opt-DDAP: Optimizable Density-Derived Atomic Point Charges via Automatic Differentiation.

Charged Systems in Absolute Binding Free Energy Calculations: An Analytical Electrostatic Approach.

Alchemical free energy perturbation (FEP) is one of the most rigorous methods for predicting protein-ligand binding affinities, yet charged-ligand calculations suffer from finite-size electrostatic artifacts introduced by periodic boundary conditions, which can bias results by several kcal·mol-1. Existing approaches each have limitations: finite-size correction methods rely on approximate dielectric models and Poisson-Boltzmann (PB) calculations, while alchemical co-ion methods introduce alchemically transformed particles, causing spurious interactions and sampling difficulties. Here we present Electrostatic Interaction Decoupling (EID), a postprocessing approach that combines an exact algebraic isolation of the ligand-environment linear electrostatic interaction under the neutral-environment condition with an analytical correction for the residual periodic-boundary offset. By separating the physical ligand-environment interaction from artifact-contaminated terms, EID corrects charge-changing FEP results without PB/continuum-electrostatics calculations or alchemically transformed particles. In benchmarks across four charged protein-ligand systems, EID achieved improved predictive accuracy and more consistent cross-system performance than both comparison methods. Because EID operates as a postprocessing step requiring no additional simulations or PB calculations, it provides a rigorous, immediately deployable solution for charge-changing free energy calculations.

HessFit: Deriving Molecule-Specific Force Fields from Quantum Mechanical Hessians.

Density Functional Theory in Modern Computational Science: Fundamentals, Methodologies, Applications and Emerging Directions

Density functional theory (DFT) has become one of the principal theoretical frameworks for investigating the electronic structure, energetics and properties of atoms, molecules, solids and interfaces. Its importance arises from its favorable balance between computational cost and predictive capability compared with many wavefunction-based electronic-structure methods. Rather than treating the many-electron wavefunction as the primary variable, DFT expresses ground-state properties through the electron density, while the Kohn–Sham formulation provides a practical route for solving the resulting equations. DFT is not a single computational method; its predictive capability depends strongly on the choice of exchange–correlation functional, basis representation, pseudopotential or core treatment, spin treatment, treatment of dispersion and, for correlated systems, possible Hubbard-type corrections. This review presents a concise overview of the theoretical foundations of DFT and the major approximations used in modern calculations. The practical workflow from structural preparation and convergence testing to geometry optimization, electronic-structure calculations and property analysis is discussed. Applications in molecular chemistry, materials discovery, defects, catalysis, photocatalysis and energy-storage materials are highlighted. Current limitations, including delocalization error, band-gap underestimation, strong electron correlation, finite-temperature effects and model-size limitations, are also examined. Finally, the integration of DFT with high-throughput computation, machine learning, multiscale modeling and inverse materials design is discussed. These developments are transforming DFT from an individual calculation technique into a central component of data-driven computational science.

A Gradient-Corrected Polarizable Continuum Model for Improved Reaction Fields at the SCF Level.

We propose an improved model, termed the gradient-corrected PCM (GCPCM), for improving the energy accuracy of the polarizable continuum model (PCM). Our previous study revealed deficiencies of PCM in describing the reaction field, i.e., the electrostatic potential generated by the solvent. These deficiencies can be partially alleviated by introducing an empirical correction to the solvent charges. As a result, solute-solvent interactions are improved at the self-consistent field level, leading to enhanced energy accuracy. The performance of GCPCM was evaluated through single-point calculations and geometry optimizations of phenol and phenolate, calculations of the free energy profile for proton transfer in glycine, and analysis of solvent responses of the HOMO and LUMO orbital energies of Brooker's merocyanine. The results demonstrate that the characteristic destabilization of charged solutes observed in conventional PCM is effectively resolved. Furthermore, despite having a computational cost comparable to that of PCM, GCPCM shows the potential to achieve an energy accuracy similar to that of 3D-RISM-SCF. The development of GCPCM enables more convenient and accurate treatment of solvation effects, which is expected to allow researchers to focus on other important challenges, such as the accurate description of electronic states.

Analytical Forces from the Bethe-Salpeter Equation for Large-Scale Excited-State Relaxation

We present an efficient plane-wave implementation of analytical nuclear forces for electronic excited states described by the Bethe-Salpeter equation (BSE). The formulation combines density-matrix perturbation theory with a Lagrangian approach, and avoids both explicit empty-state summations and the response calculations for each atomic displacement, required by conventional approaches based on density functional perturbation theory. Together with GPU acceleration, these advances make BSE forces calculations tractable for solid-state systems containing hundreds of atoms. We demonstrate the method on two point defects with distinct dielectric environments: the nitrogen-vacancy center in diamond, where BSE and time-dependent density functional theory (TDDFT) yield consistent excited-state relaxations, and the carbon-dimer defect in two-dimensional hexagonal boron nitride, where the screened electron-hole interaction included in the BSE stabilizes the localized defect excitation and corrects the relaxation pattern predicted by semilocal TDDFT. These results establish a scalable framework for BSE-level studies of excited-state relaxation and vibronic coupling in heterogeneous condensed systems.

On calculating polar solvation energy of nonrigid proteins in the Poisson-Boltzmann theory

The generalized PB theory is validated using a perturbed two-atom system and a diverse set of proteins with different structures in vacuum and water, demonstrating its accuracy and robustness, regardless of the choice of sharp-interface and diffuse-interface PB models and different numerical solvers.