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This paper proves a conditional structural uniqueness theorem for induced weight on robust record sectors within an admissible Hilbert record layer. Its theorem target and additive carrier differ from those of the standard Born-rule routes: additivity is not placed on the full projector lattice, but on disjoint admissible continuation bundles through an extensive bundle valuation, from which the sector-level additive law is inherited under admissible refinement. Accordingly, the result is not a Gleason-type representation theorem in different language, but a distinct uniqueness theorem about induced sector weight inherited from bundle additivity on admissible continuation structure. Under two explicit structural conditions, internal equivalence of admissible binary refinement profiles and sufficient admissible refinement richness, the quadratic assignment is the only non-negative refinement-stable induced weight on robust record sectors. In the main theorem, refinement richness is secured by admissible binary saturation. A supplementary proposition shows that dense admissible saturation already suffices if continuity of the profile function is added. Under normalization, the result

Achieving chemical accuracy for molecular simulations remains a central challenge in computational chemistry. Here, we present an embedded correlated wavefunction transfer learning (ECW-TL) framework for accurately simulating molecular dynamics in the condensed phase. ECW-TL incorporates high-level electron exchange and correlation effects in ECW theory while preserving training and computational efficiency of machine learned interatomic potentials. We demonstrate the framework on Ca2+-CO32- ion pairing in aqueous solution, a key process underlying CO2 mineralization in seawater. As proof of principle, we first show that finetuning a DFT-revPBE-D3(BJ) baseline model with embedded-DFT-SCAN data reproduces the DFT-SCAN free-energy surface within 1 kcal/mol across all solvation states. Extending the framework to embedded MP2 and localized natural-orbital CCSD(T) further refines the free-energy profile, revealing the crucial role of exact electron exchange and correlation in determining ion-pair stability and structure. ECW-TL thus provides a general, data-efficient route for transferring CW accuracy to large-scale simulations of complex aqueous and interfacial chemical processes.

A physically motivated equation that determines the number of electrons of a molecule is proposed based on chemical common sense. It shows that all molecules are entangled in the number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case. Application of wavefunction theory to the principle shows that an individual molecule with a noninteger number of electrons is locally physical albeit locally unreal. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. The continuity of the number of electrons allows the definition of an electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable. The aforementioned physical principle can alternatively be expressed as a simple additivity with the new state function. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing the same chemical potential.

Developing accurate models for chemical reactors is often challenging due to the complexity of reaction kinetics and process dynamics. Traditional approaches require retraining models for each new system, limiting generalizability and efficiency. In this work, we take a step toward foundation models for chemical reactor modeling by introducing a neural network framework that generalizes across diverse reactor types and rapidly adapts to new chemical processes. Our approach leverages meta-learning to pretrain the model on a broad set of reactor dynamics, enabling efficient adaptation to unseen reactions with minimal data. To further enhance generalizability, we incorporate physics-informed fine-tuning, ensuring physically consistent adaptation to new reactor conditions. Our framework is evaluated across three integer-order fundamental reactor types - continuous stirred tank reactors, batch reactors, and plug flow reactors - demonstrating superior few-shot adaptation compared to conventional data-driven, physics-informed, and transfer learning approaches. By combining meta-learning with physics-informed adaptation, this work lays the foundation for a generalizable modeling framework,

In this work, we study an integrated fault detection and classification framework called FARM for fast, accurate, and robust online chemical process monitoring. The FARM framework integrates the latest advancements in statistical process control (SPC) for monitoring nonparametric and heterogeneous data streams with novel data analysis approaches based on Riemannian geometry together in a hierarchical framework for online process monitoring. We conduct a systematic evaluation of the FARM monitoring framework using the Tennessee Eastman Process (TEP) dataset. Results show that FARM performs competitively against state-of-the-art process monitoring algorithms by achieving a good balance among fault detection rate (FDR), fault detection speed (FDS), and false alarm rate (FAR). Specifically, FARM achieved an average FDR of 96.97% while also outperforming benchmark methods in successfully detecting hard-to-detect faults that are previously known, including Faults 3, 9 and 15, with FDRs being 97.08%, 96.30% and 95.99%, respectively. In terms of FAR, our FARM framework allows practitioners to customize their choice of FAR, thereby offering great flexibility. Moreover, we report a significa

