Search NASA⌕ Search

SEARCH · Search NASA

Results for “Manifold sampling”

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 OSTI2018

Chemical Conversion of Anhydrous Hydrogen Fluoride for Safe Disposal

A procedure for the safe conversion of a small (~ 1 gram) quantity of anhydrous hydrogen fluoride to calcium fluoride is described. The purpose of the conversion is to put the toxic, corrosive, gaseous compound into a chemical form that is a less toxic solid (calcium fluoride) and easier to dispose of. The hydrogen fluoride, which was contained in a 50 cc metal sample cylinder, was drawn by a small mechanical vacuum pump through an all-metal gas manifold and into a metal trap containing alternating layers of calcium oxide powder and Teflon turnings. The anhydrous hydrogen fluoride reacts with the calcium oxide to produce calcium fluoride and water vapor. Because some of the calcium oxide powder was drawn out of the trap and into the vacuum tubing, it was not possible to quantify the amount of anhydrous hydrogen fluoride converted to calcium fluoride. However, it was noted that there was a temperature rise in the trap when the gas was flowing through it, and no HF gas was detected at the vacuum pump exhaust at this time using a colorimetric Dräger tube. The trap was sealed and disposed of as solid chemical waste.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Airfoil Computational Fluid Dynamics - 2k shapes, 25 AoA's, 3 Re numbers

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 1,830 airfoil shapes computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this dataset, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We sampled airfoil designs over both parameter spaces to explore the full range of possible shape variations. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, for or three different Reynolds' numbers (3M, 6M, and 9M), and for 25 angles of attack from -4 deg. to 20 deg. with 1 degree increments. Across all these various parameters, this dataset includes the results from over 250,000 CFD simulations. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy, in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_2k_data.ipynb.

2k↗
DOE OSTI2023

Airfoil Computational Fluid Dynamics - 9k shapes, 2 AoA's

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 8,996 airfoil shapes, computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this data, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We fixed the linear deformations to be the mean over the database and sampled new shapes over a four-dimensional parameter space of higher-order perturbation. This sampling approaches allows for isolated analysis of non-linear airfoil shape deformations while holding other aspects (e.g., airfoil thickness) approximately constant. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, Reynolds number of 9M, and at two angles of attack, 4 deg. and 12 deg. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_9k_data.ipynb.

9k↗
NASA NTRS2006

Analysis of N-Nitrosodimethylamine and N-Nitrodimethylamine in Groundwater

A method for the analytical determination of N-nitrosodimethylamine (NDMA) and N-nitrodimethylamine (DMN) at parts-per-trillion (ppt) concentrations in groundwater is reported. The method uses a solid phase extraction (SPE) cartridge containing 2 g of activated coconut charcoal to extract a 500-mL water sample. NDMA and DMN are eluted from the SPE cartridge using acetone. The acetone is concentrated and brought to a final volume of 1.0 mL, which results in a theoretical 500-fold concentration of the analytes. The extracts are analyzed by gas chromatography (GC) with a nitrogenphosphorous detector (NPD), which is a highly sensitive and relatively inexpensive technique. The measured extraction efficiencies averaged 61 percent for NDMA and 74 percent for DMN. Extraction efficiencies were independent of NDMA and DMN concentrations from 40 to 2000 ppt. Several samples could be extracted then analyzed in a single day with the use of an extraction manifold and GC autosampler. A reporting limit of 10 ppt for NDMA and DMN was achieved. The MDLs for NDMA and DMN were 6.4 and 5.8 ppt, respectively. A typical turn-around time from beginning of extraction to reporting was 4 h. The method avoids the use of halogenated solvents, such as dichloromethane, and subsequent solvent exchange procedures necessary for use of the NPD detector.

Greene, Ben↗
DOE OSTI2016

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.

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

Efficient Intermolecular Energy Exchange and Soft-ionization of Water at Nanoplatelet Interfaces

X-ray, energetic photon and electron irradiation can ionize and electronically excite target atoms and molecules. These excitations undergo complicated relaxation and energy transfer processes that ultimately determine the manifold of system responses to the deposited excess energy. In weakly bound gas- and solution-phase samples, intermolecular Coulomb decay (ICD) and electron-transfer mediated decay (ETMD) can occur with neighboring atoms or molecules leading to efficient transfer of the excess energy to the surroundings. In ionic solids such as metal-oxides, intra- and inter-atomic Auger decay produces localized final states that lead to lattice damage and typically removal of cations from the substrate. The relative importance of Auger stimulated damage (ASD) versus ICD and ETMD in micro-solvated nanoparticle interfaces is not known. Though ASD is generally expected, essentially no lattice damage and very efficient ICD and ETMD resulting from ionization and electronic excitation of micro-solvated boehmite (AlOOH) nanoplatelets has been observed. Efficient energy transfer and soft ionization of interfacial molecules is likely a general phenomenon at gas-oxyhydroxide nanoparticle interfaces where the density of states of the ionized chemisorbed species significantly overlap the core hole states of the solid.

