The structure of isolated, monomeric M-CH3 (M=Li, Na) and M-CCH (M=Li, Na, K) has been recently determined by millimeter/submillimeter rotational spectroscopy. These accurate experimental results offer the opportunity for an extensive ab initio study of these molecules in order to assess the accuracy of the latest developments in density functional theory (DFT). As a general trend, DFT results from hybrid functionals (B1LYP, mPW1PW91, and PBE0) are in very good agreement with experiment while conventional functionals (BLYP) show slightly larger errors. In addition, DFT methods show rapid basis set convergence, whereas post-HF techniques [MP2, QCISD, and CCSD(T)] give comparably good results only using large basis sets. The properties derived from the electron density are computed to a fairly similar accuracy by all methods, provided a large basis set is used. The importance of a proper treatment of electron correlation in the description of the bond between the carbon and the alkali metal atom is emphasized.