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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.

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At least 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Correlative 3D X-ray fluorescence and ptychographic tomography of frozen-hydrated green algae

Accurate knowledge of elemental distributions within biological organisms is critical for understanding their cellular roles. The ability to couple this knowledge with overall cellular architecture in three dimensions (3D) deepens our understanding of cellular chemistry. Using a whole, frozen-hydrated Chlamydomonas reinhardtii cell as an example, we report the development of 3D correlative microscopy through a combination of simultaneous cryogenic x-ray ptychography and x-ray fluorescence microscopy. By taking advantage of a recently developed tomographic reconstruction algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE), we produce high-quality 3D maps of the unlabeled alga’s cellular ultrastructure and elemental distributions within the cell. We demonstrate GENFIRE’s ability to outperform conventional tomography algorithms and to further improve the reconstruction quality by refining the experimentally intended tomographic angles. As this method continues to advance with brighter coherent light sources and more efficient data handling, we expect correlative 3D x-ray fluorescence and ptychographic tomography to be a powerful tool for probing a wide range of frozen-hydrated biological specimens, ranging from small prokaryotes such as bacteria, algae, and parasites to large eukaryotes such as mammalian cells, with applications that include understanding cellular responses to environmental stimuli and cell-to-cell interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Multiscale thermal hydraulic coupling methods for boiling water reactor simulation

During the last two years, the Virtual Environment for Reactor Applications (VERA) has been extended to simulate boiling water reactors (BWRs). The thermal hydraulic effects present in BWRs are far more complex than those in pressurized water reactors (PWRs). Therefore, the runtime is significantly increase and convergence behavior worse compared to PWRs. Most of the additional runtime is spent during the first few coupled iterations, when the power shape is still rapidly evolving, dramatically affecting the thermal hydraulics (TH). To alleviate the increased computational expense, a multiscale TH coupling approach was developed in VERA in which a highly efficient, simplified TH model is solved for several coupled iterations until the power shape is partially converged. The simplified solution is used to inform the assembly-wise flow distribution in the high-fidelity TH solver CTF, reducing the amount of work required to properly balance the pressure drop in each channel and reducing runtime for the couple calculation. Because the final TH calculations are performed with CTF, there is ultimately no impact on the accuracy of the converged solution. This paper presents the details of this multiscale TH coupling approach, along with results for a 4x4 array of GE-14 fuel bundles and whole-core coupled simulations of the Hatch core. These two cases show that the multiscale approach dramatically reduces the runtime of coupled BWR simulations. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

LandScan Mosaic

The LandScan program at Oak Ridge National Laboratory (ORNL), in collaboration with the National Geospatial-Intelligence Agency (NGA), continues to deliver the most accurate and up to date global, high resolution gridded population data. Additionally, the latest advancements in the LandScan HD methodology led to reduced latency in development of rapid updates for geopolitical events. With momentum towards reporting more up to date population estimates, feedback from the user community expressed interest in reporting population estimates in ranges - whether to express a level of uncertainty or confirm to leadership and stakeholders the modeled data are estimates. Building upon the need to understand uncertainty or confidence in the modeled data and report ranges at the global scale, LandScan Mosaic was developed. LandScan Mosaic represents the next generation of high-resolution population modeling, building upon the established success of previous LandScan HD iterations. While LandScan HD employed a deterministic big data fusion approach, LandScan Mosaic enhances this methodology by integrating advanced machine learning techniques to impute missing, yet crucial, population model parameters. This advancement allows for probabilistic modeling of building occupancy and population distribution, incorporating uncertainty quantification through Monte Carlo sampling methods. By combining big data fusion with machine learning-driven imputation and stochastic modeling, LandScan Mosaic provides a more comprehensive and robust representation of population dynamics. LandScan Mosaic will be following the in the footsteps of its longstanding counterpart LandScan Global and releasing a global gridded population raster, at the 3-arcsecond resolution. This technical report documents the current stage of development of LandScan Mosaic, detailing the methodologies and data sources behind the modeling. Stakeholders are encouraged to use this document as an authoritative reference for insight into Mosaic’s data development processes. However, readers should note that LandScan Mosaic remains in a late-stage research and development phase, and methodologies and data presented here are subject to refinements ahead of the anticipated global release in Summer 2025. Feedback and inquiries from users and stakeholders are welcomed as we continue to refine and enhance this important population resource.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A multisite decomposition of the tensor network path integrals

Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the non-equilibrium dynamics of extended quantum systems coupled with local dissipative environments. In this work, we extend the tensor network path integral (TNPI) framework to efficiently simulate such extended systems. The Feynman–Vernon influence functional is a popular approach used to account for the effect of environments on the dynamics of the system. In order to facilitate the incorporation of the influence functional into a multisite framework (MS-TNPI), we combine a matrix product state (MPS) decomposition of the reduced density tensor of the system along the sites with a corresponding tensor network representation of the time axis to construct an efficient 2D tensor network. The 2D MS-TNPI network, when contracted, yields the time-dependent reduced density tensor of the extended system as an MPS. The algorithm presented is independent of the system Hamiltonian. We outline an iteration scheme to take the simulation beyond the non-Markovian memory introduced by solvents. Applications to spin chains coupled to local harmonic baths are presented; we consider the Ising, XXZ, and Heisenberg models, demonstrating that the presence of local environments can often dissipate the entanglement between the sites. We discuss three factors causing the system to transition from a coherent oscillatory dynamics to a fully incoherent dynamics. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault-tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show that the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. Additional linear systems are also explored, one with a more dense sparsity pattern and one that includes advection. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Temperature-dependent mechanical properties and crystal plasticity parameters for additively manufactured Haynes-214 alloy: Experiments and numerical modeling

Our experimental mechanical testing data demonstrated that the additively manufactured (AM) laser powder bed fusion (L-PBF) Haynes-214 alloy exhibits non-linear mechanical properties as the temperature rises from ambient to 870 °C. Crystal plasticity (CP) simulations provide an effective approach to gaining deeper insights into microstructure-property linkages under thermomechanical loading. This method can reduce the need for costly high-temperature mechanical testing while accounting for the effects of crystallographic texture and grain morphology on the mechanical behavior of AM materials. However, calibrating a CP model is time-consuming because individual simulations are computationally expensive and hundreds (or more) of iterations over parameter sets may be required. To address this issue, we have designed a machine learning-differential evolution (ML-DE) CP framework that can accurately interpolate the tensile properties of AM L-PBF Haynes-214 alloy across a wide temperature range from ambient to 870 °C, with minimal reliance on experimental data. The framework uses electron backscatter diffraction (EBSD) measurements to generate statistically equivalent microstructural volume elements to serve as inputs to the CP modeling framework. Stress–strain curves were generated from 1000 CP simulations, which serve as the training data set for the three ML regression algorithms explored: linear, extra-trees, and multi-layer perceptron. These three regression models were independently evaluated to compare their efficiency and identify the most suitable algorithm for the given problem. Results revealed that the extra-trees ML regressor outperforms the other models in both qualitative and quantitative aspects with an R 2 of 0.98. Subsequently, the differential evolution optimization approach is employed to calibrate the ML-based CP material parameters with experimental results obtained at various temperatures. Finally, temperature-dependent CP material parameters are formulated. The effectiveness and efficiency of the designed framework are validated through comparison with experimental results, demonstrating a high degree of agreement. These calibrated parametric constitutive equations enable further use of the CP model to study the deformation behavior of this alloy under a wide range of thermo-mechanical loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

An Overview of the Molten Salt Thermal Properties Database–Thermophysical, Version 2.1.1 (MSTDB-TP v.2.1.1)

The current status of the Molten Salt Thermodynamic Database- Thermal Physical (MSTDB-TP) is reported. Building off of MSTDB-TP and through the direction of the Roadmap for thermal property measurement of Molten Salt Reactor systems, MSTDB-TP 2.1.1 has now been released containing a total 448 salt entries (data from 140+independent studies) compared to the original commit of 62, containing thermophysical properties including density, viscosity, thermal conductivity, and heat capacity. Along with the new database release, further advancement of Saline, a C++application programming interface (API), and a graphical user interface (GUI) has facilitated increased user/developer interaction with the database. Furthermore, estimation techniques, first principles calculations (Ab-Initio) and interpolation/extrapolation methods (Redlich-Kister/Muggianu), have shown great promise in the future of thermophysical property determination for filling out compositional spaces and investigating experimentally difficult salts (hazardous/expensive). This report describes the database composition, development and advancement of database tools, and the strategy of advancing and implementing estimation data into future iterations of the database for MSTDB-TP.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Efficient convolutional sparse coding

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers

We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.

