The diatomic X ≡ Y and the triatomic X = Y = Z species containing phosphorus and second-row atoms are screened for possible new compounds, mostly at the HF and MP2/6-31G* level. The heats of formation are estimated and compared for nitrogen and phosphorus compounds, E = N and E = P, with the species EO-3and EO3-4included in the comparison. The CO4-4and OO2-4neighbours of the known NO3-4have weaker bonds. One predicted species, PBP3-, has been made independently by von Schneringet al., and itsReandvevalues agree with those predicted. The so-far unknown species PCP2-, PCO-and OPO+are proposed as possible new solid-state species, while CP-is found to be thermodynamically less favoured. The experimentally unknown CP-, SiP-, PS+, PF2+, PNe3+, PBF-, PCO-, PNN-, NPN-, PNP-, PPN-, OPO+and PNF+are proposed as new gas-phase species.