Abstract
It has been extremely difficult for conventional computational approaches to reliably predict the properties of multireference systems (i.e., systems possessing radical character) at the nanoscale. To resolve this, we employ thermallyassistedoccupation density functional theory (TAODFT) to predict the electronic and hydrogen storage properties of Literminated linear boron chains (Li_{2}B_{n}), with n boron atoms (n = 6, 8, …, and 16). From our TAODFT results, Li_{2}B_{n}, which possess radical character, can bind up to 4 H_{2} molecules per Li, with the binding energies in the desirable regime (between 20 and 40 kJ/mol per H_{2}). The hydrogen gravimetric storage capacities of Li_{2}B_{n} range from 7.9 to 17.0 wt%, achieving the ultimate goal of the United States Department of Energy. Accordingly, Li_{2}B_{n} could be promising media for storing and releasing H_{2} at temperatures much higher than the boiling point of liquid nitrogen.
Introduction
Hydrogen (H_{2}) is a clean energy carrier, because only water vapor is emitted when converted into energy. Besides, hydrogen is quite plentiful on Earth in compound form (e.g., water (H_{2}O)). Moreover, in terms of mass, the energy content of hydrogen is approximately three times that of gasoline. Hence, hydrogen can be a clean and green fuel, and has the potential to replace fossil fuels. Nonetheless, in terms of volume, the energy content of hydrogen is extremely low, when compared with that of gasoline. Therefore, efficient, economical, and safe hydrogen storage methods need to be developed for adopting hydrogen as a fuel in fuel cell vehicles^{1,2,3,4,5,6}. The conventional highpressure method where hydrogen is stored in carbon fiber reinforced plastic (CFRP) tanks at rather high pressures (e.g., between 350 and 700 bar) and the cryogenic method where hydrogen is stored at temperatures below the boiling point of H_{2} (about 20 K) are both unsuitable for onboard vehicle applications, due to the safety issues and high energy costs, respectively. Accordingly, it remains very difficult to efficiently store hydrogen in a lightweight and safe container^{6}.
Presently, metalorganic frameworks (MOFs) and metal hydrides are adopted for storing hydrogen. As far as MOFs are concerned, the hydrogen storage capacities can be large due to the pore structure and high surface area of MOFs. Nevertheless, the hydrogen desorption temperatures for MOFs are rather low. On the other hand, in spite of their large hydrogen storage capacities, the hydrogen desorption temperatures for metal hydrides (e.g., MgH_{2}, AlH_{3}, LiBH_{4}, and NaAlH_{4}) can be very high, and the kinetics can be very slow (due to the formation/breaking of covalent and/or ionic bonds during the adsorption/desorption of hydrogen). Based on simple thermodynamic arguments, the hydrogen binding energy on a hydrogen storage material (HSM) has to lie between 20 and 40 kJ/mol per H_{2}, for hydrogen uptake and release at nearambient conditions^{7,8,9}. However, among existing MOFs and metal hydrides, none can satisfy all the required conditions in order to use as an efficient HSM in onboard vehicles. Furthermore, on the basis of the ultimate goal of the United States Department of Energy (USDOE), a hydrogen gravimetric storage capacity of 6.5 wt% is required for a driving range of about 500 km^{6}. Consequently, finding a HSM with all desirable properties has been very challenging.
Recently, carbon nanostructures have emerged as the potential materials for technological applications. The flexible bond formation (sp^{1}, sp^{2}, and sp^{3} hybridization) of carbon yields a very wide range of nanostructures which possess unique properties^{10}. These nanostructures have been the test ground for studying many exotic phenomena. Especially, the discovery of C_{60} fullerene and the onedimensional (1D) carbon nanotubes has revealed the potential of nanomaterial applications in diverse fields. Later, the discovery of graphene, the first ever twodimensional (2D) material, has unlocked new possibilities in nanoscience and nanotechnology. This yields other 2D and quasi2D materials, such as silicene, phosphorene, boron nitride nanomaterials, transitionmetal dichalcogenides, single layers of metal oxides, and very recently, boron nanomaterials^{11,12}. Since graphene is a semimetal or zerogap semiconductor, its applications in electronics are impossible, unless a band gap can be opened by means of doping, defect formation, functionalization, and so on. Therefore, searching for other nanomaterials with better properties than graphene is in full swing.
