B_(12)M_4（M=Li，Ti，Sc）结构及储氢性能的密度泛函理论研究
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摘要
氢气储量丰富，具有高的质量燃烧值且燃烧产物清洁无污染，被认为是替代化石燃料的新一代能源载体。但是氢气的存储却成为在运输行业中实际应用的“瓶颈”。作为理想的储氢材料，应该满足以下特定要求：高的储氢量(包括质量密度和体积密度)、温和条件下快速的吸/脱附动力学、合适的工作温度、可逆循环性能、材料成本低以及安全性好等。为了在温和的条件下完成充放氢气，氢气与储氢材料间的结合能应该介于物理吸附与化学吸附之间，而且氢气主要以分子形式存在。为此，人们研究和探索了很多储氢方法，包括压缩储氢、液化储氢以及利用金属或金属复合物吸附储氢。尽管这些方法在某些方面都有各自的优点，但都不足以满足氢能在交通运输方面的实际要求。
本论文中，我们由早先研究的以B_(12)为核心的B_(12)CO_(12)得到启发，提出利用金属掺杂的B_(12)团簇进行储氢，其中研究的金属以碱金属Li和过渡金属Sc，Ti为主。所有异构体均使用高斯03程序，在密度泛函理论(DFT)下用B3LYP方法进行计算。使用标准劈裂共价基组6-31G (d, p)描述介入的所有原子轨道。几何优化没有对称制约。通过频率计算来确认它们是势能面的能量极小值。所有分析数据在B_3LYP/6-31G (d, p)水平下得到。平均结合能定义为：
Ea= {E [B_(12)X_4-nH_2] - E [B_(12)X_4]–nE[H_2]} /n (X=Li, Ti, Sc)
许多研究显示，MP2方法计算弱相互作用较好。因此，为得到准确性平均氢气结合能，在MP2下对各结构行单点计算以计算平均氢分子吸附能。计算中还考虑了基组重叠误差（BSSE）。
对锂掺杂B12团簇的结构稳定性及其储氢性能系统研究结果表明，最佳掺杂方案为锂缀加在B12Li4的六元环上，在B12Li4团簇中，金属原子都倾向于束缚到B原子周围，而不是形成金属簇。每个锂原子至少可以吸附3个氢分子，物理吸附储氢量达到13.32 wt%，平均氢分子吸附能在0.033-0.089eV之间。自然电荷布局分析(NBO)显示B_(12)Li_4中平均锂原子所带电荷为0.727|e|，且在吸附氢气过程中，极化诱导作用最为关键。
采用密度泛函理论对Ti掺杂B12团簇的结构稳定性及其储氢性能进行了理论计算，讨论了掺杂团簇的结构以及电荷转移。结果表明，我们研究的最稳定结构和次稳定结构均可避免金属团聚问题。其中D2d对称性的最稳定结构至多吸附8个H_2分子，平均结合能为0.521 eV。具有Td对称性的次稳定结构中强的M-B键将金属固定在六元环上，可以通过Kubas作用吸附16H_2，平均吸附能为0.434 eV/H2，相应质量分数为9.125 wt%。当每个Ti吸附3个H2时，平均吸附能为0.310 eV/H_2，可使H2在常温常压下容易吸附和脱附，相应质量分数为6.952 wt%。
对Sc掺杂B_(12)团簇的结构稳定性及其储氢性能进行了理论计算，结果表明，B_(12)Sc_4可吸附12个H2分子，平均结合能为0.108 eV，非常有趣的是在提出的最稳定的B12Ti4和B12Sc4中，每个B3可以把视为一个具有s-，p-和d-轨道的超原子。B_(12)Sc_4中Sc主要是通过诱导作用吸附H2分子。
本研究得到国家973预研究课题(210CB635110)和国家自然科学基金重点项目(21031003)基金的资助。
Hydrogen is widely viewed as the next generation of energycarrier to replace the fossil fuels due to its abundance, high chemicalenergy, and pollution-free burning. However, hydrogen storage is the“bottleneck”for the on-board application of hydrogen as energycarrier. Materials suitable for hydrogen storage of vehicularapplications must meet some rigid requirements, such as highvolumetric and gravimetric densities, fast kinetics for adsorption aswell as desorption of molecular hydrogen at ambient conditions,recyclability. To achieve the reversible hydrogen uptaking andreleasing at near ambient conditions, the H_2binding energy should besomewhat intermediate between that of physisorption andchemisorption where the hydrogen is stored mainly in molecular form.Several ways have been investigated and developed to store hydrogengas, involving its compression, liquefaction, and adsorption in severalmetals and metal alloys and so on. Unfortunately, none of thesetechnologies is good enough to satisfy the on-board application ofhydrogen energy, even though each way possesses desirablecharacteristics in certain areas.