Optical detection of magnetic resonance enables spin-based quantum sensing with high spatial resolution and sensitivity-even at room temperature-as exemplified by solid-state defects. Molecular systems provide a complementary, chemically tunable, platform for room-temperature optically detected magnetic resonance (ODMR)-based quantum sensing. A critical parameter governing sensing sensitivity is the optical contrast-i.e., the difference in emission between two spin states. In state-of-the-art solid-state defects such as the nitrogen-vacancy center in diamond, this contrast is approximately 30%. Here, capitalizing on chemical tunability, we show that room-temperature ODMR contrasts of 40% can be achieved in molecules. Using a nitrogen-substituted analogue of pentacene (6,13-diazapentacene), we enhance contrast compared to pentacene and, by determining the triplet kinetics through time-dependent pulsed ODMR, show how this arises from accelerated anisotropic intersystem crossing. Furthermore, we translate high-contrast room-temperature pulsed ODMR to self-assembled nanocrystals. Overall, our findings highlight the synthetic handles available to optically readable molecular spins and t

Record linkage (de-duplication or entity resolution) is the process of merging noisy databases to remove duplicate entities. While record linkage removes duplicate entities from such databases, the downstream task is any inferential, predictive, or post-linkage task on the linked data. One goal of the downstream task is obtaining a larger reference data set, allowing one to perform more accurate statistical analyses. In addition, there is inherent record linkage uncertainty passed to the downstream task. Motivated by the above, we propose a generalized Bayesian record linkage method and consider multiple regression analysis as the downstream task. Records are linked via a random partition model, which allows for a wide class to be considered. In addition, we jointly model the record linkage and downstream task, which allows one to account for the record linkage uncertainty exactly. Moreover, one is able to generate a feedback propagation mechanism of the information from the proposed Bayesian record linkage model into the downstream task. This feedback effect is essential to eliminate potential biases that can jeopardize resulting downstream task. We apply our methodology to multip

We develop a framework for on-the-fly machine learned force field molecular dynamics simulations based on the multipole featurization scheme that overcomes the bottleneck with the number of chemical elements. Considering bulk systems with up to 6 elements, we demonstrate that the number of density functional theory calls remains approximately independent of the number of chemical elements, in contrast to the increase in the smooth overlap of atomic positions scheme.

Diffusion models revolutionize image generation by leveraging natural language to guide the creation of multimedia content. Despite significant advancements in such generative models, challenges persist in depicting detailed human-object interactions, especially regarding pose and object placement accuracy. We introduce a training-free method named Reasoning and Correcting Diffusion (ReCorD) to address these challenges. Our model couples Latent Diffusion Models with Visual Language Models to refine the generation process, ensuring precise depictions of HOIs. We propose an interaction-aware reasoning module to improve the interpretation of the interaction, along with an interaction correcting module to refine the output image for more precise HOI generation delicately. Through a meticulous process of pose selection and object positioning, ReCorD achieves superior fidelity in generated images while efficiently reducing computational requirements. We conduct comprehensive experiments on three benchmarks to demonstrate the significant progress in solving text-to-image generation tasks, showcasing ReCorD's ability to render complex interactions accurately by outperforming existing metho

[Abridged] This review paper discussed which chemical effects may be at play in a planet-forming disk midplane, which effects are relevant under different conditions, and which tools are available for modelling chemical kinetics in a disk midplane. The review goes on to discuss some important efforts in the planet formation modelling community to treat chemical evolution, and, vice versa, efforts in the chemical modelling community to implement more physical effects related to planet formation into the chemical modelling. The aim of this review is both to outline some concepts related to planet formation chemistry, but also to encourage, not just collaboration between the planet formation modelling community and the astrochemical community, but also assistance and guidance from one community to the other. Guidance, regarding which effects, out of many, might be more relevant than others under certain planet formation conditions, and regarding why certain included effects lead to certain important modelling outcomes. As the research fields of exoplanet atmospheres and protoplanetary disks near new frontiers in observational insights with upcoming facilities, developing appropriate m

