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⁺, HCO, HNO, HOO, HOO^-, , and CH₃. 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 (830), 2175 (2184), and 3083 (3089) cm^-1 in HCO⁺; 1079 (1081), 1874 (1868), 2432 (2434) cm^-1 in HCO; 1503 (1501), 1572 (1565), and 2683 (2684) cm^-1 in HNO; 1121 (1098), 1399 (1392), and 3447 (3436) cm^-1 in HOO; 739, 1088, and 3587 cm^-1 in HOO^-; 1383 (1359 ± 7), 1384 (1370 ± 7), 2940, and 3096 (3108) cm^-1 in  ; 565 (606), 1377, 3002 (3004), and 3139 (3161) cm^-1 in CH₃. The mean absolute deviation in the predicted frequencies is 11 cm^-1.