Abstract
Accurate prediction of the electronic and hydrogen storage properties of linear carbon chains (C_{ n }) and Literminated linear carbon chains (Li_{2}C_{ n }), with n carbon atoms (n = 5–10), has been very challenging for traditional electronic structure methods, due to the presence of strong static correlation effects. To meet the challenge, we study these properties using our newly developed thermallyassistedoccupation density functional theory (TAODFT), a very efficient electronic structure method for the study of large systems with strong static correlation effects. Owing to the alteration of the reactivity of C_{ n } and Li_{2}C_{ n } with n, oddeven oscillations in their electronic properties are found. In contrast to C_{ n }, the binding energies of H_{2} molecules on Li_{2}C_{ n } are in (or close to) the ideal binding energy range (about 20 to 40 kJ/mol per H_{2}). In addition, the H_{2} gravimetric storage capacities of Li_{2}C_{ n } are in the range of 10.7 to 17.9 wt%, satisfying the United States Department of Energy (USDOE) ultimate target of 7.5 wt%. On the basis of our results, Li_{2}C_{ n } can be highcapacity hydrogen storage materials that can uptake and release hydrogen at temperatures well above the easily achieved temperature of liquid nitrogen.
Introduction
Hydrogen (H_{2}), as a pure energy carrier, has many attributes. Being lightweight, it carries 142 MJ/kg of energy, which is approximately three times the energy content of gasoline, in terms of mass. Also, it is highly abundant on the earth in the form of water. More importantly, when hydrogen is burned with oxygen, it releases water vapor as the only effluent. Despite these advantages, there remain several problems to be clarified for the use of hydrogen. For example, hydrogen is highly flammable, and hence, if it comes in contact with the environment, it will burst. Another problem is related to its low energy content in terms of volume: it has only 0.0180 MJ/L, which is very low relative to gasoline (34.8 MJ/L). Moreover, over the past few years, the storage of hydrogen for onboard applications has been an active arena, which also requires a lightweight storage medium. Because of these reasons, storing a large amount of hydrogen reversibly in a small and lightweight container safely has been the biggest challenge in realizing a hydrogenbased economy^{1,2,3,4,5}.
Over the years, the United States Department of Energy (USDOE) has monitored the research progress in the development of hydrogen storage materials for consumer vehicles. In 2015, the USDOE set the ultimate target of 7.5 wt% for the gravimetric storage capacities of onboard hydrogen storage materials for lightduty vehicles^{5}. As of now, there have been several methods for the storage of hydrogen^{1,2,3,4}. The conventional methods for storing hydrogen are the high pressure method and the cryogenic method. In the high pressure method, one adopts carbon fiber reinforced tanks, which can withstand very high pressures (e.g., 350 to 700 bar), to store a large amount of completely recoverable hydrogen. In the cryogenic method, hydrogen is stored at very low temperatures (e.g., 20 K), typically requiring an expensive liquid helium refrigeration system. Both of these methods are not suitable for onboard automobile applications, because of the associated risk, high cost, and heavy weight. The storage of hydrogen in a metal hydride seems to be a convincing solution, but the irreversibility, slow kinetics, and high desorption temperature associated with this method are the problems yet to be overcome. Another promising solution is the storage of hydrogen in high surface area materials (e.g., graphene, carbon nanotubes, and metalorganic frameworks) through the adsorptionbased methods. As high surface area materials could adsorb large amounts of hydrogen, the corresponding H_{2} gravimetric storage capacities could be rather high. Nevertheless, these materials bind H_{2} molecules very weakly (i.e., mainly governed by van der Waals (vdW) interactions), and hence, they perform properly only at very low temperatures.
