This dataset contains data used for testing a new and efficient approach for describing strongly anharmonic systems using a VSCF method. The new method uses calculated force data to improve the mapping of the Born-Oppenheimer surface, an integral part of the problem. This is compared to the previous version of the VSCF method, which did not make use of forces. The systems tested are molecular hydrogen, three phases of solid high pressure hydrogen, and the bcc phases of lithium and zirconium. The dataset consists of significant numbers of density functional theory calculations, performed using CASTEP 8.0, and then the analyses of these results to obtain the anharmonic vibrational energy and wavefunction for each test case for each method.