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Electronic structures, chemical bonds, and stabilities of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters: Anion photoelectron spectroscopy and theoretical calculations

Zhang Chao-Jiang Xu Hong-Guang Xu Xi-Ling Zheng Wei-Jun

Zhang Chao-Jiang, Xu Hong-Guang, Xu Xi-Ling, Zheng Wei-Jun. Electronic structures, chemical bonds, and stabilities of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters: Anion photoelectron spectroscopy and theoretical calculations. Acta Phys. Sin., 2021, 70(2): 023601. doi: 10.7498/aps.70.20201351
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Electronic structures, chemical bonds, and stabilities of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters: Anion photoelectron spectroscopy and theoretical calculations

Zhang Chao-Jiang, Xu Hong-Guang, Xu Xi-Ling, Zheng Wei-Jun
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  • The electronic structures, chemical bonds and stabilities of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters are investigated by combining anion photoelectron spectroscopy with theoretical calculations. The vertical detachment energy values of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) anions are measured to be (1.16 ± 0.08), (1.35 ± 0.08), (1.51 ± 0.08), (1.30 ± 0.08), and (1.86 ± 0.08) eV, and the electron affinities of neutral Ta4Cn (n = 0–4) are estimated to be (1.10 ± 0.08), (1.31 ± 0.08), (1.44 ± 0.08), (1.21 ± 0.08), and (1.80 ± 0.08) eV, respectively. It is found that the geometry structure of ${\rm{Ta}}_4^- $cluster is a tetrahedron, and the most stable structure of ${\rm{Ta}}_4{\rm{C}}_1^{-} $ has a carbon atom capping one face of the ${\rm{Ta}}_4^- $ tetrahedron, while in the ground state structure of ${\rm{Ta}}_4{\rm{C}}_2^{-} $ cluster, two carbon atoms cap two faces of the${\rm{Ta}}_4^- $ tetrahedron, respectively. The lowest-lying isomer of ${\rm{Ta}}_4{\rm{C}}_3^{-} $ cluster holds a cube-cutting-angle structure. The ground state structure of ${\rm{Ta}}_4{\rm{C}}_4^{-} $ is a 2 × 2 × 2 cube. The neutral Ta4Cn (n = 0–4) clusters have similar structures to their anionic counterparts and the neutral Ta4C4 cluster can be considered as the smallest cell for α-TaC face-centered cube crystal. The analyses of molecular orbitals reveal that the SOMO of ${\rm{Ta}}_4{\rm{C}}_3^{-} $ is mainly localized on one tantalum atom, inducing a low VDE. Our results show that the Ta-Ta metal bonds are replaced by Ta-C covalent bonds gradually as the number of carbon atoms increases in ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters. The per-atom binding energy values of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters are higher than those of ${\rm{Ta}}_{4+n}^{-/0} $ (n = 0–4) clusters, indicating that the formation of Ta-C covalent bonds may raise the melting point. The per-atom binding energy of neutral Ta4C4 is about 7.13 eV, which is quite high, which may contribute to the high melting point of α-TaC as an ultra-high temperature ceramic material.
      PACS:
      36.40.Mr(Spectroscopy and geometrical structure of clusters)
      36.40.Wa(Charged clusters)
      36.40.Cg(Electronic and magnetic properties of clusters)
      Corresponding author: Xu Xi-Ling, xlxu@iccas.ac.cn ; Zheng Wei-Jun, zhengwj@iccas.ac.cn
    • Funds: Project supported by the Beijing Municipal Science & Technology Commission, China (Grant No. Z191100007219009) and the Chinese Academy of Sciences (Grant No. QYZDB-SSW-SLH024)