Jones, Brant M.↗
DOE OSTI2024

MULTI-LEADER: MULTI-source LEarning-Accelerated Design of high-Efficiency multi-stage compRessor (Final Technical Report)

The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2016

Rapid Production of Graphite Without Contamination for Biomedical AMS

The application of AMS to the detection of 14 C makes possible a new class of sensitive experiments in molecular biology. Such experiments inherently produce large numbers of samples for the determination of biological variability in molecular interactions. The samples vary in 14 C concentration over many orders of magnitude. We added TiH 2 to aid the reduction of CO 2 by zinc in a sealed tube to reproducibly make graphite without sample cross-contamination. The CO 2 is transferred from a combustion tube to the reaction tube through a disposable plastic manifold. The sealed tubes are heated to a single-reaction temperature in a muffle furnace. The process is complete within 5 h. Bulk isotopic fractionation in the finished graphite is less than 0.5%.

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

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Abstract A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low‐dimensional representation of the underlying behavior of physical/mathematical systems with respect to uncertain input parameters. Using this representation, GH, an out‐of‐sample extension technique, is employed to create a global map from the input parameter space to a Grassmannian diffusion manifold. GH is further employed to locally map points on the diffusion manifold onto the tangent space of a Grassmann manifold. The exponential map is then used to project the points in the tangent space onto the Grassmann manifold, where reconstruction of the full solution is performed. The performance of the proposed surrogate model is verified with three examples. The first problem is a toy example used to illustrate the technique. In the second example, errors associated with the various mappings are assessed by studying response predictions of the electric potential of a dielectric cylinder in a homogeneous electric field. The last example applies the method for uncertainty prediction in the strain field evolution in a model amorphous material using the shear transformation zone theory of plasticity.

42 ENGINEERING↗
NASA NTRS1980

Process and apparatus for analyzing specimens for the presence of microorganisms therein

Microorganisms in a specimen are detected, identified, and enumerated by introducing the specimen into a sampling cartridge and diluting the specimen with a known volume of water within the cartridge. The cartridge has a manifold and several cassettes attached to the manifold. Each cassette contains a serpentine flow channel having a series of filters therein and a detection cell located downstream from each filter. The flow channel in each cassette also contains a culture medium which is freeze dried and is highly selective in the sense that it promotes the growth of one type of microorganism, but not others. The mixture of the specimen and water flows from the manifold into the flow channel of each cassette where it rehydrates the culture medium therein and further flows through the filters. Each filter removes a known proportion of the microorganisms from the mixture of specimen, water and medium, thereby effecting a serial dilution. After the cassettes are heated to incubate the microoganisms, the detection cells are observed for growth of the microorganisms therein which is manifested in a change in the light transmitting characteristics of the mixtures within the cells.

Aldridge, Jr., Clifton↗
DOE OSTI2016

In Situ Sample Environment for Studying Corrosion of Nuclear Materials

Currently there is lack of fundamental understanding of kinetics and reaction mechanisms that occur at nuclear cladding-steam interface under extreme environments in the nuclear reactors. Such understanding is vital to design and develop advanced cladding materials for more economical and safer nuclear power. We present advanced in situ sample environment for probing solid-fluid interfaces using high resolution synchrotron methods for studying early stages of corrosion including development of oxide layer as corrosion proceeds. Both X-ray diffraction and X-ray fluorescence methods will be discussed to probe structural and elemental composition changes under steam environment using corrosion resistant cell at high temperatures. High intensity and brightness of synchrotron coupled with advanced in situ sample environment developed, presents an opportunity to understand the fundamental interfacial processes involved in degradation of materials. The in situ sample environment is optimized for XRD and XRF data collection at NSLS-II and will be available to all users through the proposal process. The in situ sample environment is built to study the interfacial interactions at temperatures and pressures up to 400 deg. C and 1500 psi. It consists of three main parts; the distribution manifold, the pressure vessel, and the reaction cell as shown in Figure 1. Water is allowed to heat up to 350 deg. C inside the pressure vessel to produce steam which is delivered to reaction cell using insulated delivery system. The cell design is adapted from J. Diefenbacher, et. al. However, it is modified for corrosion applications in steam environments. The reaction cell and sample holder are made from hastelloy due to its high corrosion resistance. The reaction cell is surrounded by copper heating block to control its temperature independently from the rest of the system. Lab view based platform is developed for remote monitoring of pressure and temperature. The sample environment was commissioned at 6-IDD beamline in the Advanced Photon Source, for grazing incidence XRD corrosion studies. Metallic Zr sample (200 μm thickness) was used due to its faster oxidation kinetics as compared to Zircaloy. Sample was exposed to steam at 350 deg. C and 50 psi for a total time of 64 hours. Results showed the presence of α-Zr as the dominant phase. After 32 hours of exposure to steam, three oxide peaks in the low diffraction angle side started to develop with time. These peaks are attributed to the growth of substoichiometric zirconium oxide phases (Zr{sub 3}O and Zr{sub 3}O{sub 1-x}). (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Trajectory design via unsupervised probabilistic learning on optimal manifolds

Abstract This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.