For reversible hydrogen adsorption and desorption at ambient conditions (298 K and 1 bar), in addition to other thermodynamic considerations, the ideal binding energies of H_{2} molecules on hydrogen storage materials should be in the range of about 20 to 40 kJ/mol per H_{2} ^{6,7,8}. Consequently, various novel methods are being explored to increase the binding energies of H_{2} molecules on high surface area materials to the aforementioned ideal range for ambient storage applications. To increase the H_{2} adsorption binding energy, the surface of the adsorbent is generally modified with substitution doping, adatom adsorption, functionalization, etc.^{2}. Among them, Li adsorption is especially attractive, because of its light weight with which a high gravimetric storage capacity could be easily achieved. Note also that Liadsorbed carbon materials have been shown to possess relatively high gravimetric storage capacities with enhanced H_{2} adsorption binding energies^{9,10,11,12,13,14,15,16,17}, through a chargetransfer induced polarization mechanism^{2, 18,19,20}.
Among carbon materials, linear carbon chains (C_{ n }), consisting of n carbon atoms bonded with sp^{1} hybridization (see Fig. 1(a), have recently attracted much attention owing to their unique electronic properties^{21,22,23,24,25,26,27,28,29,30,31,32,33,34,35}. Note that C_{ n } may be considered for hydrogen storage applications due to their onedimensional (1D) structures and the feasibility of synthesis of C_{ n } and their derivatives^{24,25,26,27,28,29,30}. Recently, Ptterminated linear carbon chains have been synthesized^{28}. As mentioned above, due to a chargetransfer induced polarization mechanism^{2, 18,19,20}, Literminated linear carbon chains (Li_{2}C_{ n }) can be good candidates for hydrogen storage materials (see Fig. 1(b–h). Because of the light elements (i.e., C and Li atoms) in Li_{2}C_{ n }, high gravimetric storage capacities could be easily achieved. However, to the best of our knowledge, there has been no comprehensive study on the electronic and hydrogen storage properties of Li_{2}C_{ n } in the literature, possibly due to the presence of strong static correlation effects in Li_{2}C_{ n } (commonly occurring in 1D structures due to quantum confinement effects)^{36}. Theoretically, the popular KohnSham density functional theory (KSDFT)^{37} with conventional semilocal^{38}, hybrid^{39,40,41,42}, and doublehybrid^{43,44,45,46} exchangecorrelation (XC) density functionals can provide unreliable results for systems with strong static correlation effects^{47}. For the accurate prediction of the properties of these systems, highlevel ab initio multireference methods are typically needed^{48}. Nonetheless, accurate multireference calculations are prohibitively expensive for large systems (especially for geometry optimization).
To circumvent the formidable computational expense of highlevel ab initio multireference methods, we have newly developed thermallyassistedoccupation density functional theory (TAODFT)^{49,50,51} for the study of large groundstate systems (e.g., containing up to a few thousand electrons) with strong static correlation effects. In contrast to KSDFT, TAODFT is a density functional theory with fractional orbital occupations, wherein strong static correlation is explicitly described by the entropy contribution (see Eq. (26) of ref. 49), a function of the fictitious temperature and orbital occupation numbers. Note that the entropy contribution is completely missing in KSDFT. Interestingly, TAODFT is as efficient as KSDFT for singlepoint energy and analytical nuclear gradient calculations, and is reduced to KSDFT in the absence of strong static correlation effects. Therefore, TAODFT can treat both single and multireference systems in a more balanced way than KSDFT. Besides, existing XC density functionals in KSDFT may also be adopted in TAODFT. Due to its computational efficiency and reasonable accuracy for large systems with strong static correlation, TAODFT has been successfully applied to the study of several strongly correlated electron systems at the nanoscale^{17, 52,53,54}, which are typically regarded as “challenging systems” for traditional electronic structure methods (e.g., KSDFT with conventional XC density functionals and singlereference ab initio methods)^{47}. Accordingly, TAODFT can be an ideal theoretical method for studying the electronic properties of Li_{2}C_{ n }. Besides, the orbital occupation numbers in TAODFT can be useful for examining the possible radical character of Li_{2}C_{ n }. For the hydrogen storage properties, as the interaction between H_{2} and Li_{2}C_{ n } may involve dispersion (vdW) interactions, electrostatic interactions, and orbital interactions^{3, 7, 55}, the inclusion of dispersion corrections^{56, 57} in TAODFT is important for properly describing noncovalent interactions. Therefore, in this work, we adopt TAODFT with dispersion corrections^{50} to study the electronic and hydrogen storage properties of Li_{2}C_{ n } with various chain lengths (n = 5–10). In addition, the electronic properties of Li_{2}C_{ n } are also compared with those of C_{ n } to examine the role of Li termination.
