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Hydrogen energy is considered a clean energy with great development prospects. In the field of hydrogen energy applications, the solid-state chemical hydrogen storage method using hydrogen storage materials as media has received widespread attention due to its safety and high hydrogen storage density. In the research on metal-N-H system hydrogen storage materials, current studies focus on improving the kinetic conditions for hydrogen storage. In this study, the B3LYP hybrid functional method of density functional theory is used to investigate the reaction mechanism between P-doped LiNH2 clusters and LiH at a cluster level, and explore the effects of doping, in addition a new hydrogen storage mechanism called “secondary hydrogen transfer” is proposed. The full-geometry optimization of (LiNH2)n (n = 1–4) clusters and their P-doped clusters at the 6-31G(d,p) basis set level are carried out, and their corresponding most stable configurations are obtained. The distribution and stability of the frontier orbitals of the relevant reactants are calculated. Using the same method and basis set, the theoretical calculation and analysis of the reaction mechanism between P-doped (LiNH2)n (n = 1–4) clusters and LiH are conducted, including the configuration optimization of the stationary points in each reaction path, and the correctness of the connection between the stationary points is determined through frequency and intrinsic reaction coordinate calculations. The results show that P doping has a small effect on the lowest unoccupied molecular orbital, while the highest occupied molecular orbital has a significant transition towards the doping atom, and the electron-deficient region is concentrated at the P atom. P doping reduces the stability of the lithium amide clusters and enhances their ability to participate in chemical reactions and reaction activity, and the reaction dehydrogenation energy barrier decreases. The reaction dehydrogenation energy barrier between P-doped LiNH2 clusters and LiH is significantly lower than that between LiNH2 and LiH, which is consistent with the analysis of reactant stability. Additionally, it is found that the reaction between P-doped LiNH2 clusters and LiH tends to dehydrogenate through the —PH2 functional group and store hydrogen at the —NH2 functional group. Therefore, a new idea of “secondary hydrogen transfer” is proposed, in which effective transfer of hydrogen between —NH2 and —PH2 functional groups takes place during the cyclic hydrogen storage process, thus the reversibility of hydrogen storage is further improved and the hydrogen desorption energy barrier of the material is reduced.
- PACS:
31.15.A- (Ab initio calculations) 31.15.es (Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies)) 82.20.Db (Transition state theory and statistical theories of rate constants) 88.30.R- (Hydrogen storage) 1. 引 言
氢能被认为是极具发展前景的清洁能源, 实现高重量、可逆的氢储存是需要解决的一个问题[1]. 以储氢材料为介质的固态化学储氢方式, 由于其安全性和储氢密度高[2], 有良好的应用前景. 金属络合物由于其储氢的百分比较高, 且有一定的可逆性, 其中的金属-N-H体系储氢材料受到广泛关注, 尤其是自Chen等[3]报道的LiNH2-2LiH能够可逆地储存氢气以来. 但金属-N-H体系普遍存在放氢温度较高的问题, 目前此类材料的研究主要集中在改善其储放氢热/动力学方面[4-10]. 马星宇等[11]在LiNH2-MgH2二元体系中引入LiH, 研究其放氢性能和机理, 发现LiH的添加能够改善材料的微观结构和抑制材料颗粒的团聚, 降低了放氢温度, 进一步添加KH形成四元体系能使放氢温度进一步降低. Wang等[12]在Mg(NH2)2-LiH体系中引入钾元素, 通过将部分LiH替换为KH, 而KH在体系中扮有重要角色. Zhang等[13]讨论了CsH对Mg(NH2)2-LiH体系材料的影响, 发现能够显著地改善体系的储氢性能. 此外, 还有很多关于金属-N-H体系材料的改性研究[14-17]. 可见, 元素掺杂可改善金属-N-H体系的储放氢性能. Orimo等[18]发现可用镁替代LiNH2中部分锂, 来破坏氨基化合物的稳定性, 指出放氢温度降低在于减弱了N-H原子之间的结合力. Zhang等[19]研究讨论了K, Ti和F对LiNH体系储氢性能的影响, 经掺杂后可以降低体系的反应活化能. P元素与N元素为同一主族元素, 最外层电子数相同, 可以考虑用P原子替代氨基锂团簇中的N原子, 预期能够减弱N—H键的作用, 降低放氢反应能垒, 改善材料的放氢性能. 另外, 邵子霁[20]对高压下三元锂磷氢化合物(LiPHn(n=1—7))的结构和相关性能进行了研究. P原子掺杂的LiNH2团簇可视为LiNH2和LiPH2的复合物. 另外, 碱金属氨基化合物的团簇模型可较好地说明其所对应晶体中氢的行为、稳定性和化学键方面的特性. 目前用P原子掺杂的LiNH2团簇及其与LiH反应机理方面的研究未见报道, 故本文运用密度泛函理论B3LYP方法, 在团簇层面研究P掺杂的(LiNH2)团簇与LiH的反应机理, 探究掺杂的影响, 在微观机理方面说明磷掺杂对弱化N—H键的作用.