42 ENGINEERING↗
DOE OSTI2020

A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch considering Wind Power Penetration

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in this stochastic economic dispatch problem for forecasting purposes, the conventional Monte-Carlo method is prohibitively time-consuming for practical applications. To overcome this problem, here we propose a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling as the computer experimental design, a Gaussian-process emulator is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated stochastic economic dispatch model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

17 WIND ENERGY↗
NASA NTRS2017

Sample Processor for Life on Icy Worlds (SPLIce): Design and Test Results

We report the design, development, and testing of the Sample Processor for Life on Icy Worlds (SPLIce) system, a microfluidic sample processor to enable autonomous detection of signatures of life and measurements of habitability parameters in Ocean Worlds. This monolithic fluid processing-and-handling system (Figure 1; mass 0.5 kg) retrieves a 50-L-volume sample and prepares it to supply a suite of detection instruments, each with unique preparation needs. SPLIce has potential applications in orbiter missions that sample ocean plumes, such as found in Saturns icy moon Enceladus, or landed missions on the surface of icy satellites, such as Jupiters moon Europa. Answering the question Are we alone in the universe? is captivating and exceptionally challenging. Even general criteria that define life very broadly include a significant role for water [1,2]. Searches for extinct or extant life therefore prioritize locations of abundant water whether in ancient (Mars), or present (Europa and Enceladus) times. Only two previous planetary missions had onboard fluid processing: the Viking Biology Experiments [3] and Phoenixs Wet Chemistry Laboratory (WCL) [4]. SPLIce differs crucially from those systems, including its capability to process and distribute L-volume samples and the integration autonomous control of a wide range of fluidic functions, including: 1) retrieval of fluid samples from an evacuated sample chamber; 2) onboard multi-year storage of dehydrated reagents; 3) integrated pressure, pH, and conductivity measurement; 4) filtration and retention of insoluble particles for microscopy; 5) dilution or vacuum-driven concentration of samples to accommodate instrument working ranges; 6) removal of gas bubbles from sample aliquots; 7) unidirectional flow (check valves); 8) active flow-path selection (solenoid-actuated valves); 9) metered pumping in 100 nL volume increments. The SPLIce manifold, made of three thermally fused layers of precision-machined cyclo-olefin polymer, supports all fluidic components (Figure 1) and integrated microchannels (125 x 250 m). Fluid is pumped by a stepper-motor-driven pump (Lee Co.). The functionality of the integrated MEMS pressure sensor (Honeywell) and passive check valves (Figure 2) were tested in conjunction with our newly designed integral bubble traps (Figure 3) and hydrophobic membrane-based concentrator (Figure 4). The concentrator (initially tested as a standalone component) demonstrated 5-fold vacuum-evaporative concentration. Polyethylene fused bead beds (PEFBBs; 50 porosity) store drylyophilized buffers, calibrants, and fluorescent dyes, and also promote mixing of sample with calibrant, dye, or H2O. Software-controlled automated tests demonstrated successful 1) fluid delivery to each component 2) valve and pump synchronization 3) sample aliquot delivery to instrument interface ports, and 4) rehydration of vacuum-dried fluorescent dye. In Figure 5, fluorescein on PEFBBs was rehydrated for 15 min using a pump-delivered water aliquot; it is displaced as H2O enters the bottom of the channel and pushes the dye into a check valve. Ultimately, SPLIce will fluorescently label amino acids in the sample for microchip-based electrophoretic (MCE) chiral separation and detection to seek and quantify key organic bio-signatures [5]; it will also deliver sample to a microfluidic version of WCL (mWCL) to measure soluble ions and redox-active species.

Life detection↗
DOE OSTI2020

Probabilistic learning and updating of a digital twin for composite material systems

This paper presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems. An example demonstrates the integration of experimental data with a computational database. The statistical approach is based on the probabilistic learning on manifolds recently developed by the authors. This approach leverages intrinsic structure detected through diffusion on graphs with projected stochastic differential equations to generate samples constrained to that structure.

42 ENGINEERING↗
DOE OSTI2017

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size, thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e., those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI algorithm. Furthermore, the cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the π space of polyacenes, and (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with an increasing rank for the first three systems, even connected octuple excitations still appear important in Cr 2 , suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