Computational Details
All calculations are performed with a development version of QChem 4.4^{58}, using the 6–31G(d) basis set with the fine grid EML(75,302), consisting of 75 EulerMaclaurin radial grid points and 302 Lebedev angular grid points. Results are computed using TAOBLYPD^{50} (i.e., TAODFT with the dispersioncorrected BLYPD XC density functional^{56} and the LDA θdependent density functional \({E}_{\theta }^{{\rm{LDA}}}\) (see Eq. (41) of ref. 49) with the fictitious temperature θ = 7 mhartree (as defined in ref. 49).
Results and Discussion
Electronic Properties
To obtain the ground state of C_{ n }/Li_{2}C_{ n } (n = 5–10), spinunrestricted TAOBLYPD calculations are performed for the lowest singlet and triplet energies of C_{ n }/Li_{2}C_{ n } on the respective geometries that were fully optimized at the same level of theory. The singlettriplet energy (ST) gap of C_{ n }/Li_{2}C_{ n } is calculated as (E _{T} − E _{S}), the energy difference between the lowest triplet (T) and singlet (S) states of C_{ n }/Li_{2}C_{ n }. As shown in Fig. 2(a), the ground states of C_{ n } and Li_{2}C_{ n } are singlets for all the chain lengths investigated.
Because of the symmetry constraint, the spinrestricted and spinunrestricted energies for the lowest singlet state of C_{ n }/Li_{2}C_{ n } should be the same for the exact theory^{49,50,51, 59}. To assess the possible symmetrybreaking effects, we also perform spinrestricted TAOBLYPD calculations for the lowest singlet energies on the corresponding optimized geometries. The spinrestricted and spinunrestricted TAOBLYPD energies for the lowest singlet state of C_{ n }/Li_{2}C_{ n } are found to be essentially the same (within the numerical accuracy of our calculations), implying that essentially no unphysical symmetrybreaking effects occur in our spinunrestricted TAOBLYPD calculations.
To assess the energetic stability of terminating Li atoms, the Li binding energy, E _{ b }(Li), on C_{ n } is computed using
where \({E}_{{{\rm{C}}}_{n}}\) is the total energy of C_{ n }, E _{Li} is the total energy of Li, and \({E}_{{{\rm{Li}}}_{2}{{\rm{C}}}_{n}}\) is the total energy of Li_{2}C_{ n }. E _{ b }(Li) is subsequently corrected for the basis set superposition error (BSSE) using the counterpoise correction^{60}, where the C_{ n } is considered as one fragment, and the 2 Li atoms are considered as the other fragment. As shown in Fig. 2(b), C_{ n } can strongly bind the Li atoms with the binding energy range of 258 to 357 kJ/mol per Li.
At the groundstate (i.e., the lowest singlet state) geometry of C_{ n }/Li_{2}C_{ n } (with N electrons), the vertical ionization potential (IP_{ v } = E _{ N−1} − E _{ N }), vertical electron affinity (EA_{ v } = E _{ N } − E _{ N+1}), and fundamental gap (E _{ g } = IP_{ v } − EA_{ v } = E _{ N+1} + E _{ N−1} − 2E _{ N }) are obtained with multiple energydifference calculations, with E _{ N } being the total energy of the Nelectron system. For each n, Li_{2}C_{ n } possesses the smaller IP_{ v } (see Fig. 3(a), EA_{ v } (see Fig. 3(b), and E _{ g } (see Fig. 4) values than C_{ n }. Note also that the IP_{ v }, EA_{ v }, and E _{ g } values of Li_{2}C_{ n } are less sensitive to the chain length than those of C_{ n }.
