The ionization energy (IE) of FeC and the 0 K bond dissociation energies (D-0) and the heats of formation at 0 K (Delta H-f0 degrees) and 298 K (Delta H-f298 degrees) for FeC and FeC+ are predicted by the single-reference wave function based CCSDTQ(Full)/CBS approach, which involves the approximation to the complete basis set (CBS) limit at the coupled cluster level up to full quadruple excitations. The zero-point vibrational energy (ZPVE) correction, the core-valence electronic corrections (up to CCSDT level), spin-orbit couplings, and relativistic effects (up to CCSDTQ level) are included in the calculations. The present calculations provide the correct symmetry predictions for the ground states of FeC and FeC+ to be (3)Delta and (2)Delta, respectively. We have also examined the theoretical harmonic vibrational frequencies of FeC/FeC+ at the ROHF-UCCSD(T) and UHF-UCCSD(T) levels. While the UHF-UCCSD(T) harmonic frequencies are in good agreement with the experimental measurements, the ROHF-UCCSD(T) yields significantly higher harmonic frequency predictions for FeC/FeC+. The CCSDTQ(Full)/CBS IE(FeC) = 7.565 eV is found to compare favorably with the experimental IE value of 7.59318 +/- 0.00006 eV, suggesting that the single-reference-based Coupled Cluster theory is capable of providing reliable IE prediction for FeC, despite its multireference character. The CCSDTQ(Full)/CBS D-0(Fe+-C) and D-0(Fe-C) give the prediction of D-0(Fe+-C) - D-0(Fe-C) = 0.334 eV, which is consistent with the experimental determination of 0.3094 +/- 0.0001 eV. The D-0 calculations also support the experimental D-0(Fe+-C) = 4.1 +/-0.3 eV and D-0(Fe-C) = 3.8 +/- 0.3 eV determined by the previous ion photodissociation study. The present calculations also provide the Delta H-f0 degrees(Delta H-f298 degrees) predictions for FeC/FeC+. The analysis of the correction terms in these calculations shows that the core-valence and valence-valence electronic correlations beyond CCSD(T) wave function and the relativistic effects make significant contributions to the calculated thermochemical properties of FeC/FeC+. For the experimental D-0 and Delta H-f0 degrees values of FeC/FeC+, which are not known to high precision, we recommend the CCSDTQ(Full)/CBS predictions [D-0(Fe-C) = 3.778 eV, D-0(Fe+-C) = 4.112 eV, Delta H-f0 degrees(FeC) = 760.8 kJ/mol and Delta H-f0 degrees(FeC+) = 1490.6 kJ/mol] based on the ZPVE corrections using the experimental vibrational frequencies of FeC and FeC+.