2. 计算方法
采用密度泛函理论杂化泛函(B3LYP)方法在6-31G(d, p)基组水平上对(LiNH2)n(n = 1—4)团簇及其P掺杂的团簇构型进行全几何参数优化, 最终得到相应的最稳定构型, 对相关反应物的前线轨道分布和稳定性进行了计算. B3LYP方法在Lee-Yang-Parr泛函的基础上加了Beck型三参数处理电子交换的泛函模型[21,22], 已被广泛应用于团簇相关问题的研究[23,24]. 对P掺杂的氨基锂团簇构型分别与LiH的反应机理进行计算分析, 包括各反应过程中的中间体、过渡态和产物的构型优化和振动频率计算, 频率计算是为了确保反应各驻点的正确性(过渡态是否有且只有一个虚频, 其他驻点无虚频). 在验证各驻点之间相互连接关系的正确性方面, 对各反应的过渡态均进行了内禀反应坐标(IRC)计算. 计算各反应各驻点相对于各自反应物的相对能量, 给出各反应的能级图. 以上相关的计算均采用Gaussian程序软件包, 用密度泛函理论B3LYP方法在6-31G(d, p)基组水平上来完成, 能量梯度和总能的收敛精度均为1×10–6.
3. 结果与讨论
3.1 团簇反应物前线轨道分布及稳定性
图1给出了(LiNH2)n(n = 1—4)团簇及P掺杂的团簇构型的前线轨道分布. 根据日本科学家福井谦一提出的前线轨道理论[25]可知, 分子的最高占据轨道(HOMO)和最低未占据轨道(LOMO)是一个体系发生化学反应的关键所在. 由图1可以看出, 各构型的LOMO轨道均主要集中分布于Li原子的附近, 对比P掺杂和未掺杂团簇构型的LOMO轨道可发现, 两方面的差别不大, 说明P掺杂对LOMO轨道影响较小, 接受电子区域基本不变, 集中在Li原子处. 而对于经P原子掺杂的各团簇的HOMO轨道分布来看, 存在较大幅度向掺杂原子处的转移, 说明经P原子替代N 原子后团簇失电子区域集中在P原子处. 另外, 对能够反映团簇动力学稳定性, 包括相关团簇的电离势、能隙和费米能等相关物理量进行了计算和分析. 如表1所列, 各反应物团簇的名称, 例如P-(LiNH2)n (n = 2—4)表示(LiNH2)n(n = 2—4)团簇中一个N原子被P原子所取代. ΔE(ELOMO – EHOMO)为能隙, 其数值大小对应了电子从最高占据轨道向最低未占据轨道跃迁的难易程度, 可以描述团簇参与化学反应的能力强弱. 能隙越大, 团簇越稳定, 越不容易发生反应; 能隙较小, 说明越容易发生反应. EIP为电离势, 反映了失电子的难易程度, 定义为团簇及其同一构型阳离子之间总能量的差. 费米能定义为最高占据轨道能量(EHOMO). 由表1数据可以看出, LiPH2 与LiNH2相比, 有较大的能隙和电离势以及较小的费米能级, 有更高的稳定性. 而P-(LiNH2)n(n = 2—4)与相应的(LiNH2)n(n = 2—4)团簇相比, 能隙和电离势均较小, 费米能级均较高, 说明经P原子掺杂, 降低了氨基锂团簇的稳定性, 增强了其参与化学反应的能力和反应活性. 值得注意的是, n = 1时, 即LiPH2与LiNH2相比稳定性更高, 与n = 2—4时的结论不一致, 很可能的原因是由于LiNH2构型是平面结构, 而LiPH2是一个四面体的立体结构, 稳定性更强的原因.
