Abstract
The problem of the anharmonic oscillator with the potential for vibrating molecules V(x) = ½ω2 x 2 + αx 3 + βx 4 is treated in the framework of the hypervirial-Padé scheme. The energy eigenvalues of various eigenstates for small α and β are accurately determined by forming the E[8, 8] Padé approximants to the energy perturbation series in α2.