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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. The constrained nuclear-electronic orbital (CNEO) framework was recently 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 using CNEO density functional theory (CNEO-DFT), focusing on evaluating existing electron–proton correlation functionals. Our results show that CNEO-DFT accurately describes proton transfer vibrational modes and significantly outperforms conventional DFT. The inclusion of the epc17-2 electron–proton correlation functional in CNEO-DFT produces similar performance to that without electron–proton correlations, while the epc17-1 functional yields less accurate results, comparable with 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 currently recommend performing vibrational spectrum calculations using CNEO-DFT without electron–proton correlation functionals. 

The hybrid quantum mechanics/molecular mechanics (QM/MM) approach, which combines the accuracy of QM methods with the efficiency of MM methods, is widely used in the study of complex systems. However, past QM/MM implementations often neglect or face challenges in addressing nuclear quantum effects, despite their crucial role in many key chemical and biological processes. Recently, our group developed the constrained nuclear-electronic orbital (CNEO) theory, a cost-efficient approach that accurately addresses nuclear quantum effects, especially quantum nuclear delocalization effects. In this work, we integrate CNEO with the QM/MM approach through the electrostatic embedding scheme and apply the resulting CNEO QM/MM to two hydrogen-bonded complexes. We find that both solvation effects and nuclear quantum effects significantly impact hydrogen bond structures and dynamics. Notably, in the glutamic acid–glutamate complex, which mimics a common low barrier hydrogen bond in biological systems, CNEO QM/MM accurately predicts nearly equal proton sharing between the two residues. With an accurate description of both quantum nuclear delocalization effects and environmental effects, CNEO QM/MM is a promising new approach for simulating complex chemical and biological systems. 

The assignment of the hydrogen bonded O–H stretch vibration in the proline matrix IR spectrum has sparked controversy. Employing constrained nuclear electronic orbital methods, we provide a clear assignment that the vibrational frequency drops to near 3000 cm−1 as a result of the interplay between electronic effects, nuclear quantum effects, and matrix effects.