表 1 反应物的动力学稳定性参数(单位: eV)Table 1. Kinetic stability parameters of reactants (unit: eV).Cluster ELOMO EHOMO ΔE EIP LiNH2 –1.143 –4.218 3.075 7.054 LiPH2 –1.633 –4.789 3.156 7.292 (LiNH2)2 –0.490 –5.306 4.816 7.607 P-(LiNH2)2 –0.707 –4.816 4.109 7.253 (LiNH2)3 –0.408 –5.714 5.306 7.678 P-(LiNH2)3 –0.490 –5.225 4.735 7.651 (LiNH2)4 –0.463 –5.823 5.360 7.548 P-(LiNH2)4 –0.490 –5.442 4.952 7.406 
图 1 反应物构型及前线轨道分布Fig. 1. Reactant configurations and front-line orbital distributions.3.2 P-(LiNH2)n(n = 1, 2)与LiH的反应
图2给出了P-(LiNH2)n(n = 1, 2)与LiH的反应势能面上各驻点的构型和部分参数. LiPH2与LiH的反应为单通道反应, 反应路径表示为: RC1→INT1→TS1→PC1, 记为Path-1. 反应物RC1首先形成中间体INT1; 中间体INT1到过渡态TS1过程中, H(2)逐渐远离P(4)原子, 键长由0.1414 nm增加到0.1905 nm, H(2)—H(6)间距变为0.0965 nm; 随后H(2)—H(6)间距继续缩小到0.0746 nm (体现出了氢分子的特征), 并进一步共同远离P(4)原子, 形成产物PC1.
图 2 P-(LiNH2)n(n = 1, 2)与LiH反应势能面上各驻点的几何结构及参数(键长/nm)Fig. 2. Geometries and parameters at the critical points of the potential energy surface of the reaction between P-(LiNH2)n(n = 1, 2) and LiH (bond lengths in nm)P-(LiNH2)2与LiH的反应, 根据反应物RC2构型设计出两条反应路径, 即与LiH反应脱氢, 分为由—NH2一侧脱氢和由—PH2一侧脱氢. 路径表示为: RC2→INT2→TS2-1→PC2-1和RC2→INT2→TS2-2→PC2-2, 分别记为Path-2, Path-3. 由INT2分别形成TS2-1和TS2-2的过程中, 分别主要对应H(9)—N(4)和H(1)—P(7)间距的显著增大(分别由0.1022 nm增加到0.1489 nm, 由0.1417 nm增加到0.1859 nm). TS2-1到PC2-1, TS2-2到PC2-2的过程中, 分别主要对应H(10)—H(9)和H(10)—H(1)间距的进一步减小(分别由0.0951 nm减小到0.0747 nm, 由0.1023 nm减小到0.0748 nm).
