Energetically low-lying states of the C2P and CNP molecular systems and their cations are studied. Geometries, harmonic frequencies, and dipole moments have been obtained at the density functional (using the Becke three-parameter Lee-Yang-Parr B3LYP functional) and coupled cluster theoretical levels in conjunction with correlation consistent basis sets. Single-point coupled cluster calculations for B3LYP geometries have been used to compute energy differences for the different states. For the C2P radical, the global minimum is linear CCP((2) Pi) followed by cyclic C2P(B-2(2)) at 5.5 kcal/mol, linear CCP((4) Sigma(-)) (21.2 kcal/mol), cyclic C2P((4)A(2)) (38.4 kcal/mol), and linear CPC((2) Pi(g)) (88.0 kcal/mol). For the C2P+ cation the following sequence of states has been established: linear CCP+(1 Sigma(+)), cyclic C2P((1)A(1)) (8.7 kcal/mol), cyclic C2P+(B-3(2)) (24.1 kcal/mol), linear CCP+((3) Pi) (29.1 kcal/mol), and linear CPC+((1) Sigma(g)(+)) (104.3 kcal/mol). For neutral PCN and PNC, the following sequence of states has been computed: linear PCN((3) Sigma(-)); linear PNC((3) Sigma(-)) (14.2 kcal/mol), linear PCN(1 Delta) (25.2 kcal/mol), cyclic CPN((3)A'') (36.2 kcal/mol), cyclic CPN((1)A'') (37.7 kcal/mol), and linear PNC(1 Delta) (38.8 kcal/mol). The ground state of the single ionized species is linear PNC+((2) Pi) followed by linear PCN+((2) Pi); the energy difference is very small: 0.8-1.4 kcal/mol. Cyclic CPN+((2)A') lies much higher in energy (13.9 kcal/mol) and was found to be a local energy minimum at the doublet surface. Predictions for IR spectra of the species are given. The computed total atomization energies are 261.7 +/- 1 kcal/mol for CCP((2) Pi) and 276.0 +/- 1 kcal/mol for PCN((3) Sigma(-)). Adiabatic ionization potentials (eV) areas follows: linear CCP((2) Pi) 9.05, cyclic C2P(B-2(2)) 9.18, linear PCN((3) Sigma(-)) 10.39, and linear PNC((3) Sigma(-)) 9.73.