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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.

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagoves̆c̆enskiı̆’s identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility.

We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

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.

This study explores the impact of coupling cumulus and planetary boundary layer (PBL) parameterizations on diurnal precipitation forecasting during the plum rainy season in Jiangsu Province, China, using a double grid‐nesting approach. Results show that coherent coupling of cumulus (only in the 15 km grid outer domain [O]) and PBL parameterizations leads to improved forecasting of diurnal variations in the morning, afternoon, and the evening. Increasing the frequency of the Kain‐Fritsch (KF) cumulus scheme in [O] enhances subgrid precipitation while reducing grid‐scale precipitation, resulting in a more accurate representation of daytime convective activities and a reduction in over‐forecasting of evening valley and early‐morning precipitation. Additionally, coupling a suitable PBL scheme mitigates the overpredicted afternoon peak by facilitating turbulent mixing to penetrate higher altitudes with a thicker layer, thereby reducing instability energy accumulation. A higher KF frequency in [O] retains less low tropospheric moisture, reducing moisture convergence into the 1 km grid inner domain [I] and decreasing overpredicted daytime precipitation in [I]. Various PBL schemes produce distinct vertical distributions of turbulent moisture and heat transport, impacting convection and precipitation in [I] resolved by cloud microphysics processes. The coherent coupling of these parameterizations maintains a balanced supply of convective energy and water vapor, significantly improving diurnal precipitation forecasts in [I]. Isolating these parameterizations between nested grids may undermine this improvement.