In this paper, inspired by our previous foundation of a B_(12)core in B_(12)CO_(12), we propose metal atoms doped B_(12)cluster, the metals weused in the paper are Li atoms (The Alkali Metal) and Ti, Sc atoms. Allthe isomers are optimized at the level of density functional theory(DFT) with Becke’s three-parameter exchange functional andLee-Yang-Parr correlation functional using the Gaussian 03 program.The standard split valence basis set 6-31G(d, p) is employed todescribe the orbital of all atoms involved. The geometry optimizationsare done with no symmetry restriction. Frequency calculations forselected structures are carried out to identify it an energy minima onthe potential energy surface. All the population analysis is also basedon the data obtained at B_3LYP/6-31G(d, p) level. The average bindingenergy per H_2(ABE/ H_2) is defined as
Ea= {E [B_(12)X_4-n H_2]-E [B_(12)X_4]–n E [H_2]}/n (X=Li, Ti, Sc)
Where, E [B_(12)X_4], E [H_2] and E [B_(12)X_4-n H_2] are the electronic energyof relaxed B_(12)X_4, H_2and B_(12)X_4-n H_2, respectively; and n is the number ofH2molecule. Many investigations demonstrate that MP2 method ismore efficient for calculating the weak interactions. So, to get theaccuracy ABE/H_2, single point energy calculations for all B12X4-n H2,the most stable B_(12)X_4and H_2are performed at MP2/6-311G(d, p) level.The basis set superposition error (BSSE) has been corrected usingthe full counterpoise method for all the B12X4-n H2complexes atMP2/6-311G(d, p) level.
The density functional theory (DFT) has been performed toinvestigate the structures and stabilities of B12Li4clusters. The Liatoms prefer the hexagon sites. Once the metals are absorbed on B12,each can bring up to four hydrogen molecules with an average bindingenergy of 0.033-0.089 eV, corresponding to 13.32 wt%. The NBO analysis indicates that the charge of Li atom in B_(12)Li_4is 0.727|e|, andinductive interaction is important for Li to adsorb the H2molecules inB_(12)Li_4.
We investigated hydrogen adsorption on Ti-doped B_(12)nanostructures. The results show that the lowest-energystructure(D2d) and the lower-lying structure(Td) of B_(12)Ti_4can avoidingthe notorious clustering problem. As for the B_(12)Ti_4with Tdsymmetry ,Ti can bind strongly to the hexagons of B_(12)to form regular tetrahedronstructure, thus it can store up to 16 H2molecules via the Kubasinteraction with an average binding energy of 0.434 eV/H2,corresponding to a gravimetric density of hydrogen storage of 9.125wt%. If each Ti adsorbs 3 H_2, the average adsorption energy is 0.26ev/H2, corresponding to a gravimetric density of hydrogen storage of6.952 wt%, while B_(12)Ti_4(D2d) can only host 8 H2molecules at mostwith an average binding energy of 0.521 eV per H2. We found that theKupas interaction dominates the attracting between Ti atoms andhydrogen molecules.
