Method For Structure Calculations Research Articles

Efficient Shift-and-Invert Preconditioning for Multi-GPU Accelerated Density Functional Calculations.

To accelerate the iterative diagonalization of electronic structure calculations, we propose a new inexact shift-and-invert (ISI) preconditioning method. The key idea is to improve shift values in the ISI preconditioning to be closer to the exact eigenvalues, leading to a significant boost in the convergence speed of the iterative diagonalization. Furthermore, we adopted a preconditioned conjugate gradient solver to rapidly evaluate an inversion process. Finally, we accelerated overall processes, including the proposed modification, with state-of-the-art graphical processing units (GPUs) and assessed its parallel efficiency with real-space density functional calculations of 1D, 2D, and 3D periodic systems. Our method attains both fast diagonalization convergence and high multi-GPU parallel efficiency. This is evident from the fact that single-point density functional calculations for hundreds of atom systems can be done in approximately 10 s using 8 GPUs. The proposed method can be generally applied to any electronic structure calculation methods involving large-scale diagonalizations.

Devising a calculation method for modern structures of current-conducting elements in large electric machines in a three-dimensional statement

The jumpers of rotor pole-to-pole connections are highly stressed elements in a hydraulic generator structure. These assemblies often fail due to deformation that exceeds the size of an air gap. Existing methods do not take into account the thermal component and attempts to improve the design are not based on mathematical models that make it possible to perform calculations with an accuracy of more than 50 %. The method devised in this work makes it possible to obtain boundary conditions of the third kind on the basis of three-dimensional mathematical modeling of the ventilation system of the hydraulic unit without simplifications. The method accuracy is explained by taking into account the spatial thermal component. The heat transfer coefficient determined by this method in the pole-to-pole connections area was ~250 W/(m2·K). Using FEM, mathematical modeling of the thermal stress state of pole-to-pole connections was carried out, taking into account mechanical and thermal factors. This made it possible to design the improved connection structure with additional fastening elements, which make it possible to reduce the displacement to 0.03 mm, and the stress to 53 MPa at the rotor rotation frequency of 880 rpm. This design makes it possible to enable reliable operation of the hydraulic unit under the condition of increasing the rotor rotation frequency to overspeed with disconnected combinatorial dependence, provided that the actual stresses are 0.95 % of the material yield strength. The convergence of the values obtained by the proposed method and by the HSS method exceeded 99 %. The practical result is the proposals for the hydraulic generator design modernization

Runtime performance of a GAMESS quantum chemistry application offloaded to GPUs

SummaryComputational chemistry is at the forefront of solving urgent societal problems, such as polymer upcycling and carbon capture. The complexity of modeling these processes at appropriate length and time scales is mainly manifested in the number and types of chemical species involved in the reactions and may require models of several thousand atoms and large basis sets to accurately capture the chemical complexity and heterogeneity in the physical and chemical processes. The quantum chemistry package General Atomic and Molecular Electronic Structure System (GAMESS) has a wide array of methods that can efficiently and accurately treat complex chemical systems. In this work, we have used the GAMESS Effective Fragment Molecule Orbital (EFMO) method for electronic structure calculation of a challenging mesoporous silica nanoparticle (MSN) model surrounded by about 4700 water molecules to investigate the strong scaling and GPU offloading on hybrid CPU‐GPU nodes. Experiments were performed on the Perlmutter platform at the National Energy Research Scientific Computing Center. Good strong scaling and load balancing have been observed on up to 88 hybrid nodes for different settings of the execution parameters for the calculation considered here. When GPUs are oversubscribed by offloading work from multiple CPU processes, using the NVIDIA multi‐process service (MPS) has consistently reduced time to solution and energy consumed. Additionally, for some configuration parameter settings, oversubscription with MPS improved performance by up to 5.8% over the case without oversubscription.

