A general scheme to predict anharmonic vibrational frequencies and vibrationally-averaged structures and rotational constants of molecules is presented with applications to some key species in hydrocarbon combustion (some also of importance in atmospheric and/or interstellar chemistry): HCO þ , HCO, HNO, HOO, HOO -,CH þ 3 , and CH 3 . A combination of coupled-cluster singles and doubles (CCSD), CCSD with a second-order perturbation correction in the space of triples [CCSD(2) T ] and in the space of triples and quadruples [CCSD(2) TQ ], and a correlation-consistent basis set series has been employed to achieve the complete-correlation, complete-basis-set limits of the potential energy surfaces (PESs) of these species near equilibrium geometries. A new, compact representation of PESs that combines two existing representations, namely, a fourth-order Taylor expansion and numerical values on a rectilinear grid, has been proposed and shown to yield accurate frequencies, when combined with vibrational general-order configuration-interaction method. The predicted frequencies (and the observed in parentheses, when available) of the fundamentals are as follows: 823 3139 (3161) cm À1 in CH 3 . The mean absolute deviation in the predicted frequencies is 11 cm À1 .