In this pursuit, boron nanostructures are currently under intensive investigation to explore their electronic properties and potential applications. Due to recent advances in theoretical methods and experimental techniques, several boron nanostructures have been predicted and/or synthesized, and some of their basic properties and potential applications have been reported^{13,14,15,16,17,18,19,20,21}. The observation of the Dirac cone^{22} in β_{12} boron sheet grown on Ag(111) has increased interest in these boron nanomaterials, due to their potential applications in electronics and possible exotic properties. The clusters \({{\rm{B}}}_{13}^{+}\) and \({{\rm{B}}}_{19}^{}\) exhibit fluxional behavior, which has the potential for molecular Wankel motors^{15}. Theoretical predictions have shown that B_{40} is a potential anode material for Liion battery applications^{23}. Apart from their interesting electronic properties, these boron nanostructures can potentially be promising HSMs, because of their lightweight and high surface area. However, as carbon nanostructures are known to bind H_{2} molecules very weakly with the hydrogen binding energies typically less than 10 kJ/mol per H_{2} (primarily due to van der Waals (vdW) interactions), it is likely that most boron nanostructures also bind H_{2} molecules with insufficient binding energies. To increase the hydrogen binding energy to the desirable regime (between 20 and 40 kJ/mol per H_{2}), the boron nanostructures can be suitably decorated/functionalized with some selective atoms (e.g., Li, Al, Ca, light transition metals, etc.)^{2}.
However, transition metals are highly prone to clustering, and hence, the hydrogen storage capacities can easily decrease. Also, the first few H_{2} molecules can be adsorbed dissociatively (i.e., undesirable for applications at ambient conditions)^{24}. Therefore, the dopant or decorating atoms should be rationally chosen with the following characteristics: a) they should be lightweight, b) they should not form clusters, and c) they can bind hydrogen molecularly. The element lithium (Li) seems to be ideal, as it can easily satisfy these conditions. When adsorbed or decorated, the 2s electron from the Li atom can be transferred to nanostructures (due to the difference between their electronegativity values), and hence, the Li atom can become a cation (i.e., a positively charged ion). The electric field from the dipole that is produced by the charge transfer is capable of polarizing the incoming H_{2} molecules (around the Li), and binding the H_{2} molecularly with the aforementioned desirable regime. This mechanism is referred to as chargetransfer induced polarization^{2,25,26}. Therefore, Limodified boron nanomaterials can potentially be HSMs.
Among boron materials, there has recently been considerable interest in linear boron chains (B_{n}), containing n boron atoms bonded with sp^{1} hybridization (see Fig. 1(a)), because of their promising electronic and mechanochemical properties. Their mechanochemistry studies have revealed that, under tension, boron atoms can form linear chains^{27}. These boron chains show an interesting reversible structural phase transition between linear twoatomwide narrow ribbons and singleatom chains under tension. The chains and narrow ribbons are linked by a tensiondriven transformation and reported to be the stable structures. Understandably, linear boron chains can potentially be HSMs, if the chains are terminated with Li atoms. Note that Literminated linear boron chains (Li_{2}B_{n}) can be promising HSMs (see Fig. 1(b–g)), as they are lightweight materials associated with the aforementioned polarization mechanism^{2,25,26}. However, it remains very challenging to synthesize Li_{2}B_{n}, as they can possess radical character (prevalent in lowdimensional systems because of quantum confinement effect^{28}). Therefore, predicting the electronic and hydrogen storage properties of Li_{2}B_{n} could pave the way for the progress in this field, and also play an important role in selecting ideal materials for nanoelectronics and optoelectronics applications.