Research on simulation calculation method of local strength of swath ship stabilizing fins based on sub-model method

Abstract At present, there is little research on the strength simulation calculation method of local steel structure at the joint between the fin stabilizer and hull of SWATH at home and abroad. Aiming at the problems of high-stress levels and difficult local strength of the local structure at the joint of SWATH submersible and stable fin, this paper, based on APDL language, takes a SWATH ship as an example, establishes a whole ship simulation model, analyses and studies the modeling scope, modeling requirements, boundary conditions, and loading methods of the local calculation model of stable fin, and puts forward an efficient simulation calculation and analysis method, namely sub-model method, which is suitable for the local strength calculation of stable fin, and provides guidance for the structural design method of the stable fin of SWATH catamaran.

COMPARATIVE ANALYSIS OF CALCULATION METHODS OF CLT STRUCTURES

One of the important tasks of modern construction is the search for new constructive solutions and the introduction of new construction technologies. Cross-Laminated Timber (CLT) technology is a new material for Ukraine that has proven itself in Europe and America as effective and environmentally friendly with many advantages. Since CLT panels are not widely distributed, studied and do not contain references in the normative literature in Ukraine, the study of these structures is extremely relevant. This paper presents a comparative analysis of the CLT calculation methods of panels: using the RFEM 6 and LIRA-FEM software and analytical calculation. The research concerns three types of panels: three-layer, five-layer, and seven-layer under the action of a load of 1.5 and 5.0 kN/m2. The main parameter under consideration is the vertical deflection of the panels. The results of all calculations are collected in one table, where you can analyze the discrepancy between different methods of calculating the CLT structures.

Excitonic Configuration Interaction: Going Beyond the Frenkel Exciton Model.

We present the excitonic configuration interaction (ECI) method─a fragment-based analogue of the CI method for electronic structure calculations of multichromophoric systems. It can also be viewed as a generalization of the exciton approach, with the following properties: (i) It constructs the effective Hamiltonian exclusively from monomer calculations. (ii) It employs the strong orthogonality assumption and is exact within McWeeny's group function theory, thus requiring only one-electron density matrices of the monomer states. (iii) It is agnostic of the monomer electronic structure method, allowing us to use/combine different methods. (iv) It includes an embedding point charge scheme (called excitonic Hartree-Fock, EHF) to improve the accuracy of the monomer states, but such that the effective full-system Hamiltonian is not explicitly dependent on the embedding. (v) It is systematically improvable, by expanding the set of monomer states and by including configurations where two or more monomers are excited (defining the ECIS, ECISD, etc., methods). The performance of ECI is assessed by computing the absorption spectrum of two exemplary multichromophoric systems, using CIS as the monomer electronic structure method. The accuracy of ECI significantly depends on the chosen embedding charges and the ECI expansion. The most accurate assessed combinations─ECIS or ECISD with EHF embedding─yield spectra that agree qualitatively and quantitatively with full-system direct calculations, with deviations of the excitation energies below 0.1 eV. We also show that ECISD based on CIS monomer calculations can predict states where two monomers are excited simultaneously (e.g., triplet-triplet double-local excitations) that are inaccessible in a full-system CIS calculation.

Random Green’s Function Method for Large-Scale Electronic Structure Calculation

We report a linear-scaling random Green’s function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H2O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H2O clusters at T = 0 K can reach an error of ∼ 1 meV per H2O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.

An efficient and unified method for band structure calculations of 2D anisotropic photonic-crystal fibers

An efficient and unified method for band structure calculations of 2D anisotropic photonic-crystal fibers

Depicted simulation model for removal of second-generation antipsychotic drugs adsorbed on Zn-MOF: adsorption locator assessment.

