Assessment of Electron-Proton Correlation Functionals for Vibrational Spectra of Shared-Proton Systems by Constrained Nuclear-Electronic Orbital Density Functional Theory

Proton transfer plays a crucial role in various chemical and biological processes. A major theoretical challenge in simulating proton transfer arises from the quantum nature of the proton. Recently, the constrained nuclear-electronic orbital (CNEO) framework has been developed to efficiently and accurately account for nuclear quantum effects, particularly quantum nuclear delocalization effects, in quantum chemistry calculations and molecular dynamics simulations. In this paper, we systematically investigate challenging proton transfer modes in a series of shared-proton systems with the CNEO framework, focusing on evaluating existing electron-proton correlation functionals. Our results show that CNEO accurately describes proton transfer vibrational modes and significantly outperforms conventional DFT. The inclusion of the epc17-2 electron-proton correlation functional in CNEO produces similar performance to CNEO without electron-proton correlations, while the epc17-1 functional yields less accurate results, comparable to conventional DFT. These findings hold true for both asymmetrical and symmetrical shared-proton systems. Therefore, until a more accurate electron-proton correlation functional is developed, we recommend performing CNEO vibrational spectrum calculations without using electron-proton correlation functionals.