    过渡金属碳化物(transition metal carbide)是一类具有高熔点、高硬度、高热稳定性以及类金属性质的物质, 广泛应用于机械切割、高温部件以及核反应堆等领域, 在开发新型超高温陶瓷材料、二维材料、电子材料、能源材料以及催化材料等方面具有重要意义[1-7]. 近年来, 人们对过渡金属碳化物相关团簇已经进行了大量的研究[8-26]. Guo等[9,10]在钛/碳团簇质谱中发现了具有特殊稳定性的${\rm{Ti}}_8{\rm{C}}_{12}^+$团簇, 并推测其结构是一个具有高对称性(Th)的十二面体金属碳笼(Metcar). Reddy等[11]采用密度泛函(density functional theory, DFT)方法研究了Ti8C12的能量、电子结构以及磁性等性质, 认为其稳定性主要归功于碳-碳以及钛-碳之间类似共价键的作用力, 钛原子的存在使团簇具有一定磁性. Wang研究组采用光电子能谱技术对第四周期过渡金属掺杂碳团簇进行了系统的研究. 他们发现${\rm{TiC}}_x^-$(x = 2—5)团簇呈环状结构[22], 而${\rm{CrC}}_n^-$(n = 2—8)团簇中则是链状和环状结构共存[23], 对于后过渡金属如Fe/Cu/Au掺杂的碳团簇更倾向于形成金属原子位于碳链末端的线性结构[24-26]. Xu等[27]结合光电子能谱和理论计算发现${\rm{MnC}}_n^{-/0} $(n = 3—10)团簇的电子结合能呈现明显的奇偶性, 结构为链状和环状竞争共存. Redondo与其合作者[28-37]对第四周期过渡金属掺杂碳团簇${\rm{MC}}_n^{+/-/0} $(M = Sc, Ti, V, Fe, Co, Zn, n = 1—8)进行了理论研究, 发现团簇结构与过渡金属3d层电子数量和碳原子数目相关. Zheng研究组[38-40]${\rm{Co}}_m{\rm{C}}_n^{-/0} $${\rm{V}}_m{\rm{C}}_n^{-/0} $团簇的研究发现${\rm{V}}_4{\rm{C}}_4^{-/0} $团簇呈立方体结构, 随着碳含量的增加, ${\rm{V}}_4{\rm{C}}_n^{-/0} $团簇稳定性逐渐增加. Wang和Cheng[21]及Wang等[41]${\rm{Ti}}_x{\rm{C}}_y^- $团簇的研究则说明钛/碳团簇负离子更倾向于在立方晶格的基础上生长. 第五周期前过渡金属碳化物${\rm{Y}}_m{\rm{C}}_n^- $, ${\rm{Nb}}_m{\rm{C}}_n^{-/0} $以及MoC等团簇已有报道[42-51]. Castleman研究组[50]采用负离子光电子能谱结合密度泛函对${\rm{Nb}}_2{\rm{C}}_n^{-} $(n = 4—9)团簇进行了研究, 并认为这些团簇是三维结构、平面结构以及线性结构共存. 相较于铌—碳键, ${\rm{Nb}}_2{\rm{C}}_n^{-} $(n = 4—9)团簇更倾向于形成铌-铌键. 第五周期的后过渡金属碳化物团簇如PtnC, Au2C2和Au(C≡C)nAu (n = 1—3)的研究亦有报道[52-56]. Harding等[53]采用振动光谱结合密度泛函理论对PtnC+(n = 3—5)团簇结构进行了表征, 结果显示Pt3C+团簇是一个具有显著稳定性的平面三配位碳结构. León等[55]采用高分辨光电子成像技术结合理论计算对Au(C≡C)nAu–/0 (n = 1—3)团簇的研究表明, ${\rm{Au}}_2{\rm{C}}_2^{-/0} $为线性类乙炔结构, ${\rm{Au}}_2{\rm{C}}_4^{-} $${\rm{Au}}_2{\rm{C}}_6^{-} $团簇负离子为低对称链状结构: Au-Au-(C≡${\rm{C}})_n^- $, 而中性Au2C4和Au2C6团簇则是高对称聚乙炔结构. Lu[57,58]报道了${\rm{Pt}}_n{\rm{C}}_2^{-/0} $(n = 1—7)团簇的理论研究, 认为当n ≥ 4时, 除了中性Pt5C2团簇外, 其余团簇中碳-碳键均断裂.

    钽/碳团簇目前也有一些研究. Gregory研究组[59-62]采用光致电离效率谱对中性TamCn团簇的研究发现: 含钽较多的团簇中不含C2单元, 这与之前中性TamCn团簇的红外振动谱的结果一致. Aravind等[63]通过分析TaC负离子的光电子能谱, 确定TaC团簇的电子亲和能(electron affinity, EA)为(1.928 ± 0.056) eV. He研究组[64-66]采用质谱与光电子能谱结合高精度量子化学计算发现${\rm{Ta}}{\rm{C}}_4^{-} $以及${\rm{Ta}}_2{\rm{C}}_4^- $负离子团簇可以活化小分子N2和CH4. Chernyy等[67]分析了中性Ta5C3团簇的红外光谱, 认为其第一电子激发态位于458 cm–1处. 碳化钽(TaC)因具有超高熔点(4153.15 K)以及较高的转换温度(Tc = 10.35 K), 在超高温陶瓷以及超导材料方面具有潜在应用[68-72]. 但是, 有关钽/碳团簇电子结构的研究依然匮乏, 钽/碳团簇的生长机制以及团簇中各原子间的成键性质仍需更加深入的研究. 本文采用负离子光电子能谱结合密度泛函方法对${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇进行了研究, 揭示了钽/碳团簇的电子结构、成键性质以及稳定性.

    实验部分是在课题组自行搭建的直线式飞行时间质谱-磁瓶式光电子能谱仪上完成的, 该装置主要由激光溅射团簇源、飞行时间质谱仪以及磁瓶式光电子能谱仪组成[73]. 实验时钽/碳样品(直径为13 mm, 钽/碳摩尔比为1∶1)被放置于可以二维移动的样品槽中, 固体纳秒Nd:YAG激光器(Continuum Surelite II-10)通过倍频产生的溅射激光(532 nm)经光学透镜聚焦后轰击样品表面产生等离子体. 同时, 脉冲阀(general valve series 9)喷出高纯氦气(压力约为4 atm)与等离子体碰撞、冷却形成钽/碳团簇. 钽/碳团簇经Skimmer准直后进入加速区. 钽/碳团簇负离子被加速后经飞行时间质谱仪分析产生钽/碳团簇负离子的质谱. ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子经质量门选质以及减速器减速后进入脱附区与脱附激光(532和266 nm)相互作用而脱附电子, 产生的光电子在磁场的作用下进入磁瓶式光电子能谱仪, 经光电子能谱仪分析产生特定团簇负离子的光电子能谱. 我们使用相似条件下Bi和Pb离子的光电子能谱对${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的光电子能谱进行标定. 本装置中磁瓶式光电子能谱仪的分辨率在光电子动能为1 eV处约为40 meV.

    ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的理论研究部分, 首先采用全局搜索软件CALYPSO[74]获得${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的初始结构. 然后使用量子化学计算软件Gaussian09[75]采用密度泛函理论对初始结构中低能量异构体进行优化. 优化过程采用Perdew-Burke-Ernzerh(PBE)[76]方法, 其中钽原子采用含有赝势的aug-cc-pVTZ-PP基组, 碳原子采用aug-cc-pVTZ基组[77]. 在结构优化的过程中, 不设置对称性限制, 考虑不同的自旋多重度, 并计算团簇的振动频率, 确保优化所得结构是势能面上的局域最小点. 在计算团簇的绝热脱附能(adiabatic detachment energy, ADE)和不同结构的相对能量时对团簇能量进行了零点能校正. 采用NBO程序(Version 6.0)[78]${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的最稳定结构进行电子分布和键级分析, 阐明团簇中原子间的相互作用.

    图1是在不同脱附激光能量(532和266 nm)条件下获得的${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的光电子能谱. 光电子能谱中第一个谱峰最高点所对应的电子结合能(electron binding energy, EBE)为团簇负离子的垂直脱附能(vertical detachment energy, VDE). 团簇的绝热脱附能则是通过沿着光电子能谱的第一个谱峰的上升沿画一条重合的直线, 该直线与谱图基线相交处的电子结合能加上仪器分辨率获得. 实验所得${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的垂直脱附能和绝热脱附能列于表1.

    图 1  在532和266 nm条件下采集的${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的光电子能谱
    Fig. 1.  Photoelectron spectra of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions recorded with 532 (left) and 266 nm (right) photons.
    表 1  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的低能量异构体的相对能量(∆E), 理论VDEs/ADEs以及实验VDEs/ADEs
    Table 1.  Relative energies (∆E ), theoretical VDEs and ADEs of the low-lying isomers for ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions, as well as the experimental VDEs and ADEs estimated from their photoelectron spectra.
    异构体电子态对称点群E/eVVDE/eVADE/eV
    理论值实验值理论值实验值
    ${\rm{Ta}}_4^{-} $0AC22B00.941.160.921.10
    0BC14A0.301.321.16
    0CD2h2B2u0.921.591.39
    ${\rm{Ta}}_4{\rm{C}}_1^{-} $1ACs2A''01.231.351.221.31
    1BC2v2B20.271.071.03
    1CC2v2B20.461.180.76
    ${\rm{Ta}}_4{\rm{C}}_2^{-} $2ACs2A''01.491.511.341.44
    2BCs2A''0.291.221.18
    2CCs4A''0.301.051.04
    ${\rm{Ta}}_4{\rm{C}}_3^{-} $3AC3v2A101.171.301.131.21
    3BCs6A''1.031.661.65
    3CC2v2A11.411.351.29
    ${\rm{Ta}}_4{\rm{C}}_4^{-} $4AD2d4B201.701.861.691.80
    4BC12A0.091.611.391.601.35
    4CD2d6A20.211.751.74
    下载: 导出CSV 
    | 显示表格

    图1可以看出, 532 nm条件下获得的光电子能谱具有较好的分辨率, 而266 nm条件下的光电子能谱则包含了团簇在高电子结合能区域的电子结构信息. 在${\rm{Ta} }_4^{-} $团簇负离子的532 nm光电子能谱上有两个中心位于1.16和1.88 eV的窄峰, 根据第一个谱峰确定了${\rm{Ta} }_4^{-} $团簇负离子的实验VDE和ADE分别为(1.16 ± 0.08) eV和(1.10 ± 0.08) eV. 除了532 nm光电子能谱中的两个信号峰外, 在其266 nm光电子能谱中还观察到两个信号较强的谱峰, 它们的电子结合能分别为2.11 eV和3.23 eV. 在$ {\rm{Ta} }_4{\rm{C} }_1^{-} $团簇负离子的532 nm光电子能谱中含有一个窄峰以及一个肩峰, 其电子结合能分别为1.35和1.84 eV. 根据第一个谱峰确定${\rm{Ta} }_4{\rm{C} }_1^{-} $团簇负离子的VDE和ADE分别为(1.35 ± 0.08) eV和(1.31 ± 0.08) eV. 在${\rm{Ta} }_4{\rm{C} }_1^{-} $团簇负离子的266 nm光电子能谱中还可以观察到位于1.94和2.19 eV处的两个较宽的谱峰和一个中心位置位于3.09 eV的谱带. 在${\rm{Ta} }_4{\rm{C} }_2^{-} $团簇负离子的532 nm光电子能谱中可以观测到两个相邻的尖峰, 它们的电子结合能分别为1.51和1.66 eV. ${\rm{Ta} }_4{\rm{C} }_2^{-} $团簇负离子的VDE和ADE分别为(1.51 ± 0.08)和(1.44 ± 0.08) eV. 532 nm中的两个峰在其266 nm光电子能谱中由于分辨率较低而无法分辨, 在266 nm谱图中可以看到两个中心位于2.25和3.25 eV处较宽的特征峰.