Introduction 1 1.0 Importance of sediments to aquatic trace element chemistry 1.1 Monitoring studies 1.2 Suspended versus bed sediments -utility for various types of studies 1.3 Partitioning of trace elements between dissolved and solid phases 1.4 Fluvial transport of trace elements by suspended sediments 1.5 Comparison of trace element concentrations in suspended and bottom sediments versus dissolved levels 1.6 Effect of suspended sediment concentration on fluvial transport of trace elements 1.7 Historical trace element levels 2.0 Physical and chemical factors affecting sediment-trace element chemistry 2.1 Introduction 2.2 Physical factors 2.2.1 Grain-size ranges and the effect of grain size 2.2.2 Chemical analysis of various grain sizes in bottom sediments 2.2.3 Chemical analysis of various grain sizes in suspended sediments 2.2.4 Effect of grain size on trace element concentrations in samples collected from the same and different basins 2.2.5 Comparison of samples having similar bulk chemistries but differing grain-size distributions 2.2.6 Effect of grain size on sediment-associated chemical transport at differing discharge rates 2.2.7 Measuring grain-size distributions 2.2.7.1 Differences in grain size distributions induced by using different techniques 2.2.7.2 Differences in grain size distributions induced by sample pretreatment 28 2.2.8 Effect of sediment surface area 2.2.9 Importance of surface area to sediment-trace element concentrations 2.2.10 Measuring surface area 2.3 Chemical factors 2.3.1 Cation exchange capacity 2.3.2 Composition significant sedimentary trace element collectors 2.3.2.1 Iron and manganese oxides 2.3.2.2 Organic matter 2.3.2.3 Clay minerals 2.3.3 Introduction to and utility of chemical partitioning 2.3.4 Chemical partitioning methods 2.3.4.1 Chemical partitioning -instrumental methods 2.3.4.2 Chemical partitioning ~ partial extraction methods 2.3.4.2.1 Chemical partitioning of suspended sediments by partial extraction 2.3.4.2.2 Chemical partitioning of bottom sediments by partial extraction IV 2.3.4.3 Chemical partitioning by density gradient and mineralogy 2.3.4.4 Chemical partitioning using statistical manipulation of data 2.3.4.5 Chemical partitioning using mathematical modelling 2.4 The interrelation and relative importance of selected physical and chemical factors affecting sediment-trace element chemistry 2.4.1 Relative importance of physical and chemical factors to sediment-trace element chemistry 2.4.1.1 The interrelation of grain size and surface area to each other and to sediment-trace element chemistry 2.4.1.2 The interrelation of grain size and geochemical substrate to each other and to sediment-trace element chemistry 2.4.1.3 The interrelation of surface area and geochemical substrate to each other and to sediment-trace element chemistry 2.4.2 The interrelation of grain size, surface area, and geochemical substrate to each other 2.4.3 Predicting sediment-trace element concentrations using physical and chemical factors 3.0 Sediment-trace element data manipulations 3.1 Introduction 3.2 Limitations of analytical data 3.3 Corrections for grain size differences 3.4 Carbonate corrections 3.5 Normalization to 'conservative' elements 3.6 Effects of applying corrections to sediment-trace element data 4.0 Sampling sediments 4.1 Sampling sediments general considerations 4.2 Bottom sediments 4.2.1 Sampling surficial bed sediment 4.2.2 Sampling bed sediments at depth 4.3 Suspended sediments 4.3.1 Sampling suspended sediment in fluvial environments 4.3.2 Cross-sectional spatial and temporal variations in suspended sediment and associated trace elements and their causes 4.3.2.1 Differences due to sampler type or sampling design 4.3.2.2 Horizontal variations 108 4.3.2.3 Vertical variations 4.3.2.4 Importance of silt/clay-versus sand-sized suspended sediment for trace element transport 4.3.2.5 Suspended sediment and associated trace element temporal variations during constant discharge 4.3.3.6 Suspended sediment and associated trace element temporal variations during changes in discharge 5.0 Summary and general considerations 118 Selected references Index 135

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration iteration, but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along th

Large Language Models (LLMs) have substantially driven scientific progress in various domains, and many papers have demonstrated their ability to tackle complex problems with creative solutions. Our paper introduces a new foundation model, nach0, capable of solving various chemical and biological tasks: biomedical question answering, named entity recognition, molecular generation, molecular synthesis, attributes prediction, and others. nach0 is a multi-domain and multi-task encoder-decoder LLM pre-trained on unlabeled text from scientific literature, patents, and molecule strings to incorporate a range of chemical and linguistic knowledge. We employed instruction tuning, where specific task-related instructions are utilized to fine-tune nach0 for the final set of tasks. To train nach0 effectively, we leverage the NeMo framework, enabling efficient parallel optimization of both base and large model versions. Extensive experiments demonstrate that our model outperforms state-of-the-art baselines on single-domain and cross-domain tasks. Furthermore, it can generate high-quality outputs in molecular and textual formats, showcasing its effectiveness in multi-domain setups.