Complexity bound↗
DOE OSTI2018

Tensor network method for reversible classical computation

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Theoretical Calculation and Simulation Studies of Axisymmetric Plasma and Halo Current Analysis in EAST

A new technology for developing fusion energy is to use hydrogen isotopes i.e., deuterium (D) and tritium (T) which is a combine effort for building up of International Thermonuclear Reactor (ITER) named as Tokamak, which will come into operation in 2020. Handsome amount of work has already been done by many researchers contingent with plasma shape, halo current and plasma equilibrium properties by numerical techniques. Halo current calculation is the most important work in fusion reactors. In this paper, we have calculated halo current and plasma cross-section energy. The research covers calculation of plasma energy and determines the force on the vessel by magnetic field transformation method, which is the essential part of calculating halo current. Further, we have developed VDE up/down halo current models. These models give total magnetic field, asymmetric forces, conducting points and poloidal halo current. Confined plasma by magnetic field is considered to be an abundant and durable source of energy for future aspects. In this paper, plasma magnetic field of each cross section was calculated by using energy integral. Transformation method has been successfully applied which provides the connection between major sideways forces acting on the plasma. Theoretical investigation and analyses of halo current have successfully been done. Two observations were analyzed, large ratio of halo current during VDE down and cancellation of specific forces at conducting point. The results obtained will be useful for equalizing the simulation and experimental results. The research will be extended to developed new models for future fusion research. (authors)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

MultiLoad-GAN: A GAN-Based Synthetic Load Group Generation Method Considering Spatial-Temporal Correlations

This paper presents a deep-learning framework, Multi-load Generative Adversarial Network (MultiLoad-GAN), for generating a group of synthetic load profiles (SLPs) simultaneously. The main contribution of MultiLoad-GAN is the capture of spatial-temporal correlations among a group of loads that are served by the same distribution transformer. This enables the generation of a large amount of correlated SLPs required for microgrid and distribution system studies. Here, the novelty and uniqueness of the MultiLoad-GAN framework are three-fold. First, to the best of our knowledge, this is the first method for generating a group of load profiles bearing realistic spatial- temporal correlations simultaneously. Second, two complementary realisticness metrics for evaluating generated load profiles are developed: computing statistics based on domain knowledge and comparing high-level features via a deep-learning classifier. Third, to tackle data scarcity, a novel iterative data augmentation mechanism is developed to generate training samples for enhancing the training of both the classifier and the MultiLoad-GAN model. Simulation results show that MultiLoad- GAN can generate more realistic load profiles than existing approaches, especially in group level characteristics. With little finetuning, MultiLoad-GAN can be readily extended to generate a group of load or PV profiles for a feeder or a service area.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Marine Algae Industrialization Consortium (MAGIC): Combining biofuel and high-value bioproducts to meet the RFS

The Marine Algae Industrialization Consortium (MAGIC) was formed to address pressing challenges in the commercialization of microalgae as a source of biofuel. The “Marine Algae Industrialization Consortium (MAGIC): Combining biofuel and high-value bioproducts to meet the RFS” project formally addressed two US Department of Energy Bioenergy Technologies Office (BETO) goals: (1) Model the sustainable supply of 1 million metric tonnes ash free dry weight (AFDW) cultivated algal biomass and (2) Demonstrate valuable co-products produced along with biofuel intermediates to increase value of algal biomass by 30%. To achieve these goals, the project demonstrated and validated high-value co-products to drive down the cost of biofuel by increasing the value of algae “co-products” towards increasing the selling price of total algae biomass as one of the key drivers of economics and adoption. This was accomplished through five core, interdependent tasks including: (1) strain selection to identify and deliver strains for mass culture, (2) mass culture using a hybrid cultivation system and following key operating parameters for downstream applications to provide algae feedstock, (3) recovery and conversion to evaluate two alternative methods to separate dry algae biomass into oil and residuals for downstream testing, (4) product assessment to determine biofuel, aquafeed or poultry feed product efficacy using algae biomass fractions as well as to provide critical performance data for valuation and (5) commercialization to use technoeconomic and life cycle assessments (TEA/LCA) as iterative design and assessment tools including consideration of target markets, competitors, and distribution channels to guide product assessment, development and valuation. A total of 46 peer-review publications, many open-access, provide detail of much of the work carried out and the results of the tasks. Additional reports and presentations provide other technical and public engagement material. At a high level, using a variety of approaches, more than 1000 marine microalgae strains were evaluated to ultimately identify the seven winners that were down-selected to be grown in mass culture. Strain selection demonstrated that there were no ‘super strains’ and that each candidate had strengths and limitations for specific products, growth conditions or operational considerations. Mass culture growth of these seven strains at >5000 L / 29 m 2 scale found that four them were suitable for product assessment. More than 250 kg of biomass was produced across hundreds of pond runs along with thousands of cultivation entries on the growth and biomass characteristics as well as environmental parameters. In the process, dozens of standard operating procedures were generated as was custom software to process and analyze cultivation data. Recovery and conversion of algae biomass demonstrated that a hexane solvent based extraction protocol was most effective at recovering oil (biocrude) from algae and four strains were processed to produce oil and lipid extracted algae (residuals) for downstream testing. Membrane-based oil separation was less successful, but may still be applicable to other commercial applications in the future. Product testing demonstrated that algae biocrude is of high quality and hydrotreating generated numerous fractions of high quality composition for fuel and lubricate based applications. Aquafeed studies performed at a variety of scales showed that both whole and defatted (lipid extracted algae) microalgae were suitable as a feed ingredient, but that the specifics of the fed animal and biochemical composition of the algae are critical factors when determining formulation. Similarly, poultry studies on whole and defatted microalgae generally showed positive outcomes on animal growth and health, with some microalgae providing enhanced nutritional composition of the animal product. Economic and life cycle assessments covered a wide range of possible commercialization and sustainability scenarios. Replacement value, improved product value added, consumer values marketing added valuation and improved animal health were considered as alternatives for microalgae valuation. Using the open pond system, algae productivity was identified as the key driver of commercialization economics, but combination of co-products (e.g. animal feed) with biofuel production substantially increased the total selling price of algae. Modeled microalgae selling price exceeded $\$$1500/tonne and could generate competitive biofuel selling prices below $\$$5 gallon gas equivalents using realistic algal productivities. Short (process scale) and longer (decadal trends) sustainability assessments show that marine microalgae can enhance the sustainability of energy production and lead to other realized benefits in water, fertilizer and land use for other sectors (e.g. agriculture). This project successfully demonstrated all of the components of an end-to-end process from mass microalgae cultivation and dewatering, to recovery and conversion of algae biomass components, to final product demonstration and process valuation; the combined results provide a framework for future commercialization of algae based biofuels.

