A simplified approach to the calculation of molecular torsion energy levels

Using a piece-wise constant potential approximation, we present an approach to one-dimensional molecular torsion calculations which avoids the step of matrix diagonalisation inherent in conventional appraoches. The eigenvalues and eigenvectors, being exact solutions to an approximated problem, are readily generated for both n-fold symmetric and asymmetric hindering potentials. An accompanying graphical approach motivates a natural classification for n-fold rotationally symmetric molecular states. The special case of 3-fold symmetry is illustrated via toluene. The splitting of degenerate levels for the case where a symmetry-breaking perturbation is added is discussed in some detail.