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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Geometry optimizations with spinor-based relativistic coupled-cluster theory

Development of analytic gradients for relativistic coupled-cluster singles and doubles augmented with a non-iterative triples [CCSD(T)] method using an all-electron exact two-component Hamiltonian with atomic mean-field spin–orbit integrals (X2CAMF) is reported. This enables efficient CC geometry optimizations with spin–orbit coupling included in orbitals. Here, the applicability of the implementation is demonstrated using benchmark X2CAMF-CCSD(T) calculations of equilibrium structures and harmonic vibrational frequencies for methyl halides, CH 3 X (X = Br, I, and At), as well as calculations of rotational constants and infrared spectrum for RaSH+, a radioactive molecular ion of interest to spectroscopic study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Nuclear–Electronic Orbital QM/MM Approach: Geometry Optimizations and Molecular Dynamics

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods allow simulations of chemical reactions in atomistic solvent and heterogeneous environments such as proteins. Herein, the nuclear–electronic orbital (NEO) QM/MM approach is introduced to enable the quantization of specified nuclei, typically protons, in the QM region using a method such as NEO-density functional theory (NEO-DFT). This approach includes proton delocalization, polarization, anharmonicity, and zero-point energy in geometry optimizations and dynamics. Expressions for the energies and analytical gradients associated with the NEO-QM/MM method, as well as the previously developed polarizable continuum model (NEO-PCM), are provided. Geometry optimizations of small organic molecules hydrogen bonded to water in either dielectric continuum solvent or explicit atomistic solvent illustrate that aqueous solvation can strengthen hydrogen-bonding interactions for the systems studied, as indicated by shorter intermolecular distances at the hydrogen-bond interface. We then performed a real-time direct dynamics simulation of a phenol molecule in explicit water using the NEO-QM/MM method. Furthermore, these developments and initial examples provide the foundation for future studies of nuclear–electronic quantum dynamics in complex chemical and biological environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

CASPT2 molecular geometries of Fe( II ) spin-crossover complexes

Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. Here we recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe–ligand bond distances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

R –8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method

The anisotropic and isotropic R –8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang–Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole–octopole polarizability tensor and the quadrupole–quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. Further, while the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang–Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗
NASA NTRS1973

Structural optimization by methods of feasible directions.

A general design algorithm based on methods of feasible directions is presented. Zoutendijk's method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.

Vanderplaats, G. N.↗
NASA NTRS1979

Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. I - Theory

A statistical technique is developed for inferring the optimum values of the ground albedo and the effective imaginary term of the complex refractive index of atmospheric particulates. The procedure compares measurements of the ratio of the hemispheric diffuse to directly transmitted solar flux density at the earth's surface with radiative transfer computations of the same as suggested by Herman et al. (1975). A detailed study is presented which shows the extent to which the ratio of diffuse to direct solar radiation is sensitive to many of the radiative transfer parameters. Results indicate that the optical depth and size distribution of atmospheric aerosol particles are the two parameters which uniquely specify the radiation field to the point where ground albedo and index of absorption can be inferred. Varying the real part of the complex refractive index of atmospheric particulates as well as their vertical distribution is found to have a negligible effect on the diffuse-direct ratio. The statistical procedure utilizes a semi-analytic gradient search method from least-squares theory and includes a detailed error analysis.

King, M. D.↗
NASA NTRS1988

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.

Smaoui, H.↗
NASA NTRS1988

Optimal cooperative time-fixed impulsive rendezvous

A method has been developed for determining optimal, i.e., minimum fuel, trajectories for the fixed-time cooperative rendezvous of two spacecraft. The method presently assumes that the vehicles perform a total of three impulsive maneuvers with each vehicle being active, that is, making at least one maneuver. The cost of a feasible 'reference' trajectory is improved by an optimizer which uses an analytical gradient developed using primer vector theory and a new solution for the optimal terminal (rendezvous) maneuver. Results are presented for a large number of cases in which the initial orbits of both vehicles are circular but in which the initial positions of the vehicles and the allotted time for rendezvous are varied. In general, the cost of the cooperative rendezvous is less than that of rendezvous with one vehicle passive. Further improvement in cost may be obtained in the future when additional, i.e., midcourse, impulses are allowed and inserted as indicated for some cases by the primer vector histories which are generated by the program.

