Accelerating Hybrid Density Functional Theory Molecular Dynamics Simulations by Seminumerical Integration, Resolution-of-the-Identity Approximation, and Graphics Processing Units

Phase Stability and Transitions in High-Entropy Alloys: Insights from Lattice Gas Models, Computational Simulations, and Experimental Validation

High-entropy alloys (HEAs) are a novel class of metallic materials composed of five or more principal elements in near-equimolar ratios. This unconventional composition leads to high configurational entropy, which promotes the formation of solid solution phases with enhanced mechanical properties, thermal stability, and corrosion resistance. Phase stability plays a critical role in determining their structural integrity and performance. This study provides a focused review of HEA phase transitions, emphasizing the role of lattice gas models in predicting phase behavior. By integrating statistical mechanics with thermodynamic principles, lattice gas models enable accurate modeling of atomic interactions, phase segregation, and order-disorder transformations. The combination of computational simulations (e.g., Monte Carlo, molecular dynamics) with experimental validation (e.g., XRD, TEM, APT) improves predictive accuracy. Furthermore, advances in data-driven methodologies facilitate high-throughput exploration of HEA compositions, accelerating the discovery of alloys with optimized phase stability and superior mechanical performance. Beyond structural applications, HEAs demonstrate potential in functional domains, such as catalysis, hydrogen storage, and energy technologies. This review brings together theoretical modeling-particularly lattice gas approaches-and experimental validation to form a unified understanding of phase behavior in high-entropy alloys. By highlighting the mechanisms behind phase transitions and their implications for material performance, this work aims to support the design and optimization of HEAs for real-world applications in aerospace, energy systems, and structural materials engineering.

Projected Wave Function Extrapolation Scheme to Accelerate Plane-Wave Hybrid Functional-Based Born-Oppenheimer Molecular Dynamics Simulations

Born-Oppenheimer molecular dynamics (BOMD) simulations are of great interest for the dynamic properties of molecular and solid systems. However, BOMD simulations necessitate not only an extensive period of dynamical evolution but also costly self-consistent-field (SCF) electronic structure calculations, especially for hybrid functional-based BOMD (H-BOMD) simulations within plane-wave basis sets. Here, we propose an improved always stable predictor-corrector (ASPC) method for the wave function extrapolation to accelerate the plane-wave H-BOMD simulations, named projected ASPC (PASPC), yielding a wave function closer to the actual solution space and efficiently reducing the number of SCF iterations at each MD step. We investigated the convergence properties of different extrapolation schemes for molecular and solid systems. Numerical results demonstrate that plane-wave H-BOMD simulations can be significantly faster than conventional cases by combining the accelerated algorithms with the PASPC method. The energy drift is also evaluated, showing that PASPC produces energy drift with smaller oscillations and can simulate a larger time step for systems containing heavy atoms, demonstrating the accuracy of the extrapolation schemes. Furthermore, H-BOMD simulations showcase more accurate power and infrared spectra of silicon dioxide and liquid water that are comparable to those of experimental measurements.

A Constraint-Based Orbital-Optimized Excited State Method (COOX)

In this work, we present a novel method to directly calculate targeted electronic excited states within a self-consistent field calculation based on constrained density functional theory (cDFT). The constraint is constructed from the static occupied-occupied and virtual-virtual parts of the excited state difference density from (simplified) linear-response time-dependent density functional theory calculations (LR-TDDFT). Our new method shows a stable convergence behavior, provides an accurate excited state density adhering to the Aufbau principle, and can be solved within a restricted SCF for singlet excitations to avoid spin contamination. This also allows the straightforward application of post-SCF electron-correlation methods like MP2 or direct RPA methods. We present the details of our constraint-based orbital-optimized excited state method (COOX) and compare it to similar schemes. The accuracy of excitation energies will be analyzed for a benchmark of systems, while the quality of the resulting excited state densities is investigated by evaluating excited state nuclear forces and excited state structure optimizations. We also investigate the performance of the proposed COOX method for long-range charge transfer excitations and conical intersections with the ground-state.

QM/MM Free Energy Calculations of Long-Range Biological Protonation Dynamics by Adaptive and Focused Sampling

Water-mediated proton transfer reactions are central for catalytic processes in a wide range of biochemical systems, ranging from biological energy conversion to chemical transformations in the metabolism. Yet, the accurate computational treatment of such complex biochemical reactions is highly challenging and requires the application of multiscale methods, in particular hybrid quantum/classical (QM/MM) approaches combined with free energy simulations. Here, we combine the unique exploration power of new advanced sampling methods with density functional theory (DFT)-based QM/MM free energy methods for multiscale simulations of long-range protonation dynamics in biological systems. In this regard, we show that combining multiple walkers/well-tempered metadynamics with an extended system adaptive biasing force method (MWE) provides a powerful approach for exploration of water-mediated proton transfer reactions in complex biochemical systems. We compare and combine the MWE method also with QM/MM umbrella sampling and explore the sampling of the free energy landscape with both geometric (linear combination of proton transfer distances) and physical (center of excess charge) reaction coordinates and show how these affect the convergence of the potential of mean force (PMF) and the activation free energy. We find that the QM/MM-MWE method can efficiently explore both direct and water-mediated proton transfer pathways together with forward and reverse hole transfer mechanisms in the highly complex proton channel of respiratory Complex I, while the QM/MM-US approach shows a systematic convergence of selected long-range proton transfer pathways. In this regard, we show that the PMF along multiple proton transfer pathways is recovered by combining the strengths of both approaches in a QM/MM-MWE/focused US (FUS) scheme and reveals new mechanistic insight into the proton transfer principles of Complex I. Our findings provide a promising basis for the quantitative multiscale simulations of long-range proton transfer reactions in biological systems.