To examine the possible radical character of C_{ n }/Li_{2}C_{ n }, we calculate the symmetrized von Neumann entropy (e.g., see Eq. (9) of ref. 59)
for the lowest singlet state of C_{ n }/Li_{2}C_{ n } as a function of the chain length, using TAOBLYPD. Here, f _{ i } the occupation number of the i ^{th} orbital obtained with TAOBLYPD, which varies from 0 to 1, is approximately equal to the occupation number of the i ^{th} natural orbital^{49,50,51, 61}. For a system without strong static correlation ({f _{ i }} are close to either 0 or 1), S _{vN} provides insignificant contributions, while for a system with strong static correlation ({f _{ i }} are fractional for active orbitals, and are close to either 0 or 1 for others), S _{vN} increases with the number of active orbitals. As shown in Fig. 5, the S _{vN} values of C_{ n } with evennumber carbon atoms and Li_{2}C_{ n } with oddnumber carbon atoms are much larger than the S _{vN} values of C_{ n } with oddnumber carbon atoms and Li_{2}C_{ n } with evennumber carbon atoms, respectively.
To illustrate the causes of the oddeven oscillations in S _{vN}, we plot the occupation numbers of the active orbitals for the lowest singlet states of C_{ n } (see Fig. 6(a) and Li_{2}C_{ n } (see Fig. 6(b), calculated using TAOBLYPD. Here, the highest occupied molecular orbital (HOMO) is the (N/2)^{th} orbital, and the lowest unoccupied molecular orbital (LUMO) is the (N/2 + 1)^{th} orbital, with N being the number of electrons in C_{ n }/Li_{2}C_{ n }. For brevity, HOMO, HOMO − 1, HOMO − 2, and HOMO − 3, are denoted as H, H − 1, H − 2, and H − 3, respectively, while LUMO, LUMO + 1, LUMO + 2, and LUMO + 3, are denoted as L, L + 1, L + 2, and L + 3, respectively. As shown, C_{ n } with evennumber carbon atoms and Li_{2}C_{ n } with oddnumber carbon atoms possess more pronounced diradical character than C_{ n } with oddnumber carbon atoms and Li_{2}C_{ n } with evennumber carbon atoms, respectively.
On the basis of several measures (e.g., the smaller ST gap, smaller E _{ g }, larger S _{vN}, and more pronounced diradical character), C_{ n } with evennumber carbon atoms and Li_{2}C_{ n } with oddnumber carbon atoms should exhibit much stronger static correlation effects than C_{ n } with oddnumber carbon atoms and Li_{2}C_{ n } with evennumber carbon atoms (i.e., possessing singlereference character), respectively. Note that KSDFT with conventional XC density functionals can be unreliable for the properties of systems with strong static correlation effects, and accurate multireference calculations are prohibitively expensive for large systems (e.g., the longer C_{ n } and Li_{2}C_{ n }). In addition, due to the alteration of the reactivity of C_{ n } and Li_{2}C_{ n } with n, it is highly desirable to adopt an electronic structure method that can provide a balanced performance for both single and multireference systems, well justifying the use of TAODFT in this study.
Hydrogen Storage Properties
As pure carbon materials bind H_{2} molecules very weakly (i.e., mainly governed by vdW interactions), they are unlikely to be promising hydrogen storage materials at ambient conditions^{6}. Similarly, C_{ n } are not ideal for ambient storage applications, since the binding energies of H_{2} molecules remain small. In addition, the number of H_{2} molecules that can be adsorbed on C_{ n } is quite limited, due to the repulsive interaction between the adsorbed H_{2} molecules at short distances^{62}. Consequently, the more the adsorbed H_{2} molecules, the less the average H_{2} binding energy on C_{ n }. Therefore, C_{ n } cannot be highcapacity hydrogen storage materials at ambient conditions.
