Ab initio methods including density functional theory are used to study alkali peroxynitrite (ONOOM, M = Li, Na, and K). The energy, optimized geometries, and vibration frequencies are presented for different conformations of alkali peroxynitrite. The cis-cis (a pseudo-five-membered ring) and trans-cis conformers are minima from a search over the dihedral angles ONOO and NOOM, respectively. Other minima that appear on the potential surfaces depend on the level of theory and the alkali atom studied. All levels of theory predict the cis-cis structures to have the lowest energy, and the stability relative to the trans-cis structures decreases from Li to Na to K. The rotational barrier of cis-cis to trans-cis isomerization is about 20 kcal/mol in ONOOLi, 27 kcal/mol in ONOONa, and 22 kcal/mol in ONOOK. The barriers for the reverse process are 12, 17, and 13 kcal/mol, respectively. Singlet-triplet UHF Hartree-Fock wave function instabilities are found in some of the ONOOM molecules, which lead-to poor values for ab initio rotational barriers, vibrational frequencies, and intensities. This leads to a survey of 22 density functional methods, with the computed Becke3-LYP vibration frequencies of cis-cis ONOOLi agreeing best with the experimental IR and Raman spectra. Density functional theory exhibits no instabilities for this class of problem molecules.