3.3 P-(LiNH2)3与LiH的反应
根据反应物RC3构型, P-(LiNH2)3与LiH的反应设计出两条反应路径, 即与LiH反应脱氢, 分别为由—NH2一侧脱氢和由—PH2一侧脱氢. 路径表示为: RC3→INT3-1→TS3-1→PC3-1和RC3→INT3-2→TS3-2→PC3-2, 分别记为Path-4和Path-5, 如图3所示. 反应物P-(LiNH2)3和LiH形成两种中间体, 由INT3-1形成TS3-1的过程中, 主要对应H(13)—N(5)间距的显著增大(由0.1022 nm增加到0.1461 nm). TS3-1到PC3-1的过程中, 主要对应H(13)—H(14)间距的进一步减小(由0.0960 nm减小到0.0747 nm). 由INT3-2形成TS3-2的过程中, 主要对应H(13)—P(11)间距的显著增大(由0.1420 nm增加到0.1614 nm). TS3-2到PC3-2的过程中, 主要对应H(13)—H(14)间距的进一步减小(由0.1315 nm减小到0.0747 nm).
图 3 P-(LiNH2)3与LiH反应势能面上各驻点的几何结构及参数(键长/nm)Fig. 3. Geometries and parameters at the critical points of the potential energy surface of the reaction between P-(LiNH2)3 and LiH (bond lengths in nm).3.4 P-(LiNH2)4与LiH的反应
如图4所示, 根据反应物RC4构型, P-(LiNH2)4与LiH的反应设计出两条反应路径, 即反应脱氢由—NH2一侧脱氢和由—PH2一侧脱氢. 路径表示为: RC4→INT4-1→TS4-1→PC4-1和RC4→INT4-2→TS4-2→PC4-2, 分别记为Path-6和Path-7. 反应物P-(LiNH2)4和LiH形成两种中间体, 由INT4-1形成TS4-1的过程中, 主要对应H(17)—N(13)间距的明显增大(由0.1022 nm增加到0.1470 nm). TS4-1到PC4-1的过程中, 主要对应H(17)—H(18)间距的进一步减小(由0.0954 nm减至0.0747 nm), 并共同远离N(13)原子. 由INT4-2形成TS4-2的过程中, 主要对应H(18)—P(15)间距的显著增大(由0.1423 nm增加到0.1613 nm). TS4-2到PC4-2的过程中, 主要对应H(18)—H(17)间距的进一步减小(由0.1319 nm减至0.0747 nm).
图 4 P-(LiNH2)4与LiH反应势能面上各驻点的几何结构及参数(键长/nm)Fig. 4. Geometries and parameters at the critical points of the potential energy surface of the reaction between P-(LiNH2)4 and LiH (bond lengths in nm).由以上对P-(LiNH2)n(n = 1—4)团簇与LiH的反应过程的描述, 可以发现各反应脱氢过程具有一定相似性, 过渡态的形成均对应了H原子与N或P原子之间间距增大的过程, 此过程是反应脱氢的关键所在; N—H键或P—H键键长的增大乃至断裂需要克服一定能垒, 反映了各反应的难易程度. 另外, 反应产物中氢分子的两个氢原子, 分别来源于P-(LiNH2)n(n = 1—4)团簇与LiH. 另外, 众所周知在Li-N-H体系中或多或少会存在NH3的释放[26], 若体系中存在LiH的话, 会迅速与氨气发生反应生成氢气[27], 可消除NH3的影响. 基于此, 关于反应脱氨的方面不做过多讨论.
3.5 反应的能量与反应机理分析
反应过程中会伴有能量的变化, 故反应过程中各驻点能量之间的关系, 对描述反应机理有重要作用.
表2列出了各反应相关驻点的能量信息和部分的振动频率, 其中Etotal为驻点总能量, Erel是以各反应物总能量为参比的相对能量(同时给出了单位为a.u.和kJ·mol–1的两列数据, 以利于直观反映和判断), Frequency为计算的各驻点的部分振动频率, 中间体无虚频, 过渡态均有且只有一个虚频. 为了更加直观反映反应过程的能量变化, 分析反应过程中的吸放热和反应能垒情况, 图5给出了以相对能量所作的势能面剖面图. 表2中, 过渡态均只有一个虚频, 可以说明所计算的过渡态构型的正确性, 但还不能确定是否为相关反应路径上的过渡态, 故进一步进行了内禀反应坐标分析, 以确定各驻点之间的连接关系.