    $ {\rm{Ta} }_4{\rm{C} }_3^{-} $团簇负离子的532 nm光电子能谱中, 可以看到一个位于1.30 eV的尖峰, 从图1中得到${\rm{Ta} }_4{\rm{C} }_3^{-} $的实验VDE和ADE分别为(1.30 ± 0.08) eV和(1.21 ± 0.08) eV. 在${\rm{Ta} }_4{\rm{C} }_3^{-} $团簇负离子的266 nm光电子能谱中还可以看到4个可分辨的谱峰, 其电子结合能分别为2.06, 2.35, 3.74和3.91 eV. 在${\rm{Ta} }_4{\rm{C} }_4^{-} $团簇负离子的532 nm光电子能谱中可以观察到一个信号比较弱的宽峰以及一个信号较强的窄峰, 其电子结合能分别为1.39和1.86 eV. 这两个谱峰从强度和形状上, 明显不同于其他团簇谱图, 说明它们可能来自于不同的异构体. 较弱的宽峰所确定的VDE和ADE分别为(1.39 ± 0.08) eV和(1.35 ± 0.08) eV, 较窄的尖峰所确定的VDE和ADE分别为(1.86 ± 0.08) eV和(1.80 ± 0.08) eV. ${\rm{Ta} }_4{\rm{C} }_4^{-} $团簇负离子的266 nm光电子能谱中, 除532 nm谱图中的信号, 还可以观察到两个信号较弱的谱带, 其中心位置的电子结合能分别为2.58和3.93 eV.

    图2为优化得到的$ {\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子低能量异构体的几何结构、相对能量以及电子态. 为了确定团簇的结构, 计算了${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子低能量异构体的理论VDEs和ADEs并列于表1. 理论VDE为具有团簇负离子基态构型的中性团簇能量与基态团簇负离子的能量差. 理论ADE指以负离子基态构型为初始结构优化所得稳定的中性团簇的能量与基态团簇负离子的能量差. 图3是根据广义上的库夫曼定理(Koopmans’ theorem, GKT)[79,80]模拟的${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的理论光电子能谱, 即态密度(density of states, DOS)谱图, 并与实验光电子能谱图进行了比对. 同时我们也对中性Ta4Cn (n = 0—4)团簇的结构进行了优化,结果如图4所示.

    图 2  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的低能量异构体. 相对能量是在PBEPBE/aug-cc-pVTZ/C/aug-cc-pVTZ-PP/Ta水平获得. 其中红色球代表碳原子, 青色球代表钽原子
    Fig. 2.  Low-lying isomers of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions. The relative energies are calculated at the PBEPBE/aug-cc-pVTZ/C/aug-cc-pVTZ-PP/Ta level. Cyan and red balls stand for the tantalum and carbon atoms, respectively.
    图 3  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的模拟光电子能谱(DOS)与实验光电子能谱对比, 竖线表示理论计算所对应的分子能级
    Fig. 3.  Comparisons of the experimental photoelectron spectra of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) with their simulated density of states (DOS) spectra. The vertical lines are the theoretically simulated spectral lines.
    图 4  中性Ta4Cn (n = 0—4)团簇的低能量异构体
    Fig. 4.  Low-lying isomers of neutral Ta4Cn (n = 0–4) clusters.

    图2第一行是${\rm{Ta}}_4^{-} $团簇负离子结构中三个较稳定的异构体. 最稳定的结构0A是一个略微扭曲的四面体, 属于C2对称点群, 电子态为2B, 团簇中钽-钽键长分别为2.53, 2.54和2.62 Å. 次稳定的异构体0B是一个变形的四面体结构, 电子态为4A. 异构体0C则是一个菱形结构, 属于D2h对称点群, 电子态为2B2u. 异构体0A的理论VDE和ADE分别为0.94和0.92 eV, 与实验值((1.16 ± 0.08) eV和(1.10 ± 0.08) eV)相吻合. 在图3中, 异构体0A的DOS谱图中谱峰的位置和强度与实验光电子能谱相一致. 异构体0B和0C理论结果与实验结果差别较大. 因此, 我们认为实验中观察到的${\rm{Ta}}_4^{-} $团簇的结构为异构体0A. 在中性Ta4团簇异构体中, 最稳定的异构体0a是一个正四面体, Td对称点群, 1A1电子态, 钽-钽键长为2.54 Å. 异构体0b和0c为Ta4四面体结构处于不同的电子态, 并有不同程度的扭曲, 其能量分别比异构体0a高0.54和1.28 eV.

    ${\rm{Ta}}_4{\rm{C}}_1^{-} $团簇负离子的低能量异构体中, 基态结构1A为一个碳原子覆盖在四面体${\rm{Ta}}_4^{-} $的一个面上方, 属于Cs点群, 2A'' 电子态, 钽-碳键长分别为1.97和2.31 Å. 异构体1B中碳原子与Ta4船型结构中的两个钽原子相连. 异构体1C中的碳原子则是覆盖到了四面体结构中的一个棱上. 异构体1A的理论VDE (1.23 eV)和ADE (1.22 eV)与实验值((1.35 ± 0.08) eV和(1.31 ± 0.08) eV)相一致, 其DOS谱图与实验谱图相吻合. 异构体1B和1C的能量比异构体1A分别高0.27 eV和0.46 eV, 它们在团簇束源中存在的可能性很小. 因此, 认为光电子能谱确定的${\rm{Ta}}_4{\rm{C}}_1^{-} $团簇负离子的结构为1A. 对于中性Ta4C1团簇, 异构体1a和1b的结构分别与团簇负离子1A和1B相似, 1b能量仅比1a高0.08 eV. 异构体1c比1a能量高0.45 eV.

