Accelerating Quantum Mechanical/Molecular Mechanical (QM/MM) Simulations with Stochastic Iso-Kinetic Nosé–Hoover Multiple Time Step Integrator in CHARMM

The high computational cost of ab initio quantum mechanical/molecular mechanical (ai-QM/MM) simulations has long been a major barrier to their widespread use in large-scale modeling of enzyme mechanisms. To overcome this limitation, we present an accelerated ai-QM/MM simulation method that combines a stochastic iso-kinetic Nosé-Hoover chain (SIN(R)) thermostat with a multiple time step (MTS) integration scheme, implemented in CHARMM. This approach reduces the number of costly ai-QM/MM calculations by applying periodic corrections at the target ai-QM/MM level of theory, while the SIN(R) thermostat minimizes resonance artifacts associated with large outer time steps. Initial tests on the SN2 reaction between CH3Cl and Cl- show that the SIN(R)-based MTS method can stably use outer time steps up to 10 fs with less than 1.0 kcal/mol errors in barrier height. Application to the hydride transfer reaction catalyzed by dihydrofolate reductase (DHFR) further demonstrates the method's applicability to complex enzymatic systems, with stability with outer steps as large as 10 fs achieved by introducing augmented MM bonded terms in the QM region and systematically correcting them during outer step integration. Furthermore, we explored the applicability of this approach for accelerating semiempirical (se) QM/MM methods by simulating the phosphoryl transfer reaction catalyzed by adenylate kinase (AK). Compared to reference simulations without MTS or augmented bonded terms, stable dynamics and accuracy were obtained with an outer time step of 2 fs, which corresponds to a 4-fold speed-up relative to conventional 0.5 fs simulations. Together, these results demonstrate that the SIN(R)-based MTS method can substantially accelerate QM/MM simulations, providing a practical tool for mechanistic studies of enzymatic catalysis.