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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. 

Proton transfer is crucial in various chemical and biological processes. Because of significant nuclear quantum effects, accurate and efficient description of proton transfer remains a great challenge. In this Communication, we apply constrained nuclear–electronic orbital density functional theory (CNEO-DFT) and constrained nuclear–electronic orbital molecular dynamics (CNEO-MD) to three prototypical shared proton systems and investigate their proton transfer modes. We find that with a good description of nuclear quantum effects, CNEO-DFT and CNEO-MD can well describe the geometries and vibrational spectra of the shared proton systems. Such a good performance is in significant contrast to DFT and DFT-based ab initio molecular dynamics, which often fail for shared proton systems. As an efficient method based on classical simulations, CNEO-MD is promising for future investigations of larger and more complex proton transfer systems.