    最稳定的${\rm{Ta}}_4{\rm{C}}_2^{-} $团簇负离子结构2A中两个碳原子分别覆盖在Ta4四面体的两个面上方, 属于Cs点群, 2A'' 电子态, 其钽-碳键长分别为1.95, 2.09, 1.99和2.18 Å. 理论获得异构体2A的VDE和ADE分别为1.49 eV和1.34 eV, 与${\rm{Ta}}_4{\rm{C}}_2^{-} $团簇负离子的实验VDE ((1.55 ± 0.08) eV)和实验ADE((1.44 ± 0.08) eV)相近. 异构体2A的DOS谱图可以复现${\rm{Ta}}_4{\rm{C}}_2^{-} $团簇负离子的光电子能谱特征. 因此, 认为实验中观测到的${\rm{Ta}}_4{\rm{C}}_2^{-} $团簇负离子是异构体2A. 异构体2B和2C的能量分别比2A高0.29 eV和0.30 eV, 它们的理论VDEs (1.22 eV和1.05 eV)与实验值差别较大, 在实验谱图中没有与它们相关的谱峰. 因此, 异构体2B和2C在团簇束流中可以被排除. 对于中性Ta4C2团簇, 异构体2a和2b与团簇负离子2A结构相似, 其电子态分别为3A''1A, 基态结构2a处于高自旋态, 说明中性Ta4C2团簇具有弱磁性. 异构体2b和2c的能量分别比基态结构2a高0.12 eV和0.13 eV.

    ${\rm{Ta}}_4{\rm{C}}_3^{-} $团簇负离子的低能量异构体中, 基态结构3A是一个缺角立方体结构, 属于C3v点群, 电子态为2A1, 钽—碳键长为2.00 Å. 异构体3A的理论VDE和ADE分别为1.17 eV和1.13 eV, 与实验值((1.30 ± 0.08) eV和(1.21 ± 0.08) eV)接近. 异构体3A的DOS谱图与实验谱图吻合. 异构体3B和3C能量分别比3A高1.03 eV和1.41 eV, 在实验中无法观测到. 因此, 实验中观测到的${\rm{Ta}}_4{\rm{C}}_3^{-} $团簇负离子为异构体3A. 在中性Ta4C3团簇中, 较低能量的异构体3a, 3b和3c均为缺角立方体结构, 电子态分别为1A1, 3A'和5A. 异构体3b和 3c比基态结构3a能量分别高0.74 eV和1.55 eV.

    ${\rm{Ta}}_4{\rm{C}}_4^{-} $团簇负离子最稳定结构4A是一个略微变形的立方体结构, 属于D2d对称点群, 电子态为4B2, 钽—碳键长为2.05和1.99 Å. 异构体4B是一个属于C1对称点群的扭曲立方体, 电子态为2A. 异构体4B的能量仅比4A高0.09 eV. 理论计算所得异构体4A的VDE/ADE(1.70 eV/1.69 eV)与${\rm{Ta}}_4{\rm{C}}_4^{-} $团簇负离子532 nm光电子能谱中的窄峰((1.86/1.80 ± 0.08) eV)符合的较好, 而异构体4B的理论VDE/ADE(1.61 eV/1.60 eV)与${\rm{Ta}}_4{\rm{C}}_4^{-} $团簇负离子532 nm光电子能谱中的宽峰((1.39/1.35 ± 0.08) eV)符合得较好. 从图3可以看出, 将异构体4A和4B的DOS谱图叠加后, 可以很好地重现${\rm{Ta}}_4{\rm{C}}_4^{-} $团簇负离子的光电子能谱. 异构体4C比4A的能量高0.21 eV, 很难在实验中观测到. 因此, 认为实验中异构体4A和4B共存. 最稳定的中性Ta4C4团簇4a是一个具有较低对称性(C2)的近似立方体结构, 电子态为3B. 异构体4b则是一个标准的立方体(Td), 电子态为5A1. 异构体4b和4c比异构体4a能量分别高0.26 和0.49 eV. 异构体4a可以看成是α-TaC晶体最小的面心立方晶胞, 具有两个未成对电子, 呈一定磁性.

    图5${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的实验VDE/ADE和理论VDE/ADE随着碳原子数目变化的趋势比对图, 可以看出实验值与理论值吻合得很好. 由于${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的基态结构与其对应的中性团簇基态结构相似, 可以认为负离子团簇的ADE对应其中性团簇的电子亲和能. 从图5可以看出${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的VDE/ADE值随碳原子数目的增加而增加, 但是在${\rm{Ta}}_4{\rm{C}}_3^{-} $团簇处出现“凹陷”. 为解释这一现象, 采用波函数分析程序Multiwfn[81]${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的最稳定结构进行了分子轨道成分分析, 结果如图6所示.

    图 5  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的实验VDE/ADE和理论VDE/ADE随碳原子增加的变化趋势
    Fig. 5.  Experimental and theoretical VDEs and ADEs of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) versus the number of carbon atoms.
    图 6  ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0—4)团簇负离子的部分分子轨道示意图
    Fig. 6.  Diagrams of the selected molecular orbitals of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions.

