A study of FeCO+ and Fe+ using both the second-order multi-configurational quasi-degenerate perturbation theory (MC-QDPT2) method and the coupled cluster theory with single and double replacements (augmented by perturbative triples) [CCSD(T)] method are presented. An all-electron triple-ζ valence plus polarization basis set was used in all calculations. The equilibrium CCSD(T) geometry of FeCO+ is found to be linear (4Σ-) with a Fe+ to CO distance of 1.905 Å and a CO bond distance of 1.133 Å. The dissociation energy D0 of 4Σ- FeCO+ to 6D Fe+ and 1Σ+ CO is predicted to be 28.8 kcal mol-1, which is within the experimental range. Excited state properties including potential energy surfaces and De are predicted for the low lying sextet and quartet states of FeCO+. The first excited state is predicted to be 4Δ with a De of 17.6 kcal mol-1. The lowest sextet state is predicted to be 6Δ with a D0 of 12.3 kcal mol-1. Several examples of pathological behavior at many levels of theory have been discovered and are discussed.