A laboratory project for the upper-division physical chemistry laboratory is described, and it combines IR and Raman spectroscopies with Gaussian electronic structure calculations to determine the structure of the oxalate anion in solid alkali oxalates and in aqueous solution. The oxalate anion has two limiting structures whose vibrational spectra have distinct differences: planar with D[subscript 2h] symmetry and nonplanar with D[subscript 2d] symmetry. In the former case, the IR and Raman spectra are complementary. Students measure the IR and Raman spectra of solid Na[subscript 2]C[subscript 2]O[subscript 4], K[subscript 2]C[subscript 2]O4, and Cs[subscript 2]C[subscript 2]O[subscript 4], and a nearly saturated aqueous solution of K[subscript 2]C[subscript 2]O[subscript 4]. They also carry out Gaussian calculations on the oxalate anion to predict the vibrational wavenumbers of both the planar and nonplanar structures and use the results to assign the spectra. By considering their results for the four samples, they decide on the oxalate structure in each and defend their choice in a report. The complexity of the project immerses the students in vibrational spectroscopy so that they learn the subject at a deeper level.