09	0.04
Li4&B36-6H2	2.315	1.687	0.748	3.080	0.53	1s22s02p0.37	0.08	0.04
(Li-H2)4&B36	2.305	1.687	0.749	2.218	0.73	1s22s02p0.20	0.13	—
(Li-2H2)4&B36	2.309	1.687	0.749	2.258	0.60	1s22s02p0.30	0.13	—
(Li-3H2)4&B36	2.326	1.687	0.749	2.416	0.54	1s22s02p0.36	0.11	—
(Li-4H2)4&B36	2.327	1.687	0.748	2.674	0.53	1s22s02p0.37	0.10	—
(Li-5H2)4&B36	2.330	1.687	0.748	2.935	0.53	1s22s02p0.37	0.08	—
(Li-6H2)4&B36	2.331	1.687	0.748	3.011	0.53	1s22s02p0.36	0.08

We calculated consecutive adsorption energy (Er) as the energy gained by successive additions of H2 molecules to evaluate the reversibility for storage of H2 molecules. The average adsorption energy (Eads) was calculated to evaluate the adsorption capability of the Li4&B36 cluster. They are defined as follows:where, , , , are the total energy of Li4&B36 cluster, H2, Li4&B36-nH2, and Li4&B36-(n-1)H2, respectively. The Er is an important index for testing the continuous hydrogen adsorption capacity of nanomaterials. The adsorption of H2 is difficult if the Er is negative[25], and the positive Er means the spontaneous adsorption can occur between the hydrogen molecule and the Li4&B36 structure. From Table 3, one can be found that the Er for the sixth H2 adsorbed by one Li atom is 0.04 eV. Therefore, we can conclude that each Li atom can at most attach six H2 molecules in stable state. We note that a Li atom in Li-decorated B40 also attach six H2 molecules at most in previous work[29]. The adsorption of 24 H2 on the present system (Li4&B36) corresponds to a gravimetric density of 10.4%. It is obvious that the gravimetric density exceeds the 5.5 wt% at 2017 specified by the US department of energy (DOE). It can be seen from Table 3 that the Eads are in the range of 0.08eV–0.14 eV calculated at the wB97x/6-311++g(2d, 2p) level of theory. These values are very close to the average bonding energy for lithium coated fullerene Li12C60[14], aromatic B6Li8[19] complex, and lithium-decorated borospherene Li6B40[29].

It can be seen from Table 3 that the Li atoms in all nH2-adsorbed species act as electron donor, and the charge transfer is decreased as the numbers of adsorbed H2 molecules increase. In addition, the 2s→2p electron promotion occurs in the Li atoms after H2 being adsorbed, which results into the non-empty occupancy in 2p orbital (0.20–0.37e) of Li atoms.

Partial density of states (PDOS) of free H2 and Li4&B36 and 20H2-adsorbed (Li-5H2)4&B36 complexes are analyzed to understand the bonding characteristics of hydrogen adsorbed systems. The PDOS plots are depicted in Fig. 4. For Li4&B36 cluster, there exists very weak orbital overlaps between B and Li atoms, which is in agreement with the ionic characters revealed by aforementioned QTAIM analyses. Comparing to the free Li4&B36 cluster, there exists new peak around −15eV in the 20H2-adsorbed complex, stemming from the 2p electron of Li atoms due to the 2 s→2p electron promotion. Additionally, the new peak can participate into the orbital overlaps with H2 molecules. This results into the physical interaction between H2 molecules and Li4&B36 cluster.

Figure 4

Partial density of states (PDOS) of isolated H2 (a) and Li4&B36 (b), adsorbed H2 (c) and Li4&B36 (d) in Li4&B36-20H2 complex.

Conclusion

The Saturn-like charge-transfer complexes Li4&B36 cluster were investigated as a candidate for hydrogen storage with density functional theory (DFT) methods. The bonding nature in bare and H2-adsorbed Li4&B36 clusters was revealed with QTAIM analyses. Our results suggest that each face-capping Li atom donates about one electron to the electron-deficient B36 core, resulting into the (Li+)4B364− charge-transfer complex. The ionic characters of Li-B bonds and covalent characters of B-B bonds are understood for bare Li4&B36 cluster. Each Li atom in Li4&B36 cluster can at most attach five H2 molecules, which results into the gravimetric density of 10.4%, exceeding the 5.5 wt% at 2017 specified by the US department of energy (DOE). The structure distortion of Li4&B36 cluster was not occurred after the H2 molecules were attached. The adsorption energies of H2 molecules on Li4&B36 cluster are in the range of 0.08-0.14 eV at the wB97x/6-311++g(2d, 2p) level of theory. These values are very close to the average bonding energy for lithium coated fullerene Li12C60, aromatic B6Li8 complex and lithium-decorated borospherene Li6B40. Our study indicates that the Li4&B36 cluster may be appropriate material for hydrogen storage, but also need further confirmation in experiment.

Method

All the calculations were carried out with G09 package[43]. The molecular structures of bare and nH2-adsorbed Li4&B36 species were fully relaxed without any symmetry constrains using wB97x functional[33]. This functional has considered the long-rang corrections, and is proved to be reliable methods to predict non-covalent interactions. The classical extended basis set 6-31 g (d, p) was utilized in the geometry optimization. By adding H2 molecules around the Li atoms to construct the starting adsorption configurations of Li4&B36-nH2 (n=1–20) which were then full relaxed at the wB97x/6-31 G(d, p) level of theory. The harmonic vibrational frequency calculations were carried out at the same level of theory to guarantee that the optimized structures correspond to local minima on the potential energy surface. The larger basis set, 6-311++g(2d, 2p), was employed in the single-point energy calculations to obtain the more reasonable adsorption energy.

To understand the bonding characters of the studied systems, the quantum theory of atoms in molecules (QTAIM)[37] and natural population analyses (NPA)[34] were performed with MULTIWFN program[44].

Supporting information