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At least 55 records · Page 3

Improving Computational Efficiency of Mechanical Finite Element Method Simulations for PV Modules: Preprint

In this work we have elucidated the trade off between structural mechanics FEM model accuracy and computation time by employing lower fidelity viscoelastic models. Results indicate that computation time can easily be cut in half while only expecting a potential maximum error of 10 % by considering lower fidelity models. A novel approach to produce the Prony Series fit for viscoelastic characterization has also been presented. Employing this approach, we were able to achieve a further 10 % reduction in computation time without further sacrificing simulation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Macroscale properties and atomic-scale mechanisms of ash removal in low-temperature hydrothermal carbonization

Biogenic ash is a significant impediment to the utilization of agricultural residues in biofuel production. Such challenge can be addressed by various treatments, as demonstrated in this study on the experimental and computational mechanisms involved in the hydrothermal treatment (HT) of wheat straw. A combination of classical (all-atom) molecular dynamics simulations of cellulose carrying silica and calcium species, along with first principles quantum chemical calculations, indicates the dissociation of inorganics from the cellulose with increased HT temperature. Here, this observation is confirmed by experimental evidence of effective ash removal by HT, showing at least 50% removal of sulfur, chlorine, potassium, and calcium, and 12.5% of silica, leading to a reduced total ash content (from 6.7% to 4.2%).Changes in structural features upon HT, such as surface cellular structure and porosity, were revealed, accompanied by an increased specific surface area (from 1.17 to 6.34 m 2 /g). Our simulations suggest that silica binds tightly to the hydrophobic face of cellulose at room temperature, but HT significantly reduces the binding free energy of association with both hydrophobic and hydrophilic surfaces. Most significantly, ash removal leads to an increased calorific value, rising from approximately 16 MJ/kg to about 19 MJ/kg, along with improved thermal behavior. The improved integration combustion index parameter S indicates that the combustion properties improve with ash removal efficiency. The proposed atomic-level mechanism for the observed removal of inorganics during mild HT underscores the potential of such treatment in producing energy-dense wheat straw, a widely available agricultural residue.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

PAGOSA Theory Manual

PAGOSA is a computational fluid dynamics program developed at LANL for the study of high-speed compressible flow and high-rate material deformation. PAGOSA is a three-dimensional Eulerian finite-difference code, solving problems with a wide variety of EOS, material strength, and explosive modeling options. This document presents the finite difference equations that are used in the PAGOSA continuum mechanics computer code. This program is especially intended to be used for the numerical simulation of the interactions of gases, fluids, and solids.

36 MATERIALS SCIENCE↗

MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data—we can combine noisy, non-nested evaluations of the information sources. Finally, numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.

97 MATHEMATICS AND COMPUTING↗

Digital image correlation and infrared thermography data for seven unique geometries of 304L stainless steel

Material Testing 2.0 (MT2.0) is a paradigm that advocates for the use of rich, full-field data, such as from digital image correlation and infrared thermography, for material identification. By employing heterogeneous, multi-axial data in conjunction with sophisticated inverse calibration techniques such as finite element model updating and the virtual fields method, MT2.0 aims to reduce the number of specimens needed for material identification and to increase confidence in the calibration results. To support continued development, improvement, and validation of such inverse methods—specifically for rate-dependent, temperature-dependent, and anisotropic metal plasticity models—we provide here a thorough experimental data set for 304L stainless steel sheet metal. The data set includes full-field displacement, strain, and temperature data for seven unique specimen geometries tested at different strain rates and in different material orientations. Commensurate extensometer strain data from tensile dog bones is provided as well for comparison. We believe this complete data set will be a valuable contribution to the experimental and computational mechanics communities, supporting continued advances in material identification methods.

36 MATERIALS SCIENCE↗

Comprehensive uncertainty quantification (UQ) for full engineering models by solving probability density function (PDF) equation

This report details a new method for propagating parameter uncertainty (forward uncertainty quantification) in partial differential equations (PDE) based computational mechanics applications. The method provides full-field quantities of interest by solving for the joint probability density function (PDF) equations which are implied by the PDEs with uncertain parameters. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known apriori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the driving (dynamics) term of the PDEs based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the dynamics term of the governing PDEs. The efficacy of the method is demonstrated by applying it to two target problems: solid mechanics explicit dynamics with uncertain material model parameters, and reacting hypersonic fluid mechanics with uncertain chemical kinetic rate parameters. A minimally invasive implementation of the method for representative codes SPARC (reacting hypersonics) and NimbleSM (finite- element solid mechanics) and associated software details are described. For solid mechanics demonstration problems the method shows order of magnitudes improvement in accuracy over traditional stochastic collocation. For the reacting hypersonics problem, the method is implemented as a streamline integration and results show very good accuracy for the approximate sample solutions of re-entry flow past the Apollo capsule geometry at Mach 30.

