Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “analytical gradients”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

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

Molecular Geometry and Electronic Structure of Copper Corroles

Copper corroles are known for their unique multiconfigurational electronic structures in the ground state, which arise from the transfer of electrons from the π orbitals of the corrole to the d-orbital of copper. While density functional theory (DFT) provides reasonably good molecular geometries, the determination of the ground spin state and the associated energetics is heavily influenced by functional choice, particularly the percentage of the Hartree–Fock exchange. Using extended multireference perturbation theory methods (XMS-CASPT2), the functional choice can be assessed. The molecular geometries and electronic structures of both the unsubstituted and the meso-triphenyl copper corroles were investigated. A minimal active space was employed for structural characterization, while larger active spaces are required to examine the electronic structure. The XMS-CASPT2 investigations conclusively identify the ground electronic state as a multiconfigurational singlet (S o ) with three dominant electronic configurations in its lowest energy and characteristic saddled structure. In contrast, the planar geometry corresponds to the triplet state (T o ), which is approximately 5 kcal/mol higher in energy compared to the S o state for both the bare and substituted copper corroles. Notably, the planarity of the T o geometry is reduced in the substituted corrole compared with that in the unsubstituted one. By analyzing the potential energy surface (PES) between the S o and T o geometries using XMS-CASPT2, the multiconfigurational electronic structure is shown to transition toward a single electron configuration as the saddling angle decreases (i.e., as one approaches the planar geometry). Despite the ability of the functionals to reproduce the minimum energy structures, only the TPSSh-D 3 PES is reasonably close to the XMS-CASPT2 surface. Significant deviations along the PES are observed with other functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Optimization of linear, controlled structures

An approach to the integrated design of linear controlled structures, which is being investigated as part of NASA's controlled structures interaction (CSI) methodology development program, is presented. The approach is integrated in the sense that the structure and its controller are simultaneously designed. The design methodology uses constrained nonlinear optimization procedures based on analytically obtained gradients of the structural responses. Design of the controller is based on the so-called Q-parameterization theory, which parameterizes all closed-loop input/output maps achievable with stabiizing linear controllers. Very general objective and constraint functions are possible, and structural shape can be included in the design variables. This method has been partially implemented and demonstrated; early findings are reported.

Hunziker, K. Scott↗
NASA NTRS1992

Tables Of Gaussian-Type Orbital Basis Functions

NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.

Partridge, Harry↗
DOE OSTI2025

A three-dimensional laser ray-tracing methodology for radiation-hydrodynamics simulations

We report on a methodology for performing laser ray-tracing in three spatial dimensions for radiation-hydrodynamics simulation codes. Our method, which is an extension of that developed in Haines et al., Comput. Fluids 201, 104478 (2020), utilizes an automatically generated separate mesh for the laser ray-tracing from the radiation-hydrodynamics mesh. This enables the laser mesh to be tailored to minimize ray noise with significantly fewer rays than would be required when the ray-tracing is performed on the radiation-hydrodynamics mesh, primarily by allowing the use of high-aspect-ratio cells that are not suitable for hydrodynamics solvers. For a planar target, we show that our method provides a ≈ 100× reduction in computational expense to achieve a fixed level of ray noise relative to ray-tracing directly on the radiation-hydrodynamics mesh. The relatively low ray requirement also enables efficient computation of cross-beam energy transfer. Each cell in the logically cubic laser mesh is a non-convex dodecahedron with triangular sides, and numerical integration of the ray trajectories and inverse bremsstrahlung is performed by mapping each cell to the unit cube. We will describe our methodology in detail as well as its implementation in the xRAGE radiation-hydrodynamics code, discuss performance, and present the results from applying the methodology to test problems with analytic solutions for laser ray-tracing through a quadratic density gradient with an analytic solution as well as for a laser-driven heat front. In 3D radiation-hydrodynamics simulations of laser-driven experiments performed on the National Ignition Facility, laser ray-tracing with our methodology uses less than 1% of total computational time while introducing acceptably low levels of ray noise.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1971

Radiative transfer effects on reflected shock waves. I - Transparent gas.

Analytical and numerical calculation of the effects of radiative cooling on the flow field and heat transfer behind a reflected shock wave. The analytical solutions are developed by an expansion procedure about the Newtonian limit - i.e., the flow variables are expanded in the small parameter epsilon representing the initial density ratio across the shock front. Solutions carried out through the zeroth- and first-orders in epsilon show an accuracy to the order of epsilon squared - namely, for the specific conditions considered the analytically calculated enthalpy changes agree to within 2% with the numerically computed changes. The numerical procedure consists of a finite-difference calculation with pressure gradients neglected. The analytical calculations show that pressure-gradient effects may be neglected, except at very long times when the shocked gas has cooled by a large amount. The present calculations show much greater shock-wave attenuation than does a previous numerical computation. This difference is attributed to a better representation of the thermodynamic properties in the present calculations.

Su, F. Y.↗
DOE OSTI2024

Gradient Technique Theory: Tracing Magnetic Field and Obtaining Magnetic Field Strength

Abstract The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfvén Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfvén Mach number M A . We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to the Davis–Chandrasekhar–Fermi way of obtaining the magnetic field strength.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Star formation rates and abundance gradients in disk galaxies

Analytic models for the evolution of disk galaxies are presented, placing special emphasis on the radial properties. These models are straightforward extensions of the original Schmidt (1959, 1963) models, with a dependence of star formation rate on gas density. The models provide successful descriptions of several measures of galactic disk evolution, including solar neighborhood chemical evolution, the presence and amplitude of metallicity and color gradients in disk galaxies, and the global rates of star formation in disk galaxies, and aid in the understanding of the apparent connection between young and old stellar populations in spiral galaxies.

