Patzschke Michael, Sundholm Dage
Department of Chemistry, University of Helsinki, P.O. Box 55 A.I. Virtanens plats 1, FIN-00014 Helsinki, Finland.
J Phys Chem B. 2005 Jun 30;109(25):12503-8. doi: 10.1021/jp045126n.
The infrared (IR) spectra of cuboidic titanium carbide (TiC) nanocrystals have been studied at the density-functional-theory (DFT) level using the Becke-Perdew (BP) functional and triple-zeta quality basis sets augmented by one set of polarization functions (TZVP). The accuracy of the calculations was checked by DFT calculations using the Perdew-Burke-Ernzerhof hybrid functional (PBE0) and up to quadruple-zeta quality basis sets augmented by one set of polarization functions (QZVP). The calculated IR spectrum for Ti(14)C(13) (3 x 3 x 3) is found to be in fair agreement with the experimental IR spectrum obtained by infrared resonance-enhanced multiphoton ionization (IR-REMPI) measurements, whereas, for Ti(18)C(18) (4 x 3 x 3) and Ti(32)C(32) (4 x 4 x 4), the calculated IR spectra differ significantly from the experimental ones. The smallest TiC cluster (Ti(4)C(4), 2 x 2 x 2) considered has not been reported in any mass-spectrometer studies. The present DFT calculations show that the vibrational modes related to the in-plane vibrations of solid TiC are not observed in the IR-REMPI spectra of nanocrystals larger than Ti(14)C(13). Contrary to solid TiC, the studied TiC nanocrystals are nonmetallic with optical gaps of 0.62 eV (0.55 eV) and 0.028 eV (0.027 eV) for Ti(32)C(32) and Ti(108)C(108) (6 x 6 x 6), calculated at the time-dependent density-functional-theory (TDDFT) level using the BP functional. The HOMO-LUMO gaps obtained in the BP DFT calculations are given within parentheses. At the PBE0 DFT level, the HOMO-LUMO gaps for Ti(32)C(32) and Ti(108)C(108) are 1.74 and 0.32 eV, respectively.
利用Becke-Perdew（BP）泛函和由一组极化函数增强的三重ζ质量基组（TZVP），在密度泛函理论（DFT）水平上研究了长方体碳化钛（TiC）纳米晶体的红外（IR）光谱。通过使用Perdew-Burke-Ernzerhof杂化泛函（PBE0）和由一组极化函数增强的高达四重ζ质量基组（QZVP）的DFT计算来检验计算的准确性。发现Ti(14)C(13)（3×3×3）的计算红外光谱与通过红外共振增强多光子电离（IR-REMPI）测量获得的实验红外光谱相当吻合，而对于Ti(18)C(18)（4×3×3）和Ti(32)C(32)（4×4×4），计算的红外光谱与实验光谱有显著差异。所考虑的最小TiC团簇（Ti(4)C(4)，2×2×2）在任何质谱研究中均未被报道。目前的DFT计算表明，在大于Ti(14)C(13)的纳米晶体的IR-REMPI光谱中未观察到与固态TiC面内振动相关的振动模式。与固态TiC相反，使用BP泛函在含时密度泛函理论（TDDFT）水平上计算，所研究的TiC纳米晶体对于Ti(32)C(32)和Ti(108)C(108)（6×6×6）是非金属的，光学带隙分别为0.62 eV（0.55 eV）和0.028 eV（0.027 eV）。括号内给出了在BP DFT计算中获得的HOMO-LUMO带隙。在PBE0 DFT水平上，Ti(32)C(32)和Ti(108)C(108)的HOMO-LUMO带隙分别为1.74和0.32 eV。