The structure and hydrogen adsorption property of a B_(12)Sc4wasinvestigated with the first principle calculations. Like the B_(12)Ti_4(D2d),in B_(12)Sc4, Metal atoms prefer binding to B atoms other than forming Ticlusters. The B_(12)Sc4can bind up to 12 H_2molecules with an averagebinding energy of 0.108 eV per H_2, It is very interesting that we findthat in B_(12)Sc_4, every B3rings can be regarded as a super atom with s-,p- and d-like orbitals.
This work was supported by National Basic Research (973)Program of China (No. 210CB635110) and National Natural ScienceFoundation of China (21031003).
本论文中，我们由早先研究的以B_(12)为核心的B_(12)CO_(12)得到启发，提出利用金属掺杂的B_(12)团簇进行储氢，其中研究的金属以碱金属Li和过渡金属Sc，Ti为主。所有异构体均使用高斯03程序，在密度泛函理论(DFT)下用B3LYP方法进行计算。使用标准劈裂共价基组6-31G (d, p)描述介入的所有原子轨道。几何优化没有对称制约。通过频率计算来确认它们是势能面的能量极小值。所有分析数据在B_3LYP/6-31G (d, p)水平下得到。平均结合能定义为：
Ea= {E [B_(12)X_4-nH_2] - E [B_(12)X_4]–nE[H_2]} /n (X=Li, Ti, Sc)
许多研究显示，MP2方法计算弱相互作用较好。因此，为得到准确性平均氢气结合能，在MP2下对各结构行单点计算以计算平均氢分子吸附能。计算中还考虑了基组重叠误差（BSSE）。
对锂掺杂B12团簇的结构稳定性及其储氢性能系统研究结果表明，最佳掺杂方案为锂缀加在B12Li4的六元环上，在B12Li4团簇中，金属原子都倾向于束缚到B原子周围，而不是形成金属簇。每个锂原子至少可以吸附3个氢分子，物理吸附储氢量达到13.32 wt%，平均氢分子吸附能在0.033-0.089eV之间。自然电荷布局分析(NBO)显示B_(12)Li_4中平均锂原子所带电荷为0.727|e|，且在吸附氢气过程中，极化诱导作用最为关键。
采用密度泛函理论对Ti掺杂B12团簇的结构稳定性及其储氢性能进行了理论计算，讨论了掺杂团簇的结构以及电荷转移。结果表明，我们研究的最稳定结构和次稳定结构均可避免金属团聚问题。其中D2d对称性的最稳定结构至多吸附8个H_2分子，平均结合能为0.521 eV。具有Td对称性的次稳定结构中强的M-B键将金属固定在六元环上，可以通过Kubas作用吸附16H_2，平均吸附能为0.434 eV/H2，相应质量分数为9.125 wt%。当每个Ti吸附3个H2时，平均吸附能为0.310 eV/H_2，可使H2在常温常压下容易吸附和脱附，相应质量分数为6.952 wt%。
对Sc掺杂B_(12)团簇的结构稳定性及其储氢性能进行了理论计算，结果表明，B_(12)Sc_4可吸附12个H2分子，平均结合能为0.108 eV，非常有趣的是在提出的最稳定的B12Ti4和B12Sc4中，每个B3可以把视为一个具有s-，p-和d-轨道的超原子。B_(12)Sc_4中Sc主要是通过诱导作用吸附H2分子。
本研究得到国家973预研究课题(210CB635110)和国家自然科学基金重点项目(21031003)基金的资助。
Hydrogen is widely viewed as the next generation of energycarrier to replace the fossil fuels due to its abundance, high chemicalenergy, and pollution-free burning. However, hydrogen storage is the“bottleneck”for the on-board application of hydrogen as energycarrier. Materials suitable for hydrogen storage of vehicularapplications must meet some rigid requirements, such as highvolumetric and gravimetric densities, fast kinetics for adsorption aswell as desorption of molecular hydrogen at ambient conditions,recyclability. To achieve the reversible hydrogen uptaking andreleasing at near ambient conditions, the H_2binding energy should besomewhat intermediate between that of physisorption andchemisorption where the hydrogen is stored mainly in molecular form.Several ways have been investigated and developed to store hydrogengas, involving its compression, liquefaction, and adsorption in severalmetals and metal alloys and so on. Unfortunately, none of thesetechnologies is good enough to satisfy the on-board application ofhydrogen energy, even though each way possesses desirablecharacteristics in certain areas.
