Computational Analysis of Vibrational Modes in Tetra-Sulfur Using Dimensionally Reduced Potential Energy Surface

Electronic structure calculations are carried out for the S4 molecule at the CCSD(T)-F12a/VTZ-F12 level of theory to map out its potential energy surface, which possesses a double-well shape with a low-energy barrier. Two degrees of freedom are considered: the distance R and the gearing motion angle α between the two weakly-perturbed S2 dimers, which form S4. Vibrational states are computed on this 2D-surface and assigned quantum numbers based on their energies and the shapes of their wave functions. Two progressions of vibrational states are identified: a long progression of easily assignable states that develop nodes along the ‘channels’ on the surface, and a shorter progression of states that develop nodes across the ‘channels’ and are much harder to assign, due to the double-well effect. Normal mode analysis indicates that these two modes in S4 represent a significant mixture of conventional bending and stretching motions. When the angle α is increased, the lower frequency mode corresponds to stretching of the distance R, while the higher frequency mode corresponds to compression of R. Frequencies of the modes, ∼180 and ∼420 cm−1, are in a qualitative agreement with earlier ab initio studies of tetra-sulfur, and with sparse experimental data