09 BIOMASS FUELS↗
DOE OSTI2016

cDPD: A new dissipative particle dynamics method for modeling electrokinetic phenomena at the mesoscale

In this work, we develop a “charged” dissipative particle dynamics (cDPD) model for simulating mesoscopic electrokinetic phenomena governed by the stochastic Poisson-Nernst-Planck and the Navier-Stokes equations. In particular, the transport equations of ionic species are incorporated into the DPD framework by introducing extra degrees of freedom and corresponding evolution equations associated with each DPD particle. Diffusion of ionic species driven by the ionic concentration gradient, electrostatic potential gradient, and thermal fluctuations is captured accurately via pairwise fluxes between DPD particles. The electrostatic potential is obtained by solving the Poisson equation on the moving DPD particles iteratively at each time step. For charged surfaces in bounded systems, an effective boundary treatment methodology is developed for imposing both the correct hydrodynamic and electrokinetics boundary conditions in cDPD simulations. To validate the proposed cDPD model and the corresponding boundary conditions, we first study the electrostatic structure in the vicinity of a charged solid surface, i.e., we perform cDPD simulations of the electrostatic double layer and show that our results are in good agreement with the well-known mean-field theoretical solutions. Furthermore, we simulate the electrostatic structure and capacity densities between charged parallel plates in salt solutions with different salt concentrations. Moreover, we employ the proposed methodology to study the electro-osmotic and electro-osmotic/pressure-driven flows in a micro-channel. In the latter case, we simulate the dilute poly-electrolyte solution drifting by electro-osmotic flow in a micro-channel, hence demonstrating the flexibility and capability of this method in studying complex fluids with electrostatic interactions at the micro- and nano-scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A practical globalization of one-shot optimization for optimal design of tokamak divertors

In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes only state residuals. Additionally, robust rank-two Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A moment-conserving discontinuous Galerkin representation of the relativistic Maxwellian distribution

Kinetic simulations of relativistic gases and plasmas are critical for understanding diverse astrophysical and terrestrial systems, but the accurate construction of the relativistic Maxwellian, the Maxwell–Jüttner distribution, on a discrete simulation grid is challenging. Difficulties arise from the finite velocity bounds of the domain, which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here, we present a novel scheme for iteratively correcting the moments of the projected distribution applicable to all grid-based discretizations of the relativistic kinetic equation. In addition, we describe how to compute the needed nonlinear quantities, such as Lorentz boost factors, in a discontinuous Galerkin scheme through a combination of numerical quadrature and weak operations. The resulting method accurately captures the distribution function and ensures that the moments match the desired values to machine precision.

astrophysical plasmas↗
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↗