Here, we investigate the hydrogen storage properties of Li_{2}C_{ n } (n = 5–10). As illustrated in Fig. 1(b–h), at the groundstate geometry of Li_{2}C_{ n }, x H_{2} molecules (x = 1–6) are initially placed on various possible sites around each Li atom, and the structures are subsequently optimized to obtain the most stable geometry. All the H_{2} molecules are found to be adsorbed molecularly to the Li atoms. The average H_{2} binding energy, E _{ b }(H_{2}), on Li_{2}C_{ n } is evaluated by
where \({E}_{{{\rm{H}}}_{2}}\) is the total energy of H_{2}, and \({E}_{{{\rm{Li}}}_{2}{{\rm{C}}}_{n}2x{{\rm{H}}}_{2}}\) is the total energy of Li_{2}C_{ n } with x H_{2} molecules adsorbed on each Li atom. Subsequently, E _{ b }(H_{2}) is corrected for BSSE using a standard counterpoise correction^{60}. As shown in Fig. 7(a), E _{ b }(H_{2}) is in the range of 19 to 27 kJ/mol per H_{2} for x = 1–4, in the range of 18 to 19 kJ/mol per H_{2} for x = 5, and about 16 kJ/mol per H_{2} for x = 6, falling in (or close to) the ideal binding energy range.
To assess if the binding energies of successive H_{2} molecules are also in (or close to) the ideal binding energy range (i.e., not just the average H_{2} binding energy), the binding energy of the y ^{th} H_{2} molecule (y = 1–6), E _{ b,y }(H_{2}), on Li_{2}C_{ n } is evaluated by
Similarly, E _{ b,y }(H_{2}) is also corrected for BSSE using a standard counterpoise correction^{60}. As shown in Fig. 7(b), E _{ b,y }(H_{2}) is in the range of 16 to 27 kJ/mol per H_{2} for y = 1–4, in the range of 11 to 12 kJ/mol per H_{2} for y = 5, and less than 5 kJ/mol per H_{2} for y = 6. Therefore, while the first four H_{2} molecules can be adsorbed on Li_{2}C_{ n } in (or close to) the ideal binding energy range, the fifth and sixth H_{2} molecules are only weakly adsorbed (i.e., appropriate only for storage at very low temperatures).
To assess the types of noncovalent interactions between H_{2} and Li_{2}C_{ n }, we compute the atomic charge on each Li atom for Li_{2}C_{ n } (n = 5–10) with x H_{2} molecules (x = 0–6) adsorbed on each Li atom (see Fig. 8), using the CHELPG (CHarges from ELectrostatic Potentials using a Grid based method) scheme^{63}, in which atomic charges are fitted to reproduce the molecular electrostatic potential at a number of points around the molecule. For further clarification, we also plot the charge density isosurfaces of C_{5} and Li_{2}C_{5} with x H_{2} molecules (x = 0–6) adsorbed on each Li atom (see Fig. 9). Similar charge density isosurfaces are also found for the longer Li_{2}C_{ n } (n = 6–10) with the same number of adsorbed H_{2} molecules. As the electronegativity of C is much higher than that of Li, the transfer of electronic charge in Li_{2}C_{ n } is from Li to C_{ n }, resulting in a positive charge of 0.67–0.79 e on each Li atom in Li_{2}C_{ n }. The positively charged Li atom can interact with more than one H_{2} molecule, but the positive charge on Li decreases for the subsequent adsorption of H_{2} molecules (up to x = 3). This type of adsorption can be attributed to the polarization of H_{2} molecules by the positively charged Li atom (i.e., chargeinduced dipole interaction)^{2, 18,19,20}, leading to the enhanced H_{2} binding energy and high hydrogen uptake in Li_{2}C_{ n }. When the number of adsorbed H_{2} molecules is large (e.g., x = 4–6), there is a significant overlap of the Li and H_{2} charge densities, enhancing orbital interactions^{3, 7, 55}. This suggests that orbital interactions should also be responsible for the H_{2} binding energy, especially when a large number of H_{2} molecules (e.g., x = 4–6) are adsorbed on the Li atom. In particular, due to the enhanced orbital interactions, when the fourth H_{2} molecule is adsorbed on the Li atom, a small fraction of electronic charge is transferred from the Li atom to the adsorbed H_{2} molecules, slightly increasing the positive charge on Li. Interestingly, there is no overlap between the charge density of the sixth H_{2} molecule and the charge densities of other molecules, supporting that the sixth H_{2} molecule is only weakly adsorbed (i.e., mainly governed by vdW interactions). Accordingly, the noncovalent interactions between H_{2} and Li_{2}C_{ n } should involve chargeinduced dipole interactions, orbital interactions, and vdW interactions.
