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 Ti14C13 (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 Ti18C18 (4 x 3 x 3) and Ti32C32 (4 x 4 x 4), the calculated IR spectra differ significantly from the experimental ones. The smallest TiC cluster (Ti4C4, 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 IRREMPI spectra of nanocrystals larger than Ti14C13. 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 Ti32C32 and Ti108C108 (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 Ti32C32 and Ti108C108 are 1.74 and 0.32 eV, respectively.