表 2 反应各驻点的能量、相对能量及部分振动频率Table 2. Total energies and relative energies at the critical points of potential energy surface and vibrational frequencies.Species Etotal/a.u. Erel/a.u. Erel/(kJ·mol–1) Frequency/cm–1 RC1 –358.15783 0 0 — — INT1 –358.23259 –0.07476 –196.28 177.1 277.4 TS1 –358.16547 –0.00764 –20.06 –740.0 163.7 PC1 –358.18721 –0.02938 –77.14 22.8 110.9 RC2 –421.73285 0 0 — — INT2 –421.80701 –0.07416 –194.71 91.7 111.7 TS2-1 –421.73051 0.00234 6.14 –924.0 60.1 PC2-1 –421.74289 –0.01004 –26.36 40.4 57.5 TS2-2 –421.7447 –0.01185 –31.11 –841.0 54.0 PC2-2 –421.7681 –0.03525 –92.55 22.0 34.2 RC3 –485.30464 0 0 — — INT3-1 –485.35191 –0.04727 –124.11 77.2 87.3 TS3-1 –485.29977 0.00487 12.79 –959.3 78.8 PC3-1 –485.31087 –0.00623 –16.36 44.2 58.8 INT3-2 –485.3685 –0.06386 –167.66 38.6 64.5 TS3-2 –485.31205 –0.00741 –19.45 –935.4 37.8 PC3-2 –485.33993 –0.03529 –92.65 26.7 31.0 RC4 –548.86487 0 0 — — INT4-1 –548.91997 –0.0551 –144.67 41.9 61.6 TS4-1 –548.86131 0.00356 9.35 –927.3 28.9 PC4-1 –548.87191 –0.00704 –18.48 29.6 45.7 INT4-2 –548.92434 –0.05947 –156.14 7.0 33.8 TS4-2 –548.87084 –0.00597 –15.67 –922.3 19.8 PC4-2 –548.89928 –0.03441 –90.34 17.7 30.4 
图 5 各个反应过程的势能面剖面图Fig. 5. Energetic profiles for potential energy surface of each reaction.由图5和表2可以看出, 各反应路径(Path-1至 Path-7, 其中Path-1, Path-3, Path-5和Path-7对应由—PH2官能团脱氢; Path-2, Path-4和Path-6对应由—NH2官能团脱氢)均为放热反应, 反应放热值依次分别为77.14, 26.36, 92.55, 16.36, 92.65, 18.48和90.34 kJ/mol, 发现由—NH2反应脱氢的放热值在20 kJ/mol左右, 而由—PH2反应脱氢的放热值在90 kJ/mol左右. LiPH2与LiH的反应决速步能垒为176.22 kJ/mol. P-(LiNH2)2与LiH的反应Path-2与Path-3对应能垒分别为200.85和163.6 kJ/mol, 判断出Path-3反应路径较好. P-(LiNH2)3与LiH的反应Path-4与Path-5对应能垒分别为136.9和148.21 kJ/mol, 判断出Path-4反应路径较好. P-(LiNH2)4与LiH的反应Path-6与Path-7对应能垒分别为154.02和140.47 kJ/mol, 判断出Path-7反应路径较好. 此外, 本课题组曾对(LiNH2)n(n = 1, 2)团簇与LiH反应机理进行过计算, 反应脱氢能垒分别为239.8和211.5 kJ/mol[15], 明显高于P-(LiNH2)n(n = 1—4) 与LiH反应脱氢能垒. 由此可知, 反应脱氢更倾向于由—PH2官能团脱氢. 同时, Path-5比Path-4所对应能垒高, 可能是由于Path-5路径上中间体INT3-2的能量过低, 稳定性更高的原因. 其对反应脱氢更倾向于由—PH2官能团脱氢的判断影响不大. 说明经P掺杂后可改善材料的放氢动力学条件. 由此结果与前文反应物稳定性方面分析可知: 经P原子掺杂, 降低了氨基锂团簇的稳定性, 增强了其参与化学反应的能力, 是和反应活性的结果相一致.
