Assessing Constrained Nuclear-Electronic Orbital Theory for the Floppy CH5+ Ion: Geometry-Dependent Zero-Point...

Recently, constrained nuclear-electronic orbital (CNEO) theory has been developed to incorporate nuclear quantum delocalization and zero-point effects into quantum chemistry calculations and ab initio molecular simulations. Motivated by discussions with John Stanton, we apply CNEO methods to protonated methane, CH5+, as a stringent test case for the quantum-corrected effective-potential framework. CH5+ is a prototypical penta-coordinated nonclassical carbonium ion with a highly anharmonic potential energy surface, many low-lying geometries connected by low barriers, and extensive fluxional motion. Using CNEO, we examine the effective structural features, hydrogen rearrangement dynamics, and simulated IR spectra of CH5+. The CNEO effective potential energy surface exhibits a minimum with C2v symmetry, which is more symmetric than the minimum-energy eclipsed-Cs structure on the conventional potential energy surface. CNEO molecular dynamics predicts more frequent hydrogen rearrangement than conventional ab initio molecular dynamics, with pronounced rearrangement observed starting from 50 K. A Fourier-filtered analysis of C-H bond-length distributions along the trajectories, combined with a Gaussian mixture model, reveals three structural and dynamical motifs: equilibrium-like, fluxional, and transition-state hovering configurations. The simulated IR spectra, which are obtained from either harmonic analysis or classical dynamics on the CNEO surface, are compared qualitatively with experimentally observed spectral features. Overall, this work assesses how the computationally efficient CNEO framework captures qualitative structural, dynamical, and spectroscopic trends in the highly fluxional CH5+, while also highlighting the challenges and shortcomings of this classical-trajectory-based method in a system where fully quantum nuclear effects beyond zero-point effects are important.