Electronic durable behavior on the material surface was accompanied by a class of antipsychotic drugs (APD) to describe the surface modification in the designed adsorption model. Hierarchically Zn-MOF system was utilized for estimating its capacity for drug molecule removal. Geometrically optimized strategy on the studied systems was performed using DFT/GGA/PBE. FMOs analysis was depicted based on the same level of calculations, and molecular electrostatic potential surface (MEP) was generated for unadsorbed and adsorbed systems to illustrate the variation in the surface-active sites. By interpreting the electronic density of states (DOS), the atomic orbital can be identified as a major or minor electronic distribution by PDOS graph. Adsorption locating behavior was considered to detect the significant surface interaction mode between APD and Zn-MOF surface based on lower adsorption energy. The stability of the adsorbed model was best described through dynamic simulation analysis with time through elevated temperatures. The non-covalent interactions were described using RDG/NCI analysis to show the major favorable surface interaction predicting the highly stable adsorption system. The most accurate geometrical computations were performed using the materials studio software followed by surface cleavage and vacuum slab generation. The first principle of DFT was used to apply CASTEP module with GGA/PBE method for band structure and DOS calculations. Three systems of antipsychotic drugs were computationally studied using CASTEP simulation package and adsorbed on an optimized Zn-MOF surface. Adsorption locator module predicted the preferred adsorption mechanistic models, in which the first model was arranged to be more stable, to confirm the occurrence of some interactions in the adsorption mechanism.

A Review of Evaluation Methods of Standards for Structural Vibration Serviceability under Crowd Walking

Structures such as long-span footbridges, floors, and long cantilevers are vulnerable to vibration serviceability problems under crowd walking, which should be taken into consideration during the structural design, operation, and maintenance stages. Standards have been developed to enable designers to assess the vibration serviceability of structures using simplified load models that simulate crowd-induced loading. To facilitate engineers in quickly selecting appropriate standards for vibration serviceability design, ten current standards were collected which deal with the assessment of structural vibration serviceability under walking loads, including the French “Assessment of vibrational behavior of footbridges under pedestrian loading” (2006), the German “Design of footbridges guideline” (2007), the Chinese “Technical standard for human comfort of the floor vibration” (2019), etc. The ten standards were reviewed and evaluated from three aspects including the crowd loading model, structural response calculation method, and vibration serviceability evaluation standard in this paper. Through summary and comparison between standards, three directions for future improvement and perfection of the standards were proposed: the challenges of the improvement of the standards focus on the establishment of the refined stochastic load model, the analysis of the crowd–structure coupling system, and the modelling of multifactor coupling serviceability evaluation indexes.

Research on Calculation Method of Bottom Isolation Shear Wall Structure Considering Fuzzy Analytic Hierarchy Rrocess

Research on Calculation Method of Bottom Isolation Shear Wall Structure Considering Fuzzy Analytic Hierarchy Rrocess

Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems.

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n-block (n = 1-4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.

Accurate state energetics in spin-crossover systems using pure density functional theory.

The energy difference between different spin states of systems with transition metals is an outstanding challenge for electronic structure calculation methods. The small energy difference between high- and low-spin states in spin-crossover systems makes most post-Hartree-Fock or density functional theory-based methods provide inaccurate values. A test case of twenty systems showing spin transitions has been used to evaluate the accuracy of a new family of training meta-GGA (Generalized Gradient Approximation) functionals. One of the functionals of this new family provides comparable or even better values than the best functional reported so far for this type of system, the TPSSh hybrid meta-GGA functional, but without having to use the exact exchange term. It also improves the results obtained with the r2SCAN meta-GGA functional, which was the best alternative to the TPSSh hybrid functional. This makes it possible to calculate the spin energetics of any kind of compound, especially large systems or periodic structures where the exact exchange requires large computational resources.

Predicting the FCI Energy of Large Systems to Chemical Accuracy from Restricted Active Space Density Matrix Renormalization Group Calculations.

We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [J. Phys. Chem. A 126, 9709] in electronic structure calculations. This yields a new extrapolation method, DMRG-RAS-X, which reaches chemical accuracy for strongly correlated systems such as the chromium dimer, dicarbon up to a large cc-pVQZ basis and even a large chemical complex such as the FeMoco with significantly lower computational demands than those of previous methods. The method is free of empirical parameters, performed robustly and reliably in all examples we tested, and has the potential to become a vital alternative method for electronic structure calculations in quantum chemistry and more generally for the computation of strong correlations in nuclear and condensed matter physics.

