Constrained Nuclear-Electronic Orbital QM/MM Approach for Simulating Complex Systems with Quantum Nuclear Delocalization Effects Incorporated

The hybrid quantum mechanics/molecular mechanics (QM/MM) approach, which combines the accuracy of quantum mechanical (QM) methods with the efficiency of molecular mechanics (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 QM/MM methods through the electrostatic embedding scheme and apply the resulting CNEO QM/MM to two hydrogen-bonded complexes in both gas and aqueous phases. 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 low barrier hydrogen bond in human transketolase, CNEO QM/MM accurately predicts nearly equal proton sharing between the two residues, with predicted oxygen-hydrogen distance in excellent agreement with experimental results. With an accurate description of both nuclear quantum effects and environmental effects, CNEO QM/MM is a promising new approach for simulating complex chemical and biological systems.