Using molecular graphics software, we have designed numerous models Of CnP3- (n = 2-8). We carried out geometry optimizations and calculations of vibrational frequency by means of the B3LYP density functional method. After comparing the total energies of the isomers, we found that the ground-state structures are straight carbon chains with a P2C ring connected at one end and a phosphorus atom at the other. The alternate behavior in electron affinity, bond length, and incremental binding energy with odd and even n match the peak pattern observed in the laser-induced mass spectra Of CnP3-(n = 2-8). Other than a number of individual isomers, the structures with carbon and phosphorus atoms connected alternately are unstable. Most of the stable models have carbon units in the form of a ring or a chain connecting to different P, P-2, and P-3 units.