The desorption temperature, T _{ D }, of the adsorbed H_{2} molecules is estimated using the van’t Hoff equation^{13, 17, 64, 65},
where E _{ b }(H_{2}) is the average H_{2} binding energy (given by Eq. (3)), ΔS is the change in hydrogen entropy from gas to liquid phase (ΔS = 13.819R taken from ref. 66), p _{0} is the standard atmospheric pressure (1 bar), p _{ eq } is the equilibrium pressure, k _{ B } is the Boltzmann constant, and R is the gas constant. As shown in Table 1, T _{ D } for Li_{2}C_{ n } (n = 5–10) with x H_{2} molecules (x = 1–4) adsorbed on each Li atom, is estimated using Eq. (5) at p _{ eq } = 1.5 bar (as adopted in ref. 6) and at p _{ eq } = 1 bar (the standard atmospheric pressure). As the E _{ b }(H_{2}) values are in the range of 19.47 to 26.53 kJ/mol per H_{2} for x = 1–4, the corresponding T _{ D } values are in the range of 165 to 224 K at p _{ eq } = 1.5 bar, and in the range of 169 to 231 K at p _{ eq } = 1 bar, well above the easily achieved temperature of liquid nitrogen (i.e., 77 K). Therefore, Li_{2}C_{ n } (n = 5–10) can be viable hydrogen storage materials that can uptake and release hydrogen at temperatures well above 77 K. Note that strictly, ΔS should be the change of total entropy before and after the hydrogenation. Therefore, the T _{ D } values given in Table 1 have to be taken as rough estimates for the desorption temperatures due to the definition of ΔS. For all metalhydrogen systems, ΔS can be roughly estimated as the entropy change from molecular hydrogen gas to dissolved solid hydrogen^{1}, that is 15.720R (taken from ref. 66), as it arises mainly from the entropy loss of gaseous hydrogen during hydrogen uptake by the metal. Since Li_{2}C_{ n } (n = 5–10) adsorb hydrogen as a form of molecule, ΔS should be smaller than 15.720R (as the entropy of adsorbed hydrogen should be positive yet nonvanishingly small). While there is no accurate estimate of the entropy of hydrogen in adsorbed state, it should be safe to assume that it is much less than that of the gas state^{67}. Therefore, we estimate ΔS as the entropy change from molecular hydrogen gas to liquid hydrogen, as suggested by previous studies^{13, 17, 64, 65}. On the basis of Eq. (5), the larger the ΔS, the lower the T _{ D } values. However, even if the maximal ΔS (i.e., 15.720R) is adopted, the corresponding T _{ D } values will be only slightly lower (i.e., within 28 K for each case) than our reported T _{ D } values given in Table 1, being also well above 77 K. Accordingly, our comments remain the same even for the extreme case.
