Cyclic molecules are a vast group with applications ranging from the petroleum industry to biochemistry and material science. In force field development, cyclic saturated hydrocarbons can be used as fragments in a step-wise parametrization for all-atom force fields (AA-FF) targeted at biomolecules. However, the conformational space of cyclic molecules is complex. The fluctuations in internal geometry induced by conformational transitions are reflected in the bond-length, bond-angles, local charges and van der Waals parameters between first and second neighbours. Parameter transferability between cyclic and linear molecules becomes, therefore, challenging. This work proposes a sampling scheme of the cyclic potential energy surface (PES) based on Cremer-Pople coordinates and representation of the PES using AA-FF. This method of sampling the conformational space provides a complete representation, including the pseudorotational transitions of five-membered rings (figure) and the first order conformational transitions of six-membered rings, while avoiding torsion-induced deformations. The resulting PES is fitted to AMBER, TEAM and CFF functional forms. Comparison between the different functional shows that while bond-lengths and frequencies are described accurately by a harmonic model, bond-angles and torsions require additional anharmonic contributions, flexible force constants and coupling terms found in CFF. This method can improve AA-FF parameters that can be used for cyclic molecules, fragments of biomolecules, small proteins and switch molecules with an interesting optical activity.

Cremer-Pople coordinate sampling and force field representation of the potential energy surfaces of small cyclic compounds

ACS Spring 2022

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