High-order finite element method for atomic structure calculations

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the κ=±1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10−8 Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram Title: featomCPC Library link to program files:https://doi.org/10.17632/962fzmm7f7.1Licensing provisions: MITProgramming language: Fortran with command-line interfacesNature of problem: Solution of the Schrödinger, Dirac, and Kohn–Sham equations of density functional theory for isolated atoms.Solution method: A high-order finite element method is used to assemble a generalized eigenproblem that is then solved for eigenvalues and orbitals. The Poisson equation is solved using the finite element method also. Self-consistent field equations are solved using Pulay mixing.Additional comments including restrictions and unusual features: Our solution methodology for the Dirac equation does not suffer from spurious states. We maintain high accuracy even for κ=±1 states. Unlike other methods, our approach is not limited to Coulombic or self-consistent potentials and can handle non-uniform meshes, including exponential meshes.Restrictions: Spherical symmetry.

Structural and molecular investigation of the impact of S30L and D88N substitutions in G9R protein on coupling with E4R from Monkeypox virus (MPXV)

Understanding the pathogenesis mechanism of the Monkeypox virus (MPXV) is essential to guide therapeutic development against the Monkeypox virus. In the current study, we investigated the impact of the only two reported substitutions, S30L, D88N, and S30L-D88N on the G9R of the replication complex in 2022 with E4R using structural modeling, simulation, and free energy calculation methods. From the molecular docking and dissociation constant (KD) results, it was observed that the binding affinity did not increase in the mutants, but the interaction paradigm was altered by these substitutions. Molecular simulation data revealed that these mutations are responsible for destabilization, changes in protein packing, and internal residue fluctuations, which can cause functional variance. Additionally, hydrogen bonding analysis revealed that the estimated number of hydrogen bonds are almost equal among the wild-type G9R and each mutant. The total binding free energy for the wild-type G9R with E4R was −85.00 kcal/mol while for the mutants the TBE was −42.75 kcal/mol, −43.68 kcal/mol, and −48.65 kcal/mol respectively. This shows that there is no direct impact of these two reported mutations on the binding with E4R, or it may affect the whole replication complex or any other mechanism involved in pathogenesis. To explore these variations further, we conducted PCA and FEL analyses. Based on our findings, we speculate that within the context of interaction with E4R, the mutations in the G9R protein might be benign, potentially leading to functional diversity associated with other proteins. Communicated by Ramaswamy H. Sarma

Gas-Pressurized Torrefaction of Lignocellulosic Solid Wastes: Deoxygenation and Aromatization Mechanisms of Cellulose.

A novel gas-pressurized (GP) torrefaction method at 250 °C has recently been developed that realizes the deep decomposition of cellulose in lignocellulosic solid wastes (LSW) to as high as 90% through deoxygenation and aromatization reactions. However, the deoxygenation and aromatization mechanisms are currently unclear. In this work, these mechanisms were studied through a developed molecular structure calculation method and the GP torrefaction of pure cellulose. The results demonstrate that GP torrefaction at 250 °C causes 47 wt.% of mass loss and 72 wt.% of O removal for cellulose, while traditional torrefaction at atmospheric pressure has almost no impact on cellulose decomposition. The GP-torrefied cellulose is determined to be composed of an aromatic furans nucleus with branch aliphatic C through conventional characterization. A molecular structure calculation method and its principles were developed for further investigation of molecular-level mechanisms. It was found 2-ring furans aromatic compound intermediate is formed by intra- and inter-molecular dehydroxylation reactions of amorphous cellulose, and the removal of O-containing function groups is mainly through the production of H2O. The three-ring furans aromatic compound intermediate and GP-torrefied cellulose are further formed through the polymerization reaction, which enhances the removal of ketones and aldehydes function groups in intermediate torrefied cellulose and form gaseous CO and O-containing organic molecules. A deoxygenation and aromatization mechanism model was developed based on the above investigation. This work provides theoretical guidance for the optimization of the gas-pressurized torrefaction method and a study method for the determination of molecular-level structure and the mechanism investigation of the thermal conversion processes of LSW.