As Li_{2}C_{ n } (n = 5–10) can bind up to 8 H_{2} molecules (i.e., each Li atom can bind up to 4 H_{2} molecules) with the average and successive H_{2} binding energies in (or close to) the ideal binding energy range, the corresponding H_{2} gravimetric storage capacity, C _{ g }, is calculated using
Here, \({M}_{{{\rm{Li}}}_{2}{{\rm{C}}}_{n}}\) is the mass of Li_{2}C_{ n }, and \({M}_{{{\rm{H}}}_{2}}\) is the mass of H_{2}. Note that C _{ g } (see Eq. (6)) is 17.9 wt% for n = 5, 15.8 wt% for n = 6, 14.1 wt% for n = 7, 12.8 wt% for n = 8, 11.7 wt% for n = 9, and 10.7 wt% for n = 10, satisfying the USDOE ultimate target of 7.5 wt%. Based on the observed trends for Li_{2}C_{ n }, the maximum number of H_{2} molecules that can be adsorbed on each Li atom with the average and successive H_{2} binding energies in (or close to) the ideal binding energy range should be 4, regardless of the chain length. Therefore, the C _{ g } value of Li_{2}C_{ n } should decrease as the chain length increases. Note, however, that the C _{ g } values obtained here may not be directly compared to the USDOE target value, which refers to the complete storage system (i.e., with the storage material, enclosing tank, insulation, piping, etc.)^{5}. Nevertheless, since the C _{ g } values obtained here are much higher (especially for the shorter Li_{2}C_{ n }) than the USDOE ultimate target, the complete storage systems based on Li_{2}C_{ n } are likely to be highcapacity hydrogen storage materials that can uptake and release hydrogen at temperatures well above the temperature of liquid nitrogen.
Conclusions
In conclusion, the search for ideal hydrogen storage materials has been extended to large systems with strong static correlation effects (i.e., those beyond the reach of traditional electronic structure methods), due to recent advances in TAODFT. In this work, we have studied the electronic properties (i.e., the Li binding energies, ST gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, and active orbital occupation numbers) and hydrogen storage properties (i.e., the average H_{2} binding energies, successive H_{2} binding energies, H_{2} desorption temperatures, and H_{2} gravimetric storage capacities) of Li_{2}C_{ n } (n = 5–10) using TAODFT. As Li_{2}C_{ n } with oddnumber carbon atoms have been shown to possess pronounced diradical character, KSDFT with conventional XC density functionals can be unreliable for studying the properties of these systems. In addition, accurate multireference calculations are prohibitively expensive for the longer Li_{2}C_{ n } (especially for geometry optimization), and hence, the use of TAODFT in this study is well justified. On the basis of our results, Li_{2}C_{ n } can bind up to 8 H_{2} molecules (i.e., each Li atom can bind up to 4 H_{2} molecules) with the average and successive H_{2} binding energies in (or close to) the ideal range of about 20 to 40 kJ/mol per H_{2}. Accordingly, the H_{2} gravimetric storage capacities of Li_{2}C_{ n } are in the range of 10.7 to 17.9 wt%, satisfying the USDOE ultimate target of 7.5 wt%. Consequently, Li_{2}C_{ n } can be highcapacity hydrogen storage materials that can uptake and release hydrogen at temperatures well above the easily achieved temperature of liquid nitrogen.
For the practical realization of hydrogen storage based on Li_{2}C_{ n }, Li_{2}C_{ n } may be adopted as building blocks. For example, we may follow the proposal of Liu et al.^{68}, and consider connecting Licoated fullerenes with Li_{2}C_{ n }, which could also serve as highcapacity hydrogen storage materials. A systematic study of the electronic and hydrogen storage properties of these systems is essential, and may be considered for future work. Since linear carbon chains^{26, 27} and Ptterminated linear carbon chains^{28} have been successfully synthesized, the realization of hydrogen storage materials based on Li_{2}C_{ n } should be feasible, and is now open to experimentalists. In the future, we plan to examine how the electronic and hydrogen storage properties of linear carbon chains vary with different metal dopants (e.g., Na, Al, Ca, Ti, etc.).
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Acknowledgements
This work was supported by the Ministry of Science and Technology of Taiwan (Grant No. MOST1042628M002011MY3), National Taiwan University (Grant No. NTUCDP105R7818), the Center for Quantum Science and Engineering at NTU (Subproject Nos.: NTUERP105R891401 and NTUERP105R891403), and the National Center for Theoretical Sciences of Taiwan. S.S. would like to thank Kerwin Hui and ChihYing Lin for useful discussions.
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Seenithurai, S., Chai, J. Effect of Li Termination on the Electronic and Hydrogen Storage Properties of Linear Carbon Chains: A TAODFT Study. Sci Rep 7, 4966 (2017). https://doi.org/10.1038/s41598017052026
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