Coupled rotational and bending dynamics of CO₂ near nanoporous graphene

The design of highly efficient gas separation membranes requires a fundamental understanding of molecular dynamics at the sub-nanometer scale. This study investigates the interaction of a linear CO $_2^{}$ molecule with a six-pore nanoporous graphene (NPG) sheet to map the energy landscape governing permeation. We specifically examine how molecular orientation and bending deformations influence transport as the molecule approaches the pore. Our results reveal that CO $_2^{}$ undergoes high-frequency angular "rattling" in the terahertz range, which enhances and splits C-H stretching signatures in the infrared spectra, indicating strong coupling between molecular rotation and lattice vibrations. Furthermore, the presence of the pore lifts the degeneracy of intrinsic CO $_2^{}$ bending modes, making them highly orientation-dependent. While bending modes remain stable at large separations, they become unstable at close proximity, shifting the permeation pathway from bending-dominated to rotation-dominated behavior. These findings suggest that selectivity in NPG membranes is governed by dynamic orientational-vibrational coupling rather than static molecular geometry, providing a basis for the "surgical" creation of pores tailored for specific gas separations.

Electronic structure calculations were performed using density functional theory (DFT) at the B3LYP/6-31++G(d,p) level. The potential energy surface was mapped via single-point energy (SPE) evaluations as a function of the molecular center-of-mass distance (z), rotational angle ( ${\theta }_{\text{rot}}$ ), and O-C-O bending angle ( ${\theta }_{\text{bend}}$ ). Permeation barrier energies were calculated for four symmetry-distinct configurations relative to the NPG plane. Vibrational frequencies and stability analyses were conducted using quadratic and cubic polynomial fits to the energy-displacement curves. All DFT calculations and infrared (IR) spectra simulations were carried out using the Gaussian 16 software suite. To validate the dynamical predictions of the DFT potential energy surface under realistic conditions, machine-learning interatomic potential molecular dynamics (MLIP-MD) simulations were performed using the ORB-v3-conservative-inf-omat potential at $T=300$  K and $P\approx 59$  atm, conditions representative of industrial CO $_2^{}$ membrane separation. The O-C-O bending angle distribution and its dependence on distance from the NPG sheet were analyzed across the trajectory.