Feynman–Hibbs corrections in molecular dynamics computer calculations of solid C60 are implemented within the classical effective pair potential approach. The potential model chosen for the site–site interactions is of the Buckingham exp-6 type (Rigby 1986 The Forces Between Molecules (New York: Oxford University Press)), fitted to the Cheng and Klein or the Kitaïgorodsky potential. Structural and thermodynamic properties of the C60 crystal lattice are investigated over a wide range of pressures and temperatures, and data obtained are compared to experimental results and those obtained from a classical approach (Baameur et al 2000 Phys. Status Solidi 220 821). It will be demonstrated that 'quantum corrections' applied in a simple quasi-classical simulations have a great influence upon most calculated properties and increase their accuracy when compared to classical approaches. The observed transition pressure with the distorted lattice and cell contraction compares favourably well with experimental data and equation of state calculations. All measured properties are reported together with the phonon density of states at different pressures.