Currently, electronic structure calculations on systems at the nanoscale are mainly performed using KohnSham density functional theory (KSDFT)^{29} with approximate exchangecorrelation (XC) density functionals^{30}. However, KSDFT with traditional XC density functionals, such as BLYPbased (e.g., BLYP^{31,32}, B3LYP^{33,34}, and B2PLYP^{35}), PBEbased (e.g., PBE^{36}, PBE0^{37}, PBE02^{38}, PBE0DH^{39}, and PBEQIDH^{40}), and ωB97based (e.g., ωB97^{41}, ωB97X^{41}, ωB97XD3^{42}, and ωB97X2^{43}) functionals, may not be reliable in predicting the properties of multireference systems (i.e., systems possessing radical character), wherein ab initio multireference electronic structure methods, such as the density matrix renormalization group (DMRG) approach and multireference configuration interaction (MRCI) methods, are usually required^{44,45}. Despite their high predictive accuracy, calculations based on ab initio multireference electronic structure methods can however be computationally infeasible for systems at the nanoscale (particularly for geometry relaxation). Consequently, the study of multireference systems at the nanoscale remains extremely difficult for conventional computational approaches.
Aiming to achieve a decent balance between accuracy and efficiency for the study of multireference systems at the nanoscale, thermallyassistedoccupation density functional theory (TAODFT)^{46} and its extensions^{47,48,49} have recently been proposed. On the basis of the physical arguments given in Section III.E of ref.^{46} and the numerical investigations presented in Section IV of ref.^{46}, the static correlation energy of a system can be properly described by the entropy contribution (i.e., a function of the fictitious temperature and orbital occupation numbers (an implicit density functional)), even when a local or semilocal XC density functional is employed in TAODFT. Similar to the static correlation energy of a system, the entropy contribution in TAODFT is always nonpositive, yielding insignificant contributions for a singlereference system, and significantly lowering the total energy of a multireference system. Note that the inclusion of fractional occupation numbers in electronic structure calculations has been recently explored in some directions. For example, the fractional occupation number weighted electron density (FOD) analysis has been recently developed for a realspace measure and visualization of static correlation effects^{50,51}, yielding promising applications to carbon nanoforms^{52}.
Note that TAODFT is similar to KSDFT in computational efficiency. Moreover, TAODFT reduces to KSDFT when the static correlation energy of a system is insignificant, enabling a wellbalanced description for both systems possessing nonradical character and systems possessing radical character^{53,54,55,56,57}. In our previous TAODFT studies, Liadsorbed acenes^{55} and Literminated linear carbon chains (Li_{2}C_{n})^{57} were found to be promising HSMs at nearambient conditions, showing that the search for promising HSMs can be extended to large systems possessing radical character. Although Li_{2}C_{n} and Li_{2}B_{n} look similar in structure, their electronic and hydrogen storage properties are distinctly different. In particular, Li_{2}C_{n} were found to exhibit oscillatory diradical behavior with increasing chain length^{57}, while Li_{2}B_{n} exhibit increasing polyradical character with the increase of chain length (as will be seen below). Owing to its reasonable accuracy in predicting the properties of multireference systems at the nanoscale, we employ TAODFT to predict the electronic and hydrogen storage properties of Li_{2}B_{n} (n = 6, 8, …, and 16) in the present study.
Computational Details
We perform all calculations with QChem 4.4^{58}. Results are obtained from TAOBLYPD^{47} (i.e., TAODFT employing the BeckeLeeYangParr XC density functional with dispersion corrections (BLYPD)^{59} and the θdependent density functional based on the local density approximation (LDA)) with the fictitious temperature θ = 7 mhartree^{46,47}, using the 6–31 G(d) basis set and the numerical grid containing 75 radial points in the EulerMaclaurin quadrature and 302 angular points in the Lebedev grid.
Results and Discussion
Electronic Properties
To begin with, we perform spinunrestricted TAOBLYPD calculations to obtain the lowest singlet and lowest triplet states of Li_{2}B_{n} (n = 6, 8, …, and 16), with the respective geometries being fully relaxed^{57}. Subsequently, we calculate the singlettriplet energy gap of Li_{2}B_{n} as
where E_{S} and E_{T} are the lowest singlet and lowest triplet energies, respectively, of Li_{2}B_{n}. As presented in Fig. 2, Li_{2}B_{n} (n = 6, 8, …, and 16) has a singlet ground state (i.e., similar to Li_{2}C_{n}^{57}). As n increases, E_{ST} changes drastically, implying that the electronic properties of Li_{2}B_{n} can be properly tuned by changing the length of Li_{2}B_{n}.