42 ENGINEERING↗

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗

Binary operations on neuromorphic hardware with application to linear algebraic operations and stochastic equations

Abstract Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.

97 MATHEMATICS AND COMPUTING↗

SimELIT: A Novel GUI-Based Comprehensive Ion Trajectory Simulation Software for Mass Spectrometry

Ion trajectory simulation in mass spectrometry systems from injection to detection is technically challenging but very important for better understanding the ion dynamics in instrument development. Here, in this work, we present SimELIT (Simulator of Eulerian and Lagrangian Ion Trajectories), a novel ion trajectory simulation platform. SimELIT is built upon a suite of multiphysics solvers compiled into OpenFOAM (an open-source numerical solver library particularly used for computational mechanics), with a simple web-based graphical user interface (GUI) allowing users to define the details of OpenFOAM cases and run simulations. SimELIT is a modular program and can provide extensions of physics (e.g., gas flows, electrodynamic fields) and thus enable ion trajectory simulations from the ion source to detector. The current version (SimELIT) provides two numerical solvers for ion trajectory simulations–(1) a Lagrangian particle tracker in vacuum and (2) a Eulerian ion density solver in background gas in the presence of electric fields. Here, we describe the architecture of SimELIT, including its use of Docker and the React Framework, and demonstrate the computation of ion trajectories of multiple m/z values in a static/linear voltage drop in vacuum (across a 1 m long flight tube). Further, the drift motion of ions under 1 Torr pressure conditions in a static background (N 2 ) gas through a 20 V/cm static electric field is shown. The results produced from SimELIT were compared with SIMION and theoretical estimates. In addition, we report the computation of ion trajectories in electrodynamic fields within a planar FAIMS device operating at atmospheric pressure.

97 MATHEMATICS AND COMPUTING↗

Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics

Abstract Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data are sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multiphysics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multiphysics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.

Computer Science↗

The Intraplate Stress Field of West Africa

West Africa continues to host a growing number of low and intermediate-magnitude earthquakes (M2-5) along its passive margins, and its continental interior. Earthquake activity in these regions raises the need to comprehend the causes and the tectonic controls of the seismicity. Unfortunately, such studies are rare. Here, we apply single-station inversion techniques to constrain fourteen focal mechanisms, computed after compiling a set of high-quality waveforms. We describe the connection between seismicity, the contemporary stress field, anthropogenic activity and Holocene fault scarps in the region. Our results indicate transpressive stresses acting on the inherited brittle structures in the passive margins. We also observe a compressive regime in the intracontinental failed rifts. We attribute the seismicity to the reactivation of “weak” faults in the Neoproterozoic and Mesozoic failed rifts, the passive transform structures, and the intracratonic Precambrian brittle shear zones.

58 GEOSCIENCES↗

A simple levelset contact algorithm for large overlap removal and robust preloads

A simple approach to simulate contact between deformable objects is presented which relies on levelset descriptions of the Lagrangian geometry and an optimization-based solver. Modeling contact between objects remains a significant challenge for computational mechanics simulations. Common approaches are either plagued by lack of robustness or are exceedingly complex and require a significant number of heuristics. In contrast, the levelset contact approach presented herein is essentially heuristic free. Furthermore, the presented algorithm enables resolving and enforcing contact between objects with a significant amount of initial overlap. Examples demonstrating the feasibility of this approach are shown, including the standard Hertz contact problem, the robust removal of overlap between two overlapping blocks, and overlap-removal and pre-load for a bolted configuration.

42 ENGINEERING↗

Charting C–C coupling pathways in electrochemical CO 2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO 2 reduction reaction (CO 2 RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C 2+ ) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO 2 RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C–C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C–C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH–CHO, *COH–*COH, and *OCH–*OCH. The most kinetically favorable path forms *COH–CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C–C coupling paths produce only *COH–*COH and *CO–*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C 2+ product formation via CO 2 RR electrocatalysts.