Mirfakhraie, Koorosh↗
NASA NTRS2002

Human motion planning based on recursive dynamics and optimal control techniques

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

Non-NASA Center↗
NASA NTRS2005

A Simple, Powerful Method for Optimal Guidance of Spacecraft Formations

One of the most interesting and challenging aspects of formation guidance law design is the coupling of the orbit design and the science return. The analyst s role is more complicated than simply to design the formation geometry and evolution. He or she is also involved in designing a significant portion of the science instrument itself. The effectiveness of the formation as a science instrument is intimately coupled with the relative geoniet,ry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a simple method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to twc missims: the Magnetospheric Mu!tiscale mission (MMS), a,nd the TJaser Interferometer Space Antenna (LISA).

Hughes, Steven P.↗
NASA NTRS2006

A Simple, Powerful Method for Optimal Guidance of Spacecraft Formations

One of the most interesting and challenging aspects of formation guidance law design is the coupling of the orbit design and the science return. The analyst's role is more complicated than simply to design the formation geometry and evolution. He or she is also involved in designing a significant portion of the science instrument itself. The effectiveness of the formation as a science instrument is intimately coupled with the relative geometry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a simple method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to two missions: the Magnetospheric Multiscale mission (MMS) , and the Laser Interferometer Space Antenna (LISA).

Hughes, Steven P.↗
DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗
NASA NTRS1978

Efficiency of unconstrained minimization techniques in nonlinear analysis

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Kamat, M. P.↗
DOE OSTI2021

Time-series dissolved oxygen, other bigeochemically-relevant analytes, and pressure gradients associated with the manuscript “Dissolved oxygen sensor in an automated hyporheic sampling system reveals biogeochemical dynamics”

This dataset contains time-series data from a vertical profile within the bed and banks of the Columbia river near Richland, WA. Water was sampled through 3 small tubes embedded in the sediment at 50,100, and 200 cm below the sediment-water interface. The goal of this study was to observe the correlations between hydraulic drivers and biogeochemical responses. The results of this study are published in the manuscript “Dissolved oxygen sensor in an automated hyporheic sampling system reveals biogeochemical dynamics”. The file types included in the data package are all time-series spreadsheet data, including hydraulic head gradients, physical parameters (temperature, pressure, SpC (specific conductivity)), and biogeochemical parameters (dissolved oxygen, pH, NO3 (nitrate) and ORP (oxidation-reduction potential)).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Impact of Analytic Derivatives on Optimization of N-Impulse Orbit Transfer

Several formulations are possible for the optimization of N-impulse two-body orbit transfers. One formulation that assumes the firstN−1impulses are design variables and implements Lambert’s algorithm in the final leg is here considered. This paper presents a derivation for the analytic expressions of the gradients needed to optimize this formulation. The impact of using these analytic expressions on the optimization computational cost is also presented. A linear system of equations is developed that approximates the Lambert’s problem solution in a way that is suitable for computing the analytic gradients. The derivations of the analytic gradients, as well as numerical case studies for 2-impulse and 3-impulse orbit transfers, are presented. The numerical case studies highlights a significant reduction in the computational cost, measured in terms of the number of function calls.

Ahmed Ellithy↗
NASA NTRS1975

Two-dimensional jet mixing with a pressure gradient

An analytical study of nonsimilar jet mixing is made for compressible, nonisoenergetic flows. The conservation equations are solved for each of the streams above and below the dividing streamline by using Meksyn's asymptotic method of integration for solving boundary-layer problems. The problem of laminar mixing between two parallel streams is investigated for the case of a constant pressure gradient. It is found that the velocity and temperature profiles from the exact solution to the nonsimilar governing equations can be well approximated by the locally similar solution.

Brink, D. F.↗