For the exact theory, the lowest singlet energies of Li_{2}B_{n} obtained with spinrestricted and spinunrestricted calculations should be identical, due to the symmetry constraint^{46,47,48,60}. To see if this property remains valid here, spinrestricted TAOBLYPD calculations are additionally performed for the lowest singlet energies on the corresponding optimized geometries. It is found that the lowest singlet energies of Li_{2}B_{n} obtained with spinrestricted and spinunrestricted TAOBLYPD calculations are numerically identical, indicating that our spinunrestricted TAOBLYPD calculations do not yield unphysical symmetrybreaking solutions.
Strong binding of terminating Li atoms in Li_{2}B_{n} is essential for reversible hydrogen storage applications. In order to know if the terminating Li atoms are stable, we calculate the Li binding energy on B_{n} using^{57}
where \({E}_{{{\rm{B}}}_{n}}\), E_{Li}, and \({E}_{{{\rm{Li}}}_{2}{{\rm{B}}}_{n}}\) are the total energies of B_{n}, Li, and Li_{2}B_{n}, respectively. Subsequently, the standard counterpoise method^{61} is employed to correct the basis set superposition error (BSSE) associated with E_{b}(Li). As can be seen in Fig. 3, the Li atoms can strongly bind with the B_{n} chain (and form Li_{2}B_{n}) with binding energies ranging from 282 to 295 kJ/mol per Li. Such high binding energies are desirable for reversible applications, as the dopant atoms should remain bound to B_{n} during the desorption of hydrogen molecules. The bonding of Li to B_{n} should be ionic due to the electronic charge transfer from Li to B_{n}, which is expected to enhance the H_{2} adsorption to the Li atoms (as will be shown and discussed later).
The possibility of Li_{2}B_{n} for photovoltaic applications is assessed here. At the optimized geometry of the lowest singlet state (i.e., the ground state) of Li_{2}B_{n}, spinunrestricted TAOBLYPD is employed to calculate the vertical ionization potential (i.e., the energy difference between the cationic and neutral charge states)
vertical electron affinity (i.e., the energy difference between the neutral and anionic charge states)
and fundamental gap
via the Δ selfconsistent field (ΔSCF) approach. As the chain length of Li_{2}B_{n} increases, IP_{v} monotonically decreases, and EA_{v} monotonically increases, yielding a monotonically decreasing E_{g} (see Fig. 4). The IP_{v} value is found to be less sensitive to the chain length of Li_{2}B_{n} than the EA_{v} and E_{g} values. Note also that the E_{g} value of Li_{2}B_{n} (n = 14 and 16) is within the most interesting range (1 to 3 eV), giving promise for applications of Li_{2}B_{n} in nanophotonics. Note that our theoretical results may guide further experimental studies on Li_{2}B_{n}.
Here, we assess the multireference character of Li_{2}B_{n} by calculating the symmetrized von Neumann entropy^{47,48,53,55,56,57,60}
for the ground state of Li_{2}B_{n}. In Eq. (6), the occupation number of the i^{th} orbital calculated by TAOBLYPD (denoted as f_{i}), which takes a value between zero and one, is close to the i^{th} natural orbital occupation number^{46,47,48}. For a singlereference system ({f_{i}} are approximately equal to either zero or one), S_{vN} is negligible. However, for a multireference system ({f_{i}} are distinctly different from either zero or one for active orbitals, and are approximately equal to either zero or one for other orbitals), S_{vN} raises with the number of fractionally occupied orbitals (i.e., active orbitals). As presented in Fig. 5, S_{vN} increases with the chain length of Li_{2}B_{n}, implying that the multireference character of Li_{2}B_{n} should generally increase with the chain length.
To further illustrate the reasons of the increase of S_{vN} with n, the active orbital occupation numbers for the ground state of Li_{2}B_{n}, obtained with TAOBLYPD, are plotted in Fig. 6. For Li_{2}B_{n} (containing N electrons), the highest occupied molecular orbital (HOMO) is given by the (N/2)^{th} orbital, and the lowest unoccupied molecular orbital (LUMO) is given by the (N/2 + 1)^{th} orbital^{46,48,53,56,57}. As shown, the number of fractionally occupied orbitals oscillatorily increases with the chain length of Li_{2}B_{n}, implying that the multireference character of Li_{2}B_{n} should generally increase with n (see Table S1 in Supplementary Information).
