An approach is described for calculating anharmonic spectra for polyatomic molecules using only the ground-state probability amplitude. The underlying theory is based on properties of harmonic oscillator wave functions and is tested for Morse oscillators with a range of anharmonicities. More extensive tests are performed with H3O2-, using the potential and dipole surfaces of Bowman and co-workers [L Am. Chem. Soc. 2004, 126, 5042]. The resulting energies are compared to earlier studies that employed the same potential surface, and the agreement is shown to be very good. The vibrational spectra are calculated for both H3O2- and D3O2-.. In the case of H3O2-, comparisons are made with a previously reported experimental spectrum below 2000 cm(-1). We also report the spectrum of H3O2- from 2400-4500 cm(-1), which extends 500 cm(-1) above the region reported earlier, revealing several new bands. As the only fundamentals in this spectral region involve the OH stretches, the spectrum is surprisingly rich. On the basis of comparisons of the experimental and calculated spectra, assignments are proposed for several of the features in this spectral region.