    ${\rm{Ta}}_4^{-} $团簇负离子的单电子最高占据轨道(singly occupied molecular orbital, SOMO)均匀分布在4个钽原子周围. ${\rm{Ta}}_4{\rm{C}}_1^{-} $团簇的SOMO成分组成为: 1Ta, 20.39%; 2Ta, 30.14%; 3Ta, 30.14%; 4Ta, 17.20%; 5C, 1.21%. 各原子的原子轨道在${\rm{Ta}}_4{\rm{C}}_2^{-} $团簇的SOMO贡献分别为: 1Ta, 28.58%; 2Ta, 20.35%; 3Ta, 21.33%; 4Ta, 28.58%; 5C, 0.44%; 6C, 0.03%. 而${\rm{Ta}}_4{\rm{C}}_3^{-} $团簇的SOMO轨道成分包含有1Ta, 4.21%; 2Ta, 4.21%; 3Ta, 4.21%; 4Ta, 84.84%; 5C, 0.34%; 6C, 0.34%; 7C, 0.34%. 最稳定的${\rm{Ta}}_4{\rm{C}}_4^{-} $团簇负离子具有3个SOMO, 其中SOMO的轨道成分为: 1Ta, 2.96%; 2Ta, 46.07%; 3Ta, 46.07%; 4Ta, 2.96%; 5C, 0.26%; 6C, 0.26%; 7C, 0.001%; 8C, 0.001%. SOMO-1的轨道成分为: 1Ta, 46.07%; 2Ta, 2.96%; 3Ta, 2.96%; 4Ta, 46.07%; 5C, 0.001%; 6C, 0.001%; 7C, 0.26%; 8C, 0.26%. 从以上轨道成分分析可以看出, ${\rm{Ta}}_4{\rm{C}}_3^{-} $团簇负离子的SOMO轨道明显不同于其他团簇, 其SOMO主要布居在一个钽原子周围, 其中的电子仅受一个钽原子的约束, 导致${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的VDE/ADE趋势图在${\rm{Ta}}_4{\rm{C}}_3^{-} $处出现“凹陷”现象.

    为了确认中性Ta4Cn(n = 0—4)团簇的结构, 在PBE/aug-cc-pVTZ/C/aug-cc-pVTZ-PP/Ta水平上对${\rm{Ta}}_4{\rm{C}}_n^{+} $(n = 0—4)团簇正离子进行了优化, 并获得中性团簇的电离能(ionization potentials, IPs). 我们得到的中性Ta4Cn(n = 0—4)团簇的理论电离能分别为5.72, 5.75, 5.52, 5.64和5.15 eV, 与文献[61]中Ta4Cn (n = 0—4)团簇的实验电离能(5.83, 5.80, 5.55, 5.79和5.15 eV)相符, 说明我们得到的中性团簇结构是合理的. 中性Ta4Cn (n = 0—4)团簇最高占据分子轨道(highest occupied molecular orbital, HOMO)和最低未占分子轨道(lowest unoccupied molecular orbital, LUMO)能级差(HOMO-LUMO能隙)分别为0.98, 0.72, 0.11, 0.95和0.03 eV. 可以看到Ta4C2和Ta4C4团簇的HOMO-LUMO能隙较小, 说明在${\rm{Ta}}_4{\rm{C}}_2^{-} $${\rm{Ta}}_4{\rm{C}}_4^{-} $团簇负离子的光电子能谱中第一个和第二个谱峰差距较小, 这与实验所得结果相吻合.

    在团簇${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)结构确定后, 计算了团簇的电荷布居(NPA)[82]以及Wiberg键级, 结果如图7所示. 从图7可以看到${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇中的电荷主要集中在碳原子周围(–0.87 |e| — –0.77 |e|), 说明钽原子的部分电荷转移到了碳原子, 我们认为这是由于碳的电负性(χ = 2.55)大于钽的电负性(χ = 1.5)所致. 钽—碳键的Wiberg键级介于1.17和1.39之间, 钽-碳之间作用力为共价键. 钽—钽键的Wiberg键级介于1.87与0.50之间, 随着碳原子的增加而降低, 说明碳原子的加入削弱了钽原子之间的作用力, 团簇中原子间作用力逐渐由钽-钽金属键转变为钽—碳共价键.

    图 7  ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的NPA电荷(Q, |e|, 红色数值)和Wiberg键级(紫色数值), 括号中为中性团簇相对应数值
    Fig. 7.  NPA charges (Q, in |e|, red values) and Wiberg bond indices (WBIs, purple values) of the most stable structures of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters. The values in parentheses are from the neutral clusters.

