Interplay of Rotational and Pseudorotational Motions in Flexible Cyclic Molecules

Solutions to the time-independent nuclear Schrodinger equation associated with the pseudorotational motion of three flexible cyclic molecules are presented and discussed. Structural relaxations related to the pseudorotational motion are described as functions of a pseudorotation angle phi which is formulated according to the definition of ring-puckering coordinates originally proposed by Cremer and Pople ( J. Am. Chem. Soc. 1975, 97 (6), 1354-1358). In order to take into account the interplay between pseudorotational and rotational motions, the rovibrational Hamiltonian matrices are formulated for the rotational quantum numbers J = 0 and J = 1. The rovibrational Hamiltonian matrices are constructed and diagonalized using a Python program developed by the authors. Suitable algorithms for (i) the construction of one-dimensional cuts of potential energy surfaces along the pseudorotation angle phi and (ii) the assignment of the vibrorotational wave functions (which are needed for the automatic calculation of rotational transition energies J = 0 -> J = 1) are described and discussed.