Based on the above results, the longer Li_{2}B_{n}, which have the smaller E_{ST} values, smaller E_{g} values, larger S_{vN} values, and more significant polyradical character, are expected to possess stronger static correlation effects than the shorter Li_{2}B_{n}. Since KSDFT employing traditional XC density functionals cannot reliably predict the properties of systems possessing radical character, and calculations based on ab initio multireference electronic structure methods are computationally infeasible for systems at the nanoscale (e.g., the longer Li_{2}B_{n}), it is well justified to employ TAODFT in the present study.
Hydrogen Storage Properties
To begin with, we first examine the potential of B_{n} for hydrogen storage applications. Our preliminary TAOBLYPD results show that B_{n} can only adsorb H_{2} molecules with very weak binding energies (i.e., less than 5 kJ/mol per H_{2}), mainly governed by vdW interactions. Therefore, B_{n} can be useful for hydrogen storage only at very low temperatures. Besides, B_{n} can only bind very few H_{2} molecules, since the interactions between the adsorbed H_{2} molecules at short separation distances are repulsive. Therefore, the average hydrogen binding energy on B_{n} should decrease, as the number of the adsorbed H_{2} molecules increases. Accordingly, B_{n} should be modified to realize a promising HSM at ambient conditions.
In the following, the hydrogen storage properties of Li_{2}B_{n} (n = 6, 8, …, and 16) are studied using TAOBLYPD. At the optimized geometry of the lowest singlet state (i.e., the ground state) of Li_{2}B_{n}, we initially put x H_{2} molecules (x = 1–5) at several locations on the chain, and subsequently optimize the structures to get the most stable geometry. However, it is found that the H_{2} molecules are adsorbed at the Li sites. All the H_{2} molecules can be adsorbed molecularly to the Li atoms, and this molecular adsorption is preferable for practical hydrogen storage applications. Here, we calculate the average hydrogen binding energy on Li_{2}B_{n} using^{57}
where \({E}_{{{\rm{H}}}_{2}}\), \({E}_{{{\rm{Li}}}_{2}{{\rm{B}}}_{n}}\), and \({E}_{{{\rm{Li}}}_{2}{{\rm{B}}}_{n}2x{{\rm{H}}}_{2}}\) are the total energies of H_{2}, Li_{2}B_{n}, and Li_{2}B_{n} with x H_{2} molecules adsorbed on each Li, respectively. Necessarily, to account for BSSE, the aforementioned counterpoise method is used^{61}. The BSSE associated with E_{b}(H_{2}) is estimated to range from 2.16 to 2.69 kJ/mol per H_{2} for x = 1–5 (see Tables S2 and S3 in Supplementary Information). There is a significant error due to BSSE, which denotes the importance of BSSE correction in H_{2} adsorption binding energy calculations. As presented in Fig. 7, E_{b}(H_{2}) ranges from 21 to 26 kJ/mol per H_{2} for x = 1–4, and ranges from 18 to 19 kJ/mol per H_{2} for x = 5, lying in (or very close to) the aforementioned desirable binding energy regime (between 20 and 40 kJ/mol per H_{2}).
Besides the average hydrogen binding energy, the successive hydrogen binding energy should also be computed to assess the actual hydrogen storage capacity. Here, we calculate the successive hydrogen binding energy on Li_{2}B_{n} using^{57}
Here, E_{b,y}(H_{2}) is the binding energy of the y^{th} H_{2} molecule (y = 1–5) on Li_{2}B_{n}. Here also, the aforementioned counterpoise method^{61} is adopted to correct the BSSE associated with the binding energies. The BSSE associated with E_{b,y}(H_{2}) is estimated to range from 1.39 to 3.18 kJ/mol per H_{2} for y = 1–5 (see Tables S4 and S5 in Supplementary Information). There is a significant error due to BSSE, which also denotes the importance of BSSE correction in such studies. As shown in Fig. 8, E_{b,y}(H_{2}) ranges from 20 to 26 kJ/mol per H_{2} for y = 1–4, and ranges from 3 to 5 kJ/mol per H_{2} for y = 5. This denotes that only the first four H_{2} molecules (on each Li) are adsorbed in the desirable binding energy regime, and the fifth H_{2} molecule is adsorbed weakly (possibly due to vdW interactions and this is useful for hydrogen storage only at ultra low temperatures).
