Calculations of the full structure and spectra of large nanotubes can be very demanding of computer resources. The advantages and limitations of the cost-effective same level different basis (SLDB) and selected normal modes (SNM) protocols are elucidated for carboxylated (4,4) armchair and (8,0) zigzag single-wall carbon nanotubes (SWNTs) with varying numbers of COOH groups on the tips of the tubes. While armchair-COOH tubes exhibit C═O stretching frequencies in the standard range of 1720–1760 cm–1, zigzag-COOH tubes display a surprising C═O band around 1660 cm–1 with much higher intensity, in addition to the higher-frequency C═O mode. This low-frequency C═O peak is very unusual for a standalone COOH group and is a fingerprint of zigzag tubes.