    为了研究团簇的稳定性随碳原子增加的演变, 结合文献[62,83]${\rm{Ta}}_n^{+} $(n = 5—11)团簇的几何结构, 计算了${\rm{Ta}}_{4+n}^{-/0} $(n = 0—4)和${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的单原子结合能(Eb). 计算方法如下:

    $\begin{split} &{E_{\rm{b}}}\left( {{\rm{T}}{{\rm{a}}_{4 + n}}} \right) = \\ &\dfrac{{\left[ {\left( {4 + n} \right) \times E\left( {{\rm{Ta}}} \right) - E\left( {{\rm{T}}{{\rm{a}}_{4 + n}}} \right)} \right]}}{{n + 4}},\end{split}$

    $\begin{split} &{E_{\rm{b}}}\left( {{\rm{T}}{\rm{a}}_{4 + n}^ - } \right) = \\ &\dfrac{{\left[ {\left( {3 + n} \right) \times E\left( {{\rm{Ta}}} \right) + E\left( {{\rm{T}}{{\rm{a}}^ - }} \right) - E\left( {{\rm{T}}{\rm{a}}_{4 + n}^-} \right)} \right]}}{{n + 4}}, \end{split}$

    $\begin{split} &{E_{\rm{b}}}\left( {{\rm{T}}{{\rm{a}}_4}{{\rm{C}}_n}} \right) = \\ &\dfrac{{\left[ {4 \times E\left( {{\rm{Ta}}} \right) + n \times E\left( {\rm{C}} \right) - E\left( {{\rm{T}}{{\rm{a}}_4}{{\rm{C}}_n}} \right)} \right]}}{{n + 4}},\end{split}$

    $\begin{split} &{E_{\rm{b}}}\left( {{\rm{T}}{{\rm{a}}_4} {\rm{C}}_n^ - } \right) = \\ &\frac{{\left[ {4 \!\times\! E\left( {{\rm{Ta}}} \right) \!+\! \left( {n \!-\! 1} \right) \!\times\! E\left( {\rm{C}} \right) \!+\! E\left( {{{\rm{C}}^ - }} \right) \!-\! E\left( {{\rm{T}}{{\rm{a}}_4} {\rm{C}}_n^ - } \right)} \right]}}{{n + 4}},\end{split}$

    其中E对应团簇或原子的能量, 所得结果如图8以及表2所列. 由图8表2可以看出, 随着原子数目的增加, ${\rm{Ta}}_{4+n}^{-/0} $(n = 0—4)和${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的Eb逐渐增加. 这说明随着原子数目的增加, 团簇解离成单个原子所需能量逐渐增加. 同时, 将${\rm{Ta}}_4{\rm{C}}_n^{-/0} $团簇的Eb与纯金属团簇${\rm{Ta}}_{4+n}^{-/0} $Eb进行比较, 发现${\rm{Ta}}_4{\rm{C}}_n^{-/0} $团簇的Eb远高于相应${\rm{Ta}}_{4+n}^{-/0} $团簇的Eb, 中性Ta4C4团簇的单原子结合能高达7.13 eV, 而中性Ta8团簇的单原子结合能仅为5.37 eV. 这说明用碳原子取代钽原子, 使得团簇解离成单个原子所需能量逐渐增加, 钽-碳共价键的形成有利于提高材料的熔点. 这也印证了碳化钽的熔点(4153.15 K)远高于钽金属的熔点(3290.15 K)[84]. 这或许可以为通过控制碳含量来调节材料的熔点提供一些思路.

    表 2  ${\rm{Ta}}_{4+n}^{-/0} $${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的单原子结合能(Eb)
    Table 2.  Binding energies per-atom (Eb) of ${\rm{Ta}}_{4+n}^{-/0} $ and ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters.
    nEb
    ${\rm{Ta}}_4{\rm{C}}_n^{-} $${\rm{Ta}}_{4+n}^{-} $Ta4CnTa4+n
    04.404.404.354.35
    15.104.785.434.65
    25.904.996.164.93
    36.565.306.815.22
    46.985.447.135.37
    下载: 导出CSV 
    | 显示表格
    图 8  ${\rm{Ta}}_{4+n}^{-/0} $${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的单原子结合能(Eb)随碳/钽原子增加变化图
    Fig. 8.  Size-dependence of binding energies per-atom (Eb) of ${\rm{Ta}}_{4+n}^{-/0} $ and ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters.

    本文采用光电子能谱结合量子化学计算方法, 对${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的电子结构、几何结构以及稳定性进行了研究. 实验测得${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的VDEs分别为(1.16 ± 0.08), (1.35 ± 0.08), (1.51 ± 0.08), (1.30 ± 0.08)和(1.86 ± 0.08) eV, 而相应的中性团簇的电子亲和能分别为(1.10 ± 0.08), (1.31 ± 0.08), (1.44 ± 0.08), (1.21 ± 0.08)和(1.80 ± 0.08) eV. ${\rm{Ta}}_4^{-/0} $团簇是四面体结构, 单个碳原子覆盖在${\rm{Ta}}_4^{-/0} $四面体的一个面上方即${\rm{Ta}}_4{\rm{C}}_1^{-/0} $团簇. 两个碳原子分别覆盖在${\rm{Ta}}_4^{-/0} $四面体的两个面上方, 即${\rm{Ta}}_4{\rm{C}}_2^{-/0} $团簇. ${\rm{Ta}}_4{\rm{C}}_3^{-/0} $团簇则是一个缺角立方体结构. ${\rm{Ta}}_4{\rm{C}}_4^{-/0} $团簇是一个略微扭曲的立方体结构, 可以认为是α-TaC晶体的一个2 × 2 × 2晶胞. 其中, 中性Ta4C2和Ta4C4团簇呈一定磁性. ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子分子轨道分析结果显示${\rm{Ta}}_4{\rm{C}}_3^{-/0} $团簇的SOMO主要布居在一个钽原子周围, 导致其VDE明显低于相邻团簇. 理论结果显示随着碳原子的增加, ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇中的钽-钽金属键逐渐变为钽-碳共价键, 单原子结合能逐渐增加且明显高于相同原子数目的${\rm{Ta}}_{4+n}^{-/0} $(n = 0—4)团簇, 说明碳的加入可以明显提升钽金属的熔点. 中性Ta4C4团簇的单原子结合能高达7.13 eV, 与碳化钽具有超高熔点特性相关.

