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.

. Nevertheless, by introducing four Li + counterions into the B 36 4− system, the neutral Saturn-like charge-transfer Li 4 &B 36 complex with D 2h symmetry can be highly stabilized 32 . In the present work, we will pay attention to the hydrogen storage capability of Li 4 &B 36 system.

Results and Discussion
Structures and bonding characters of Li 4 &B 36 cluster. In previous work, the extensive structural search has found that the most stable structure of Li 4 &B 36 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 D 2h , this structure corresponds to a closed-shell electronic state (ES) ( 1 A g ). 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 B 36 core acts as electron donor, resulting into the (Li + ) 4 B 36 4− charge-transfer complex. From the electron configuration of Li atoms (C Li ) in Li 4 &B 36 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 Li 4 &B 36 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 Li 4 &B 36 cluster.
The bonding nature of Li 4 &B 36 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 (∇ 2 ρ(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 ∇ 2 ρ(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 ∇ 2 ρ(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 Li 4 &B 36 show typical ionic and covalent natures, respectively, which is also supported by the electron localization function (ELF) 40,41 shown in Table 2 The nH 2 -adsorbed configurations were extensively optimized to probe into the hydrogen storage stability. Vibrational frequency calculations confirmed that all the relaxed nH 2 -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 Li 4 &B 36 cluster can attach six H 2 molecules at most. The average Li-B and B-B bond lengths of nH 2 -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 H 2 molecules increase due to the increased interaction between Li atoms and H 2 molecules. The largest elongation of 0.025 Å is found for (Li-6H 2 ) 4 &B 36 species. Therefore, the H 2 adsorptions do not result into the high structure distortion of Li 4  We calculated consecutive adsorption energy (E r ) as the energy gained by successive additions of H 2 molecules to evaluate the reversibility for storage of H 2 molecules. The average adsorption energy (E ads ) was calculated to evaluate the adsorption capability of the Li 4 &B 36 cluster. They are defined as follows:  25 , and the positive E r means the spontaneous adsorption can occur between the hydrogen molecule and the Li 4 &B 36 structure. From Table 3, one can be found that the E r for the sixth H 2 adsorbed by one Li atom is 0.04 eV. Therefore, we can conclude that each Li atom can at most attach six H 2 molecules in stable state. We note that a Li atom in Li-decorated B 40 also attach six H 2 molecules at most in previous work 29  It can be seen from Table 3 that the Li atoms in all nH 2 -adsorbed species act as electron donor, and the charge transfer is decreased as the numbers of adsorbed H 2 molecules increase. In addition, the 2s→2p electron    36 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 Li 12 C 60 , aromatic B 6 Li 8 complex and lithium-decorated borospherene Li 6 B 40 . Our study indicates that the Li 4 &B 36 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 nH 2 -adsorbed Li 4 &B 36 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 H 2 molecules around the Li atoms to construct the starting adsorption configurations of Li 4 &B 36 -nH 2 (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 .