Picosecond vibrational echo studies of the asymmetric stretching mode (2010 cm(-1)) of (acetylacetonato)dicarbonylrhodium(I) [Rh(CO)(2)acac] in liquid and glassy dibutyl phthalate (DBP) (3.5 K to 250 K) are reported and compared to previous measurements of a similar mode of tungsten hexacarbonyl [W(CO)(6)]. The Rh(CO)(2)acac pure dephasing shows a T-1 dependence on temperature at very low temperature with a change to an exponentially activated process (Delta E congruent to 400 cm(-1)) above similar to 20 K. There is no change in the functional form of the temperature dependence in passing from the glass to the liquid. It is proposed that the T-1 dependence arises from coupling of the vibration to the glass's tunneling two level systems. The activated process arises from coupling of the high-frequency CO stretch to the 405 cm(-1) Rh-C stretch. Excitation of the Rh-C stretch produces changes in the back donation of electron density from the rhodium d(pi) orbital to the CO pi* antibonding orbital, shifting the CO. stretching transition frequency and causing dephasing. In contrast, W(CO)(6) displays a T-2 dependence below T-g in DBP and two ether solvents. Above T-g, there is a distinct change in the functional form of the temperature dependence. In 2-methylpentane, a Vogel-Tammann-Fulcher-type temperature dependence is observed above T-g. It is proposed that the triple degeneracy of the T-1a mode of W(CO)(6) is broken in the glassy and liquid solvents. The closely spaced levels that result give rise to unique dephasing mechanisms not available in the nondegenerate Rh(CO)(2)acac system.