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  • 图 1  在532和266 nm条件下采集的${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的光电子能谱

    Figure 1.  Photoelectron spectra of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions recorded with 532 (left) and 266 nm (right) photons.

    图 2  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的低能量异构体. 相对能量是在PBEPBE/aug-cc-pVTZ/C/aug-cc-pVTZ-PP/Ta水平获得. 其中红色球代表碳原子, 青色球代表钽原子

    Figure 2.  Low-lying isomers of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions. The relative energies are calculated at the PBEPBE/aug-cc-pVTZ/C/aug-cc-pVTZ-PP/Ta level. Cyan and red balls stand for the tantalum and carbon atoms, respectively.

    图 3  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的模拟光电子能谱(DOS)与实验光电子能谱对比, 竖线表示理论计算所对应的分子能级

    Figure 3.  Comparisons of the experimental photoelectron spectra of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) with their simulated density of states (DOS) spectra. The vertical lines are the theoretically simulated spectral lines.

    图 4  中性Ta4Cn (n = 0—4)团簇的低能量异构体

    Figure 4.  Low-lying isomers of neutral Ta4Cn (n = 0–4) clusters.

    图 5  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的实验VDE/ADE和理论VDE/ADE随碳原子增加的变化趋势

    Figure 5.  Experimental and theoretical VDEs and ADEs of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) versus the number of carbon atoms.

    图 6  ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0—4)团簇负离子的部分分子轨道示意图

    Figure 6.  Diagrams of the selected molecular orbitals of ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions.

    图 7  ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的NPA电荷(Q, |e|, 红色数值)和Wiberg键级(紫色数值), 括号中为中性团簇相对应数值

    Figure 7.  NPA charges (Q, in |e|, red values) and Wiberg bond indices (WBIs, purple values) of the most stable structures of ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters. The values in parentheses are from the neutral clusters.

    图 8  ${\rm{Ta}}_{4+n}^{-/0} $${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的单原子结合能(Eb)随碳/钽原子增加变化图

    Figure 8.  Size-dependence of binding energies per-atom (Eb) of ${\rm{Ta}}_{4+n}^{-/0} $ and ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters.

    表 1  ${\rm{Ta}}_4{\rm{C}}_n^{-} $(n = 0—4)团簇负离子的低能量异构体的相对能量(∆E), 理论VDEs/ADEs以及实验VDEs/ADEs

    Table 1.  Relative energies (∆E ), theoretical VDEs and ADEs of the low-lying isomers for ${\rm{Ta}}_4{\rm{C}}_n^{-} $ (n = 0–4) cluster anions, as well as the experimental VDEs and ADEs estimated from their photoelectron spectra.

    异构体电子态对称点群E/eVVDE/eVADE/eV
    理论值实验值理论值实验值
    ${\rm{Ta}}_4^{-} $0AC22B00.941.160.921.10
    0BC14A0.301.321.16
    0CD2h2B2u0.921.591.39
    ${\rm{Ta}}_4{\rm{C}}_1^{-} $1ACs2A''01.231.351.221.31
    1BC2v2B20.271.071.03
    1CC2v2B20.461.180.76
    ${\rm{Ta}}_4{\rm{C}}_2^{-} $2ACs2A''01.491.511.341.44
    2BCs2A''0.291.221.18
    2CCs4A''0.301.051.04
    ${\rm{Ta}}_4{\rm{C}}_3^{-} $3AC3v2A101.171.301.131.21
    3BCs6A''1.031.661.65
    3CC2v2A11.411.351.29
    ${\rm{Ta}}_4{\rm{C}}_4^{-} $4AD2d4B201.701.861.691.80
    4BC12A0.091.611.391.601.35
    4CD2d6A20.211.751.74
    DownLoad: CSV

    表 2  ${\rm{Ta}}_{4+n}^{-/0} $${\rm{Ta}}_4{\rm{C}}_n^{-/0} $(n = 0—4)团簇的单原子结合能(Eb)

    Table 2.  Binding energies per-atom (Eb) of ${\rm{Ta}}_{4+n}^{-/0} $ and ${\rm{Ta}}_4{\rm{C}}_n^{-/0} $ (n = 0–4) clusters.

    nEb
    ${\rm{Ta}}_4{\rm{C}}_n^{-} $${\rm{Ta}}_{4+n}^{-} $Ta4CnTa4+n
    04.404.404.354.35
    15.104.785.434.65
    25.904.996.164.93
    36.565.306.815.22
    46.985.447.135.37
    DownLoad: CSV
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Metrics
  • Abstract views:  6605
  • PDF Downloads:  208
Publishing process
  • Received Date:  17 August 2020
  • Accepted Date:  01 September 2020
  • Available Online:  11 January 2021
  • Published Online:  20 January 2021

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