Quantum defect and Rydberg energy level calculations for 85Rb and 87Rb by Weakest Bound Electron Potential Model

The Weakest Bound Electron Potential Model (WBEPM) is an effective emerging method for atomic structure calculations that gives results compatible with the experimental observations. In this paper, we have done theoretical calculations of quantum defects and Rydberg energies of high-lying Rydberg energy levels for 85Rb and 87Rb of nS1/2 (n= 14 – 85, 87Rb), nP3/2 (n= 31 – 100, 85Rb), nD3/2 (n= 14 – 85, 87Rb) and nD5/2 (n= 14 – 85, 87Rb) series, through WBEPM. The spectral coefficients for each Rydberg energy level series are determined from Martin's formula and are used to calculate the quantum defects and energy values of the Rydberg energy levels. The obtained results are compared with the available experimental data and show a minimum deviation of the theoretically calculated values from the experimental data. For more insight into the results, values of the Rydberg energy levels and the quantum defects are plotted as a function of the principal quantum number, respectively.

Analytical method for deformation and stress calculation of bell-and-spigot joints in PVC-U pipes

The stable operation of water supply pipelines relies significantly on the structural safety of pipe joints. A novel analytical pipe joint structural calculation method based on the Novozhilov thin shell theory was proposed to calculate the deformation and stress of bell-and-spigot joints in unplasticized polyvinyl chloride (PVC-U) pipes under internal pressure. An equivalent stress index was established to investigate and evaluate the safety performance of pipe joints. The effects of various factors, including spigot insertion depth, the clearance between the bell and spigot, internal pressure, and different pipe nominal outside diameter (DN) and nominal pressure (PN) series, on the maximum equivalent stress of pipe joints, were thoroughly analyzed. The results indicate that the maximum equivalent stress under nominal pressure is located on the inner surface of the bell and consistently exceeds the design stress. The influence of spigot insertion depth on the maximum equivalent stress is minimal. However, as the clearance value between the bell and spigot decreases and the internal pressure increases, the maximum equivalent stress increases significantly. Pipes with smaller DN and PN series result in a higher maximum equivalent stress at the joint. The analytical method indicates that increasing pipe thickness and reinforcing the bell with continuous carbon fiber filament winding are two potentially effective methods to enhance the mechanical performance of the joint and reduce the maximum equivalent stress. This study's findings offer valuable theoretical support for designing and selecting joints in PVC-U pipelines.

Analysis of the single reference coupled cluster method for electronic structure calculations: the full-coupled cluster equations

The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian—a semi-unbounded, self-adjoint operator acting on an L^2-type Hilbert space of antisymmetric functions. Coupled cluster (CC) methods, which are based on a non-linear parameterisation of the sought-after eigenfunction and result in non-linear systems of equations, are the method of choice for high-accuracy quantum chemical simulations. The existing numerical analysis of coupled cluster methods relies on a local, strong monotonicity property of the CC function that is valid only in a perturbative regime, i.e., when the sought-after ground state CC solution is sufficiently close to zero. In this article, we introduce a new well-posedness analysis for the single reference coupled cluster method based on the invertibility of the CC derivative. Under the minimal assumption that the sought-after eigenfunction is intermediately normalisable and the associated eigenvalue is isolated and non-degenerate, we prove that the continuous (infinite-dimensional) CC equations are always locally well-posed. Under the same minimal assumptions and provided that the discretisation is fine enough, we prove that the discrete Full-CC equations are locally well-posed, and we derive residual-based error estimates with guaranteed positive constants. Preliminary numerical experiments indicate that the constants that appear in our estimates are a significant improvement over those obtained from the local monotonicity approach.