Chemical reaction prediction, involving forward synthesis and retrosynthesis prediction, is a fundamental problem in organic synthesis. A popular computational paradigm formulates synthesis prediction as a sequence-to-sequence translation problem, where the typical SMILES is adopted for molecule representations. However, the general-purpose SMILES neglects the characteristics of chemical reactions, where the molecular graph topology is largely unaltered from reactants to products, resulting in the suboptimal performance of SMILES if straightforwardly applied. In this article, we propose the root-aligned SMILES (R-SMILES), which specifies a tightly aligned one-to-one mapping between the product and the reactant SMILES for more efficient synthesis prediction. Due to the strict one-to-one mapping and reduced edit distance, the computational model is largely relieved from learning the complex syntax and dedicated to learning the chemical knowledge for reactions. We compare the proposed R-SMILES with various state-of-the-art baselines and show that it significantly outperforms them all, demonstrating the superiority of the proposed method.

Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries. This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids. The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li$_x$FePO$_4$.

Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the CME, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the mo

We developed a multiscale approach (MultiSCAAL) that integrates the potential of mean force (PMF) obtained from all-atomistic molecular dynamics simulations with a knowledge-based energy function for coarse-grained molecular simulations in better exploring the energy landscape of a small protein under chemical interference such as chemical denaturation. An excessive amount of water molecules in all-atomistic molecular dynamics simulations often negatively impacts the sampling efficiency of some advanced sampling techniques such as the replica exchange method and it makes the investigation of chemical interferences on protein dynamics difficult. Thus, there is a need to develop an effective strategy that focuses on sampling structural changes in protein conformations rather than solvent molecule fluctuations. In this work, we address this issue by devising a multiscale simulation scheme (MultiSCAAL) that bridges the gap between all-atomistic molecular dynamics simulation and coarse-grained molecular simulation. The two key features of this scheme are the Boltzmann inversion and a protein atomistic reconstruction method we previously developed (SCAAL). Using MultiSCAAL, we were able

The origin of a chemical reaction between two reactant atoms is associated to the activation energy, with the assumption that, high-energy collisions between these atoms, are the ones that overcome the activation energy. Here, we (i) show that a stronger attractive van der Waals (vdW) and electron-ion Coulomb interactions between two polarized atoms are responsible to initiate a chemical reaction, either before or after the collision. We derive this stronger vdW attraction formula exactly using the quasi one-dimensional Drude model within the ionization energy theory and the energy-level spacing renormalization group method. Along the way, we (ii) expose the precise physical mechanism responsible for the existence of a stronger vdW interaction for both long and short distances, and also show how to technically avoid the electron-electron Coulomb repulsion between polarized electrons from these two reactant atoms. Finally, we properly and correctly associate the existence of this stronger attraction to Ramachandran's 'normal limits' (distance shorter than what is allowed by the standard vdW bond) between chemically nonbonded atoms.

Macroscopic entropy production $σ^{(tot)}$ in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: $σ^{(tot)}=σ^{(fd)}+σ^{(hk)}$; $σ^{(fd)}=-\rd A/\rd t$, where $A$ is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation $\rd A/\rd t=-σ^{(tot)}+σ^{(hk)}$, which is on a par with celebrated entropy balance equation $\rd S/\rd t=σ^{(tot)}+η^{(ex)}$ where $η^{(ex)}$ is the rate of entropy exchange with the environment.For kinetic systems with complex balance, $σ^{(fd)}$ and $σ^{(hk)}$ are the macroscopic limits of stochastic free energy dissipation and house-keeping heat, which are both nonnegative, in the Delbrück-Gillespie description of the stochastic chemical kinetics.Therefore, we show that a full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.