To examine the nature of the hydrogen binding energies on Li_{2}B_{n}, the Li atomic charge for Li_{2}B_{n} (n = 6, 8, …, and 16) with x H_{2} molecules (x = 0–5) adsorbed on each Li (see Fig. 9), is calculated by the CHELPG (CHarges from ELectrostatic Potentials using a Grid based method) scheme^{62}. In addition, the isosurfaces of charge density for B_{6} and Li_{2}B_{6} with x H_{2} molecules (x = 0–5) adsorbed on each Li are also plotted (see Fig. 10). For the longer Li_{2}B_{n}, the isosurfaces of charge density remain similar. The charge transfer is from Li to B_{n} in Li_{2}B_{n} due to the difference between their electronegativity values, yielding 0.6–0.7 e on each Li for Li_{2}B_{n}. This is also evidenced by the depleted charge around each Li. While the charge depleted Li is able to bind more than one H_{2} molecule, the Li atomic charge reduces with the number of the adsorbed H_{2} molecules (x = 0–3). This kind of adsorption should be due to that the charge depleted Li can polarize the incoming H_{2} molecules (i.e., governed by the aforementioned chargeinduced dipole interactions^{2,25,26}), yielding the enhanced hydrogen binding energy and high hydrogen storage capacity for Li_{2}B_{n}. However, when there are many H_{2} molecules adsorbed on each Li (e.g., x = 4), the charge densities of the Li atom and the adsorbed H_{2} molecules can be substantially overlapped, which can enhance orbital interactions^{3,7}. Therefore, when there are many H_{2} molecules adsorbed on each Li, orbital interactions are expected to be important for the hydrogen binding energies as well. Because of the enhanced orbital interactions, when the fourth H_{2} molecule is adsorbed on the Li atom, some electronic charge can be moved from the Li atom to the adsorbed H_{2} molecules, yielding a slight increase in the positive charge on Li. As the fifth H_{2} molecule is adsorbed very weakly (primarily due to vdW interactions), there is no significant change in the charge on Li. Consequently, the hydrogen adsorption in Li_{2}B_{n} can be due to not only chargeinduced dipole interactions, but also orbital interactions and vdW interactions.
For practical applications, we estimate the desorption temperature, T_{D}, of the adsorbed H_{2} molecules by
Note that Eq. (9) is the van’t Hoff equation^{55,57,63,64}, where E_{b}(H_{2}) is calculated using Eq. (7). As suggested by previous studies^{55,57}, the total entropy change before and after the hydrogenation, ΔS, is approximated by the change in hydrogen entropy from gas to liquid phase (ΔS = 13.819R^{65}). Besides, p_{0}, p_{eq}, k_{B}, and R are the standard atmospheric pressure (1 bar), the equilibrium pressure, the Boltzmann constant, and the gas constant, respectively. As listed in Table 1, T_{D} for Li_{2}B_{n} (n = 6, 8, …, and 16) with x H_{2} molecules (x = 1–4) adsorbed on each Li, is calculated by Eq. (9) at p_{eq} = 1.5 bar^{8} and at p_{eq} = 1 bar. Since the E_{b}(H_{2}) values range from 21.13 to 26.42 kJ/mol per H_{2} for x = 1–4, the respective T_{D} values range from 179 to 223 K at p_{eq} = 1.5 bar, and range from 184 to 230 K at p_{eq} = 1 bar. These desorption temperatures are all well above 77 K (i.e., the boiling point of liquid nitrogen), which can be easily achieved. Therefore, Li_{2}B_{n} (n = 6, 8, …, and 16) can be promising HSMs for storing and releasing H_{2} at temperatures much higher than the boiling point of liquid nitrogen.