另外, 各反应的逆反应能垒(Path-1至 Path-7)依次为: 57.08, 32.5, 61.44, 29.15, 73.2, 27.83和74.67 kJ/mol, 可知储氢到—NH2的能垒约在30 kJ/mol, 储氢到—PH2的能垒在60 kJ/mol左右的范围内, 说明氢更容易储存在—NH2官能团处.
综上所讨论可知, 在—NH2官能团处储氢容易放氢难, 而由—PH2官能团放氢容易储氢难, 预想二者复合的情况下, 若能实现氢在两官能团之间的有效转移, 可进一步改善该材料的储放氢的可逆性, 降低放氢能垒. 在降低放氢反应能垒方面, 目前多是通过金属阳离子替代和掺杂等方式, 而根据本文结果, 提出一种“二次氢转移”的新思路, 如图6所示, 为该方法循环储放氢过程的示意图, 是以中间体INT2进行储放氢为例来说明的. 其储氢和放氢的情况, 前文已经有相关讨论, 而另一关键点在于H从N原子处转移到P原子处的过程, 且应该是有效转移, 反应势垒较小. 为此, 对该氢转移的过程进行了计算分析, 图7所示为此过程的势能面剖面图, 可以看到单纯的、不加任何辅助修饰的情况下, 氢转移需克服能垒仍然较高, 数值为190.51 kJ/mol, 但与Path-2过程对应的脱氢能垒200.85 kJ/mol相比, 有所减小, 这间接说明了此过程的可行性.
图 6 循环储放氢机制示意图Fig. 6. Diagram of circulating hydrogen storage and desorption mechanism.
图 7 氢转移过程的势能面剖面图Fig. 7. Energetic profiles for potential energy surface of hydrogen transfer process.4. 结 论
(LiNH2)n(n = 1—4)团簇经P掺杂后对LOMO影响较小, 接受电子区域基本不变, 集中在Li原子处; HOMO分布存在较大幅度向掺杂原子处的转移, 团簇失电子区域集中在P原子处. 经P原子掺杂, 降低了氨基锂团簇的稳定性, 增强了其参与化学反应的反应活性.
N—H键或P—H键键长的增大乃至断裂需要克服一定能垒, 此过程是反应脱氢的关键所在, 反应产物中氢分子的两个氢原子, 分别来源于P-(LiNH2)n(n = 1—4)团簇与LiH. 反应脱氢更倾向于由—PH2官能团脱氢, 经P掺杂后可降低反应脱氢能垒, 改善材料的放氢动力学条件. 在氢储存方面, 氢更容易储存在—NH2官能团处. 提出了一种“二次氢转移”的新思路, 在循环储放氢过程中, 需实现氢在—NH2和—PH2官能团之间的有效转移, 可进一步改善该材料的储放氢的可逆性, 降低放氢能垒. 经过计算发现单纯的、不加任何辅助修饰的情况下, 氢转移需克服能垒仍然较高, 但与直接从—NH2官能团一次脱氢相比, 脱氢能垒有所减小, 间接说明了此过程的可行性.
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图 1 反应物构型及前线轨道分布
Figure 1. Reactant configurations and front-line orbital distributions.
图 2 P-(LiNH2)n(n = 1, 2)与LiH反应势能面上各驻点的几何结构及参数(键长/nm)
Figure 2. Geometries and parameters at the critical points of the potential energy surface of the reaction between P-(LiNH2)n(n = 1, 2) and LiH (bond lengths in nm)
图 3 P-(LiNH2)3与LiH反应势能面上各驻点的几何结构及参数(键长/nm)
Figure 3. Geometries and parameters at the critical points of the potential energy surface of the reaction between P-(LiNH2)3 and LiH (bond lengths in nm).
图 4 P-(LiNH2)4与LiH反应势能面上各驻点的几何结构及参数(键长/nm)
Figure 4. Geometries and parameters at the critical points of the potential energy surface of the reaction between P-(LiNH2)4 and LiH (bond lengths in nm).
