The adapted Numerov approach was extended to periodic problems and applied to the torsional tunneling splitting of six increasingly complex target systems carrying a hydroxy-group. The deviations from experiment remained on the order of 1 cm(-1), except for phenol in which the exceptionally small ground-state tunneling-splitting of 0.0017 cm(-1) was found in very good agreement with the experimental value of 0.0019 cm(-1). Overall, the accuracy of the periodic Numerov approach for the treatment of torsional tunneling is on the same order as alternative approaches, but at a substantially reduced computational demand due to the restriction of the problem to the respective degree of freedom.