Interplay of Rotational and Pseudorotational Motions in Flexible Cyclic Molecules

Abstract

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.

Structure and dynamics of 3′-aminoacetophenone and 4′-aminoacetophenone from rotational spectroscopy

“…For instance, from the free-jet millimetre-wave spectrum of methacrylamide, 4 which is a small organic molecule with two C-C rotatable bonds (CH 3 -C(CH 2 )-CONH 2 ), two conformers (one planar and the other with non-planar doubly degenerate skeletal arrangement) were detected and their energy difference was determined (4 kJ mol À1 ). Moreover, splittings due to the torsion around both the C-C bonds were observed and analyzed with appropriate Hamiltonian models 5,6 achieving the barrier for the methyl internal rotation of both planar and non-planar conformers (10.2 and 7.4 kJ mol À1 , respectively) as well as the interconversion barrier between the two equivalent non-planar forms (3.6 kJ mol À1 ). It is worth noting that in methacrylamide the amino group is part of an amide group and therefore its inversion motion is hindered because of resonance with the carbonyl group.…”

Potential Energy Surfaces Sampled in Cremer–Pople Coordinates and Represented by Common Force Field Functionals for Small Cyclic Molecules

“…Sampling the conformational space via dihedral angles is a common practice. − However, this method is not efficient for exploring the conformational space of small cyclic molecules and produces ambiguous samplings due to the redundancy of internal coordinates. As a result, only a portion of the PES is sampled, and the poor representations of the conformational space often require further refinements of the torsion parameters. ,,, More importantly, the dihedral-based sampling fails to account for the underlying physics ,,− of conformational transitions, a feature critical − for predicting solvation properties. This problem is more pronounced in the development of machine-learned force fields (FFs), where adequately sampling the PESs is crucial. − …”

Potential-Energy Surfaces Sampled in Cremer–Pople Coordinates and Represented by Common Force Field Functionals for Small-cyclic Molecules

“…As a result, only a portion of the PES is sampled and the poor representations of the conformational space often require further refinements of the torsion parameters 20,33,[39][40] . More importantly, the dihedral-based sampling fails to account for the underlying physics 25,30,[41][42][43][44][45][46] of conformational transitions, a feature critical [47][48][49] for predicting solvation properties. This problem is more pronounced in the development of machine-learned force fields (ML-FF), where adequately sampling the PESs is crucial [50][51][52][53] .…”