图 5 各个反应过程的势能面剖面图
Figure 5. Energetic profiles for potential energy surface of each reaction.
图 6 循环储放氢机制示意图
Figure 6. Diagram of circulating hydrogen storage and desorption mechanism.
图 7 氢转移过程的势能面剖面图
Figure 7. Energetic profiles for potential energy surface of hydrogen transfer process.
表 1 反应物的动力学稳定性参数(单位: eV)
Table 1. Kinetic stability parameters of reactants (unit: eV).
Cluster ELOMO EHOMO ΔE EIP LiNH2 –1.143 –4.218 3.075 7.054 LiPH2 –1.633 –4.789 3.156 7.292 (LiNH2)2 –0.490 –5.306 4.816 7.607 P-(LiNH2)2 –0.707 –4.816 4.109 7.253 (LiNH2)3 –0.408 –5.714 5.306 7.678 P-(LiNH2)3 –0.490 –5.225 4.735 7.651 (LiNH2)4 –0.463 –5.823 5.360 7.548 P-(LiNH2)4 –0.490 –5.442 4.952 7.406 
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表 2 反应各驻点的能量、相对能量及部分振动频率
Table 2. Total energies and relative energies at the critical points of potential energy surface and vibrational frequencies.
Species Etotal/a.u. Erel/a.u. Erel/(kJ·mol–1) Frequency/cm–1 RC1 –358.15783 0 0 — — INT1 –358.23259 –0.07476 –196.28 177.1 277.4 TS1 –358.16547 –0.00764 –20.06 –740.0 163.7 PC1 –358.18721 –0.02938 –77.14 22.8 110.9 RC2 –421.73285 0 0 — — INT2 –421.80701 –0.07416 –194.71 91.7 111.7 TS2-1 –421.73051 0.00234 6.14 –924.0 60.1 PC2-1 –421.74289 –0.01004 –26.36 40.4 57.5 TS2-2 –421.7447 –0.01185 –31.11 –841.0 54.0 PC2-2 –421.7681 –0.03525 –92.55 22.0 34.2 RC3 –485.30464 0 0 — — INT3-1 –485.35191 –0.04727 –124.11 77.2 87.3 TS3-1 –485.29977 0.00487 12.79 –959.3 78.8 PC3-1 –485.31087 –0.00623 –16.36 44.2 58.8 INT3-2 –485.3685 –0.06386 –167.66 38.6 64.5 TS3-2 –485.31205 –0.00741 –19.45 –935.4 37.8 PC3-2 –485.33993 –0.03529 –92.65 26.7 31.0 RC4 –548.86487 0 0 — — INT4-1 –548.91997 –0.0551 –144.67 41.9 61.6 TS4-1 –548.86131 0.00356 9.35 –927.3 28.9 PC4-1 –548.87191 –0.00704 –18.48 29.6 45.7 INT4-2 –548.92434 –0.05947 –156.14 7.0 33.8 TS4-2 –548.87084 –0.00597 –15.67 –922.3 19.8 PC4-2 –548.89928 –0.03441 –90.34 17.7 30.4
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[1] Schlapbach L, Zuttel A 2001 Nature 414 353
Google Scholar
[2] 马通祥, 高雷章, 胡蒙均, 胡丽文, 温良英, 扈玫珑 2018 功能材料 49 4001
Google Scholar
Ma T X, Gao L Z, Hu M J, Hu L W, Wen L Y, Hu M L 2018 J. Funct. Mater. 49 4001
Google Scholar
[3] Chen P, Xiong Z, Luo J, Lin J, Tan K L 2002 Nature 420 302
Google Scholar
[4] Zhang X, Sun Y, Xia G, Yu X 2022 J. Alloys Compd. 899 163254
Google Scholar
[5] Sitthiwet C, Plerdsranoy P, Utke O, Nijpanich S, Chanlek N, Eiamlamai P, Utke R 2022 J. Alloys Compd. 909 164673
Google Scholar
