Finite-Temperature Double Proton Transfer in Formic Acid Dimer via Constrained Nuclear-Electronic Orbital Molecular Dynamics: Lower Barriers and Enhanced Rates from Nuclear Quantum Delocalization.

Proton transfer plays a crucial role in various chemical and biological processes, yet accurately and efficiently describing such reactions remains challenging due to nuclear quantum effects (NQEs). In this work, we employ constrained nuclear-electronic orbital molecular dynamics (CNEO-MD), a method that inherently incorporates NQEs into classical dynamics to investigate double proton transfer in the formic acid dimer (FAD). Leveraging machine learning techniques, we efficiently construct free energy landscapes with NQEs at finite temperatures and obtain transition state theory (TST) rates. Transmission coefficients are further evaluated using flux-side correlation functions to obtain corrected rates that account for recrossing effects. CNEO-MD predicts significantly lowered free energy barriers and enhanced rates compared to conventional DFT-based ab initio molecular dynamics (AIMD), agreeing qualitatively with previous path-integral simulations. Additionally, we explore solvent effects using CNEO-MD with a dielectric continuum solvent model and find the change of the solvent model makes negligible effects. Our findings demonstrate the effectiveness of CNEO-MD in describing proton transfer reactions at finite temperatures and highlight its potential for applications in more complex systems.