In this paper, inspired by our previous foundation of a B_(12)core in B_(12)CO_(12), we propose metal atoms doped B_(12)cluster, the metals weused in the paper are Li atoms (The Alkali Metal) and Ti, Sc atoms. Allthe isomers are optimized at the level of density functional theory(DFT) with Becke’s three-parameter exchange functional andLee-Yang-Parr correlation functional using the Gaussian 03 program.The standard split valence basis set 6-31G(d, p) is employed todescribe the orbital of all atoms involved. The geometry optimizationsare done with no symmetry restriction. Frequency calculations forselected structures are carried out to identify it an energy minima onthe potential energy surface. All the population analysis is also basedon the data obtained at B_3LYP/6-31G(d, p) level. The average bindingenergy per H_2(ABE/ H_2) is defined as
Ea= {E [B_(12)X_4-n H_2]-E [B_(12)X_4]–n E [H_2]}/n (X=Li, Ti, Sc)
Where, E [B_(12)X_4], E [H_2] and E [B_(12)X_4-n H_2] are the electronic energyof relaxed B_(12)X_4, H_2and B_(12)X_4-n H_2, respectively; and n is the number ofH2molecule. Many investigations demonstrate that MP2 method ismore efficient for calculating the weak interactions. So, to get theaccuracy ABE/H_2, single point energy calculations for all B12X4-n H2,the most stable B_(12)X_4and H_2are performed at MP2/6-311G(d, p) level.The basis set superposition error (BSSE) has been corrected usingthe full counterpoise method for all the B12X4-n H2complexes atMP2/6-311G(d, p) level.
The density functional theory (DFT) has been performed toinvestigate the structures and stabilities of B12Li4clusters. The Liatoms prefer the hexagon sites. Once the metals are absorbed on B12,each can bring up to four hydrogen molecules with an average bindingenergy of 0.033-0.089 eV, corresponding to 13.32 wt%. The NBO analysis indicates that the charge of Li atom in B_(12)Li_4is 0.727|e|, andinductive interaction is important for Li to adsorb the H2molecules inB_(12)Li_4.
We investigated hydrogen adsorption on Ti-doped B_(12)nanostructures. The results show that the lowest-energystructure(D2d) and the lower-lying structure(Td) of B_(12)Ti_4can avoidingthe notorious clustering problem. As for the B_(12)Ti_4with Tdsymmetry ,Ti can bind strongly to the hexagons of B_(12)to form regular tetrahedronstructure, thus it can store up to 16 H2molecules via the Kubasinteraction with an average binding energy of 0.434 eV/H2,corresponding to a gravimetric density of hydrogen storage of 9.125wt%. If each Ti adsorbs 3 H_2, the average adsorption energy is 0.26ev/H2, corresponding to a gravimetric density of hydrogen storage of6.952 wt%, while B_(12)Ti_4(D2d) can only host 8 H2molecules at mostwith an average binding energy of 0.521 eV per H2. We found that theKupas interaction dominates the attracting between Ti atoms andhydrogen molecules.
The structure and hydrogen adsorption property of a B_(12)Sc4wasinvestigated with the first principle calculations. Like the B_(12)Ti_4(D2d),in B_(12)Sc4, Metal atoms prefer binding to B atoms other than forming Ticlusters. The B_(12)Sc4can bind up to 12 H_2molecules with an averagebinding energy of 0.108 eV per H_2, It is very interesting that we findthat in B_(12)Sc_4, every B3rings can be regarded as a super atom with s-,p- and d-like orbitals.
This work was supported by National Basic Research (973)Program of China (No. 210CB635110) and National Natural ScienceFoundation of China (21031003).
引文
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