30 DIRECT ENERGY CONVERSION↗

Probing phonon focusing, thermomechanical behavior, and moiré patterns in van der Waals architectures using surface acoustic waves

Surface acoustic waves (SAWs) propagate along solid-air, solid-liquid, and solid-solid interfaces. Their characteristics depend on the elastic properties of the solid. Combining transmission electron microscopy (TEM) experiments with molecular dynamics (MD) simulations, we probe atomic environments around intrinsic defects that generate SAWs in vertically stacked two-dimensional (2D) bilayers of MoS 2 . Our joint experimental-simulation study provides insights into SAW-induced structural and dynamical changes and thermomechanical responses of MoS 2 bilayers. Using MD simulations, we compute mechanical properties from the SAW velocity and thermal conductivity from thermal diffusion of SAWs. The results for Young’s modulus and thermal conductivity of an MoS 2 monolayer are in good agreement with experiments. The presence of defects, such as nanopores which generate SAWs, reduces the thermal conductivity of 2D-MoS 2 by an order of magnitude. We also observe dramatic changes in moiré patterns, phonon focusing, and cuspidal structures on 2D-MoS 2 layers.

36 MATERIALS SCIENCE↗

Development of Digital Twin Predictive Model for PWR Components: Updates on Multi Times Series Temperature Prediction Using Recurrent Neural Network, DMW Fatigue Tests, System Level Thermal-Mechanical-Stress Analysis

The long-term operation (LTO) of nuclear power plant (NPP) beyond their original design life of 40 years, can lead to more material damage associated with cyclic fatigue under thermal-mechanical loading cycles and associated long-term exposure of reactor material to the deleterious reactor-coolant environments. However, under this LTO condition the reactor components can still safely operate but may require more frequent Nondestructive Evaluation (NDE) of reactor components. Frequent NDE requirement may lead to frequent shutdown of the NPP. This in turn can lead to power outage and additional NDE-inspection-cost related economic loss. The economic loss can be minimized by reducing uncertainty in life estimation of safety-critical pressure boundary components and by implementing more digital approach such as by using upcoming digital-twin (DT) technology for predicting the structural states (e.g., time and location dependent inside/outside thickness temperature, stress, strain, plastic deformation, etc.) and associated fatigue life of a component in real time. Towards this goal Argonne National Laboratory (ANL) with the sponsorship of DOE Light Water Reactor Sustainability (LWRS) program is working on the development of a DT framework that can be used for real time environmental fatigue prediction of reactor components. The DT framework is based on limited experiment-data, Artificial-intelligence (AI) – Machine-Learning (ML) - Deep-Learning (DL) based techniques and Multiphysics-computational-mechanics such as finite element (FE) based modeling tools. Towards this overall goal, following are some of the major contributions made during the FY21: 1) Multiple 82/182 dissimilar metal weld (DMW) specimens (both solid-weld and joint-weld representing the actual reactor multi-metal nozzles) were fatigue tested. The resulting fatigue lives were compared to the NUREG-6909 based best-fit and design fatigue curves. Additionally, the results of 52/152 DMW fatigue specimens (which were recently tested at Republic of Korea under the sponsorship of International Nuclear Energy Research Initiative - INERI program) were compared to the NUREG-6909 based best-fit and design fatigue curves. From the comparison of 82/182 and 52/152 DMW test data with NUREG-6909 best-fit curve, most of the reported test data fall way away from the NUREG-6909 suggested best-fit or mean curve. The NUREG-6909 suggested best-fit curve is the best-fit curve of austenitic stainless steel and due to lack of enough data on Nickel-based welds, this is currently being used for predicting the life of Nickel-alloy-based welded components. However, the above observation may require higher scaling factor (e.g., ASME suggested factor of 20 on cycles rather than the current NUREG-6909 suggested factor of 12 on cycles) for scaling the austenitic-stainless-steel best-fit-curve for estimating the design or safe-life of a welded component. Accordingly, for example, if a DMW component experience a strain amplitude of 0.6% the PWR-water life of the component would be 52 cycles instead of 85 cycles. However, more DMW tests are required to further ascertain the above-mentioned observations. 2) A system level CAD and finite element model were developed which consists of reactor pressure vessel (RPV), part of steam generator (SG), part of pressurizer (PRZ), hot leg (HL), and surge line (SL). This is with detailed nozzle geometry and thermal-mechanical material properties of different metals to simulate realistic thermal-mechanical stress under connected system global thermal-mechanical boundary conditions. 3) Different system level heat transfer analyses were performed with estimation of relevant heat transfer coefficients. The resulting data were used in subsequent system level thermal-mechanical stress analysis and for generating spatial-temporal training and validation data for a system level digital-twin based temperature predictor. Transient heat transfer analyses were performed considering thermal boundary condition under design-basis (DB) loading and EDF (Électricité de France) data-based grid-load-following (EDF-GLF) loading cycles. 4) System level thermal-mechanical stress analysis was performed for identifying damage-prone hotspots and for future extension of the model for cyclic state prediction. From the system-level model simulation under DB loading cycle it is found that HL and the SL nozzle that connect to the HL can experience significant stress and strain and could be one of the weakest links in the overall reactor coolant system (RCS). 5) An AI/ML based DT model was developed for multi-time-series temperature prediction at any inside/outside thickness locations of PWR pressure boundary components. This is by using Recurrent-neural-network (RNN) and keras machine learning libraries. The RNN model was validated against two laboratory test-based data sets with one obtained through ANL’s in-air fatigue test system and other through PWR-water test loop. The experimentally validated DT model further validated against FE model results to predict thermal scarification related spatialtemporal temperatures at random locations of a component. The well validated DT model was then used for demonstrating spatial-temporal temperature prediction under 100+ years of reactor operation subjected to combined DB, EDF-GLF and randomized grid-load-following (RANDOMGLF) loading Cycles. The expert-elicitation DT model framework was developed assuming field/input/process measurements can be available from a few existing plant sensors and can readily be used by the NPP operators. The above temperature prediction model will feed to the next-step stress analysis model based on which the life of a component can be predicted in realtime, which is one of our future works.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗

Algorithm advances and applications of time‐dependent first‐principles simulations for ultrafast dynamics

Abstract Far from equilibrium phenomenon is a central theme of contemporary material research. Such phenomenon can exhibit itself in atomic structure and dynamics, but very often it also happens as non‐equilibrium phenomenon in the electronic structure. In ab initio material simulation, density functional theory (DFT) has played an essential role in studying electronic ground state problems. For excited states, besides many‐body perturbation theory, another powerful tool is the time dependent DFT (TDDFT) method. In particular, the real‐time TDDFT (rt‐TDDFT) method can be used to simulate many non‐equilibrium phenomena directly. Here we introduce our works on some algorithm advances based on our recently rt‐TDDFT method. This method uses the plane‐wave basis set, and significantly accelerates its efficiency by increasing the time step from 0.1–1 as in traditional methods to 0.2–0.5 fs. The noncollinear magnetic moments and spin–orbit coupling have also been included in our rt‐TDDFT method. Furthermore, a Boltzmann‐TDDFT algorithm has been developed to solve the hot carrier overheating problem in Ehrenfest dynamics, and a natural orbital branching algorithm has been developed to overcome the mean‐field approximation in Ehrenfest dynamics nuclear trajectory, thus allows stochastic multiple paths in chemical reactions. Utilizing these methods, we have studied the photoinduced ultrafast demagnetization, ultrafast phase transition, energy transfer between plasmon and hot carriers, as well as the high‐energy ion implantation and low‐energy atomic diffusion in semiconductors. We believe the tools as the ones introduced here can enable us to study a wide range of phenomena which are of great interest in modern day material research. This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Liu, Wen‐Hao↗

Chemical transformations and transport phenomena at interfaces

Abstract Interfaces, the boundary that separates two or more chemical compositions and/or phases of matter, alters basic chemical and physical properties including the thermodynamics of selectivity, transition states, and pathways of chemical reactions, nucleation events and phase growth, and kinetic barriers and mechanisms for mass transport and heat transport. While progress has been made in advancing more interface‐sensitive experimental approaches, their interpretation requires new theoretical methods and models that in turn can further elaborate on the microscopic physics that make interfacial chemistry so unique compared to the bulk phase. In this review, we describe some of the most recent theoretical efforts in modeling interfaces, and what has been learned about the transport and chemical transformations that occur at the air–liquid and solid–liquid interfaces. This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Structure and Mechanism > Computational Materials Science Software > Quantum Chemistry Software > Simulation Methods

Hao, Hongxia↗