Solutions to the
time-independent nuclear Schrödinger 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 ϕ which is formulated according to the definition of ring-puckering
coordinates originally proposed by Cremer and Pople (
J. Am. Chem. Soc.
1975
97
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 ϕ
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.