Wyse, Rosemary F. G.↗
NASA NTRS1974

Four-body trajectory optimization

A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.

Pu, C. L.↗
DOE OSTI2023

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. Finally, the predicted values support the relaxation mechanisms reported in previous studies.

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

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. Here, this study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Ground and excited state gradients with end-to-end differentiable semiempirical quantum chemistry

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born–Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree–Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Extending XACC for Quantum Optimal Control

Quantum computing vendors are beginning to open up application programming interfaces for direct pulse-level quantum control. With this, programmers can begin to describe quantum kernels of execution via sequences of arbitrary pulse shapes. This opens new avenues of research and development with regards to smart quantum compilation routines that enable direct translation of higher-level digital assembly representations to these native pulse instructions. In this work, we present an extension to the XACC system-level quantum-classical software framework that directly enables this compilation lowering phase via user-specified quantum optimal control techniques. This extension enables the translation of digital quantum circuit representations to equivalent pulse sequences that are optimal with respect to the backend system dynamics. Our work is modular and extensible, enabling third party optimal control techniques and strategies in both C++ and Python. We demonstrate this extension with familiar gradient-based methods like gradient ascent pulse engineering (GRAPE), gradient optimization of analytic controls (GOAT), and Krotov's method. Our work serves as a foundational component of future quantum-classical compiler designs that lower high-level programmatic representations to low-level machine instructions.

Nguyen, Thien↗
DOE OSTI2023

GOAT. jl

SF-23-008 This project is a Julia implementation of the Gradient Optimization of Analytic conTrols (GOAT) optimal control methodology. It integrates with other packages in Julia's ecosystem to provide memory-efficient, parallelized solutions to quantum optimal control tasks. A prototype implementation of some of these algorithms was initially developed and funded by the ASCR Early Career Research Award program under PI Travis Humble at Oak Ridge National Laboratory. The current version was funded under the ASCR AIDE-QC Program under PI Paul Hovland. The current package to be released has a novel implementation, syntax, and structure making it substantially different than the original prototype (which was not released under copyright to the best of my knowledge).

KAIRYS, PAUL↗
DOE OSTI2023

Trivializing Flow in 2D-O(3) model

The two dimensional O(3) sigma model, just as quantum chromodynamics, is an asymptotically free theory with a mass gap. Therefore, it is an interesting and simple toy model to investigate algorithms for Markov Chain Monte Carlo simulations of quantum chromodynamics. In this talk, we discuss the construction of a trivializing map, a field transformation from a given theory to a trivial one, through a suitably chosen gradient flow. An analytic solution for the generating functional of this trivializing flow has been obtained by a perturbative expansion in the flow time. Utilizing this solution allows for new approaches to be considered when proposing updates for a Markov Chain Monte Carlo algorithm.

Chamness, Christopher↗
DOE OSTI2024

The AGORA High-resolution Galaxy Simulations Comparison Project. IV. Halo and Galaxy Mass Assembly in a Cosmological Zoom-in Simulation at z ≤ 2

In this fourth paper from the AGORA Collaboration, we study the evolution down to redshift z = 2 and below of a set of cosmological zoom-in simulations of a Milky Way mass galaxy by eight of the leading hydrodynamic simulation codes. We also compare this CosmoRun suite of simulations with dark matter-only simulations by the same eight codes. We analyze general properties of the halo and galaxy at z = 4 and 3, and before the last major merger, focusing on the formation of well-defined rotationally supported disks, the mass–metallicity relation, the specific star formation rate, the gas metallicity gradients, and the nonaxisymmetric structures in the stellar disks. Codes generally converge well to the stellar-to-halo mass ratios predicted by semianalytic models at z ~ 2. We see that almost all the hydro codes develop rotationally supported structures at low redshifts. Most agree within 0.5 dex with the observed mass–metallicity relation at high and intermediate redshifts, and reproduce the gas metallicity gradients obtained from analytical models and low-redshift observations. We confirm that the intercode differences in the halo assembly history reported in the first paper of the collaboration also exist in CosmoRun, making the code-to-code comparison more difficult. We show that such differences are mainly due to variations in code-dependent parameters that control the time stepping strategy of the gravity solver. We find that variations in the early stellar feedback can also result in differences in the timing of the low-redshift mergers. All the simulation data down to z = 2 and the auxiliary data will be made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

Atmospheric wave-induced instability in the nighttime E-region.

Examination of the perturbed continuity equation when the perturbations are the result of an internal atmospheric gravity wave in the E region. The transient response of the ionization is interpreted as the gradient instability and the values of the vertical and horizontal wave numbers that will induce it are plotted for various heights. Only in the presence of westward directed electric fields, which are believed to occur only at night, will the gravity waves induce the gradient instability. Approximate analytic expressions are obtained for the permitted wave numbers as well as for the instability growth times. In the course of this analysis it is shown that in the D region all irregularities, even those that are field-aligned, will tend to move with the ion velocity.

Beer, T.↗