[6] Bai Z X, Zeng W, Tang B, Fan D H, Liu Q J, Jiang C L, Chang X H 2022 Int. J. Mod. Phys. B 36 2250074
Google Scholar
[7] Chen Y, Sun X, Zhang W K, Gan Y P, Xia Y, Zhang J, Huang H, Liang C, Pan H 2020 ACS Appl. Mater. Interfaces 12 15255
Google Scholar
[8] Li C, Li C, Fan M, Chen H, Shu K, Zhang Y, Gao M, Liu Y, Pan H 2019 J. Energy Chem. 35 37
Google Scholar
[9] Goshome K, Jain A, Miyaoka H, Yamamoto H, Kojima Y, Ichikawa T 2019 Molecules 24 1348
Google Scholar
[10] Shukla V, Bhatnagar A, Singh S, Soni P K, Verma S K, Yadav T P, Shaz M A, Srivastava O N 2019 Dalton Trans. 48 30
Google Scholar
[11] 马星宇, 王二锐, 邱树君, 褚海亮, 邹勇进, 向翠丽, 闫二虎, 徐芬, 孙立贤 2016 材料导报 30 206
Google Scholar
Ma X Y, Wang E R, Qiu S J, Chu H L, Zou Y J, Xiang C L, Yan E H, Xu F, Sun L J 2016 Mater. Rep. 30 206
Google Scholar
[12] Wang J, Liu T, Wu G, Li W, Liu Y, Araujo C M, Scheicher R H, Blomqvist A, Ahuja R, Xiong Z, Yang P, Gao M, Pan H, Chen P 2009 Angew. Chem. Int. Ed. 48 5828
Google Scholar
[13] Zhang J, Liu Y, Zhang X, Yang Y, Zhang Q, Jin T, Wang Y, Gao M, Sun L, Pan H 2016 Int. J. Hydrogen Energy 41 11264
Google Scholar
[14] Zhang B, Yuan J, Wu Y 2018 Int. J. Hydrogen Energy 44 19294
Google Scholar
[15] Qiu S, Gao W, Ma X, Chu H, Zou Y, Xiang C, Zhang H, Xu F, Sun L 2018 Int. J. Hydrogen Energy 43 13975
Google Scholar
[16] Zhu X L, Han S M, Zhao X, Li Y, Liu B Z 2014 Rare Met. 33 86
Google Scholar
[17] Rohit R, Rajesh K, Vivek S, Ashish B, Srivastava O 2017 Int. J. Hydrogen Energy 42 29350
Google Scholar
[18] Orimo S, Nakamori Y, Kitahara G, Miwa K, Ohba N, Noritake T, Towata 2004 Appl. Phys. A 79 1765
Google Scholar
[19] Zhang Y R, Dong B X, Zhao J, Teng Y L, Li Z W, Wang L 2017 Int. J. Hydrogen Energy 42 17149
Google Scholar
[20] 邵子霁 2019 博士学位论文 (长春: 吉林大学)
Shao Z J 2019 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese)
[21] Lee C, Yang W, Parr R G 1988 Phys. Rev. B 37 785
Google Scholar
[22] Becke, Axel D 1993 J. Chem. Phys. 98 5648
Google Scholar
[23] 张陈俊, 王养丽, 陈朝康 2018 物理学报 67 113101
Google Scholar
Zhang C J, Wang Y L, Chen C K 2018 Acta Phys. Sin. 67 113101
Google Scholar
[24] Ivakhnenko E, Malay V, Demidov O, Starikov A, Minkin V 2022 Tetrahedron 103 132575
Google Scholar
[25] Fukui K, Yonezawa T, Shingu H 1952 J. Chem. Phys. 20 722
Google Scholar
[26] Ichikawa T, Isobe S, Hanada N, Fujii H 2004 J. Alloys Compd. 365 271
Google Scholar
[27] Janot R, Eymery J B, Tarascon J M 2007 J. Power Sources 164 496
Google Scholar
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其他类型引用(1)
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