Several ab initio methods are applied to the study of two linear isomers of methylidyne phosphine, HCP and HPC. Single-reference correlation methods ranging from second-order Moller-Plesset theory to coupled cluster singles and doubles theory with noniterative inclusion of connected triple excitations were applied in a variety of basis sets of increasing size. Ln addition, complete active space self-consistent field wave functions, multireference singles and doubles configuration interaction, and averaged coupled pair functional theory were also applied to HPC. For HCP comparison of the single-reference based results is made with experimental data and previous theory to assess the accuracy of the methods employed. The same single-reference-based methods are then applied to linear HPC in order to assess whether it is a stable minimum or a transition state (imaginary frequencies in two dimensions). It is found that linear HPC is not a minimum on the groundstate potential surface. However, relatively high levels of correlation must be used when single-reference-based methods are employed to arrive at this conclusion. The multireference-based methods are then applied to HPC, and they too predict that it is not a minimum on the ground electronic potential surface. The qualitative nature of linear HPC is examined using CASSCF and CCSD wave functions.