Systematic QM/MM Study for Predicting 31P NMR Chemical Shifts of Adenosine Nucleotides in Solution and Stages of ATP Hydrolysis in a Protein Environment

NMR (nuclear magnetic resonance) spectroscopy allows for important atomistic insights into the structure and dynamics of biological macromolecules; however, reliable assignments of experimental spectra are often difficult. Herein, quantum mechanical/molecular mechanical (QM/MM) calculations can provide crucial support. A major problem for the simulations is that experimental NMR signals are time-averaged over much longer time scales, and since computed chemical shifts are highly sensitive to local changes in the electronic and structural environment, sufficiently large averages over representative structural ensembles are essential. This entails high computational demands for reliable simulations. For NMR measurements in biological systems, a nucleus of major interest is 31P since it is both highly present (e.g., in nucleic acids) and easily observable. The focus of our present study is to develop a robust and computationally cost-efficient framework for simulating 31P NMR chemical shifts of nucleotides. We apply this scheme to study the different stages of the ATP hydrolysis reaction catalyzed by p97. Our methodology is based on MM molecular dynamics (MM-MD) sampling, followed by QM/MM structure optimizations and NMR calculations. Overall, our study is one of the most comprehensive QM-based 31P studies in a protein environment and the first to provide computed NMR chemical shifts for multiple nucleotide states in a protein environment. This study sheds light on a process that is challenging to probe experimentally and aims to bridge the gap between measured and calculated NMR spectroscopic properties.

Exploring Chemical Space Using Ab Initio Hyperreactor Dynamics

In recent years, first-principles exploration of chemical reaction space has provided valuable insights into intricate reaction networks. Here, we introduce ab initio hyperreactor dynamics, which enables rapid screening of the accessible chemical space from a given set of initial molecular species, predicting new synthetic routes that can potentially guide subsequent experimental studies. For this purpose, different hyperdynamics derived bias potentials are applied along with pressure-inducing spherical confinement of the molecular system in ab initio molecular dynamics simulations to efficiently enhance reactivity under mild conditions. To showcase the advantages and flexibility of the hyperreactor approach, we present a systematic study of the method's parameters on a HCN toy model and apply it to a recently introduced experimental model for the prebiotic formation of glycinal and acetamide in interstellar ices, which yields results in line with experimental findings. In addition, we show how the developed framework enables the study of complicated transitions like the first step of a nonenzymatic DNA nucleoside synthesis in an aqueous environment, where the molecular fragmentation problem of earlier nanoreactor approaches is avoided.

Improved Sampling of Adaptive Path Collective Variables by Stabilized Extended-System Dynamics

Because of the complicated multistep nature of many biocatalytic reactions, an a priori definition of reaction coordinates is difficult. Therefore, we apply enhanced sampling algorithms along with adaptive path collective variables (PCVs), which converge to the minimum free energy path (MFEP) during the simulation. We show how PCVs can be combined with the highly efficient well-tempered metadynamics extended-system adaptive biasing force (WTM-eABF) hybrid sampling algorithm, offering dramatically increased sampling efficiency due to its fast adaptation to path updates. For this purpose, we address discontinuities of PCVs that can arise due to path shortcutting or path updates with a novel stabilization algorithm for extended-system methods. In addition, we show how the convergence of simulations can be further accelerated by utilizing the multistate Bennett's acceptance ratio (MBAR) estimator. These methods are applied to the first step of the enzymatic reaction mechanism of pseudouridine synthases, where the ability of path WTM-eABF to efficiently explore intricate molecular transitions is demonstrated.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

Distributed memory, GPU accelerated Fock construction for hybrid, Gaussian basis density functional theory

With the growing reliance of modern supercomputers on accelerator-based architecture such a graphics processing units (GPUs), the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development GPU accelerated, distributed memory algorithms for many modern electronic structure methods, the primary focus of GPU development for Gaussian basis atomic orbital methods has been for shared memory systems with only a handful of examples pursing massive parallelism. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact exchange matrices for hybrid Kohn-Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.

Analytic gradients for local density fitting Hartree-Fock and Kohn-Sham methods

We present analytic gradients for local density fitting Hartree-Fock (HF) and hybrid Kohn-Sham (KS) density functional methods. Due to the non-variational nature of the local fitting algorithm, the method of Lagrange multipliers is used to avoid the solution of the coupled perturbed HF and KS equations. We propose efficient algorithms for the solution of the arising Z-vector equations and the gradient calculation that preserve the third-order scaling and low memory requirement of the original local fitting algorithm. In order to demonstrate the speed and accuracy of our implementation, gradient calculations and geometry optimizations are presented for various molecular systems. Our results show that significant speedups can be achieved compared to conventional density fitting calculations without sacrificing accuracy.