Since Li_{2}B_{n} (n = 6, 8, …, and 16) is able to adsorb a total of 8 H_{2} molecules (i.e., 4 per Li), where both the average hydrogen binding energies and successive hydrogen binding energies are in the aforementioned desirable regime, we calculate the respective hydrogen gravimetric storage capacity using^{57}
where \({M}_{{{\rm{Li}}}_{2}{{\rm{B}}}_{n}}\) is the mass of Li_{2}B_{n}, and \({M}_{{{\rm{H}}}_{2}}\) is the mass of H_{2}. As shown in Table 1, C_{g} ranges from 7.9 to 17.0 wt%, achieving the USDOE ultimate goal of 6.5 wt%. It can be inferred from the H_{2} adsorption patterns of Li_{2}B_{n} that Li_{2}B_{n} is able to adsorb up to a total of 8 H_{2} molecules with both the average hydrogen binding energies and successive hydrogen binding energies being in the desirable regime, independent of the value of n. Accordingly, the C_{g} value of Li_{2}B_{n} should decrease with increasing chain length. Nevertheless, it may not be justified to directly compare the C_{g} values presented in this work with the USDOE ultimate goal of 6.5 wt%, as the latter is for the entire system of hydrogen storage (which includes the HSM, surrounding container, insulation equipment, and so on)^{6}. However, the C_{g} values of Li_{2}B_{n} presented in this work are rather high (particularly for the smaller n), when compared with the USDOE ultimate goal. Therefore, the entire systems of hydrogen storage via Li_{2}B_{n} can still be promising HSMs for storing and releasing H_{2} at temperatures much higher than the boiling point of liquid nitrogen.
Conclusions
In conclusion, because of the recent developments of TAODFT, calculations on large systems possessing radical character are now feasible. Accordingly, it is now possible to look for desirable HSMs among multireference systems at the nanoscale (i.e., extremely difficult systems for conventional computational approaches). In this work, the electronic properties (e.g., E_{b}(Li), E_{ST}, IP_{v}, EA_{v}, E_{g}, S_{vN}, and the occupation numbers of active orbitals) and hydrogen storage properties (e.g., E_{b}(H_{2}), E_{b,y}(H_{2}), T_{D}, and C_{g}) of Li_{2}B_{n} (n = 6, 8, …, and 16) have been studied using TAODFT. As the ground states of Li_{2}B_{n} exhibit multireference character, KSDFT with traditional XC functionals may not reliably predict the properties of Li_{2}B_{n}, and calculations based on ab initio multireference electronic structure methods can be computationally infeasible due to the large electronic systems considered here. Therefore, it is well justified to adopt TAODFT in the present study. From our TAODFT results, Li_{2}B_{n} is able to adsorb a total of 8 H_{2} molecules, where both the average hydrogen binding energies and successive hydrogen binding energies are in the desirable regime (between 20 and 40 kJ/mol per H_{2}). Hence, the C_{g} values of Li_{2}B_{n} range from 7.9 to 17.0 wt%, achieving the USDOE ultimate goal of 6.5 wt%. Accordingly, Li_{2}B_{n} could be promising HSMs for storing and releasing H_{2} at temperatures much higher than the boiling point of liquid nitrogen, which can be easily achieved.
Because of recent advances in the synthesis of nanomaterials, it may be feasible to practically realize hydrogen storage via Li_{2}B_{n}. For example, Li_{2}B_{n} can be adopted as building blocks. As proposed by Liu et al.^{66}, we can connect Licoated fullerenes with Li_{2}B_{n}, which may be promising HSMs as well. It will then be necessary to comprehensively study the relevant properties of these systems, which can be a possible future study. Furthermore, as the syntheses of Ptterminated linear carbon chains have been feasible^{67}, the syntheses of Li_{2}B_{n} may be feasible in near future, and are now open to experimentalists.
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Acknowledgements
This work was supported by the Ministry of Science and Technology of Taiwan (Grant Nos MOST1072628M002005MY3; MOST1042628M002011MY3), National Taiwan University (Grant Nos NTUCC107L892906; NTUCCP106R891706; NTUCDP105R7818), and the National Center for Theoretical Sciences of Taiwan.
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This work was initiated and designed by S.S. and J.D.C. The calculations were performed by S.S. The data analysis was performed by S.S. and J.D.C. The manuscript was written by S.S. and J.D.C.
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Seenithurai, S., Chai, J. Electronic and Hydrogen Storage Properties of LiTerminated Linear Boron Chains Studied by TAODFT. Sci Rep 8, 13538 (2018). https://doi.org/10.1038/s41598018319479
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