Results for “Text Analytics” — Page 2

DOE OSTI2026

An analytic result for the 0 → ggHHH amplitude

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, gg → HHH, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and p-adic evaluations, multivariate partial fraction decompositions, and primary decompositions to identify common numerator factors. Although full analytic results are given in the text and in the supplementary material, the main thrust of this paper is to further test and illustrate these analytic reconstruction techniques in a concrete physical example. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives. Full analytic control of the leading-order, loop-induced amplitude is an important step towards handling more complex 2-loop or real-radiation corrections to this and related processes.

Campbell, John M. [Fermilab] (ORCID:00000002136193↗

DOE OSTI2020

Kinetic Simulations of Microstructural Evolution (KSOME)

"Kinetic simulations of microstructural evolution" (KSOME) is an object Kinetic Monte Carlo (OMKC) simulation code. It is developed to simulate microstructural evolution in materials during irradiation. KSOME is developed from ground up with priority given to the flexibility, ease of upgradability, and computation efficiency, in that order. With previously developed simulation codes, various processes (more precisely, the diffusion-reaction processes) that can occur in a system were hardwired into the code. Hence, to perform higher fidelity simulations, a significant coding effort was required every time to incorporate either a more accurate description of existing processes or new processes. With KSOME, the necessity for frequent code upgrades whenever there is a need to perform higher fidelity simulations is either eliminated or reduced significantly. In KSOME, the categories of various diffusion-reaction processes and the data-management system are hardwired, while the execution of the diffusion-reaction processes specific to a system is specified via input files. In the present version of KSOME, the analytical expression required to calculate defect interaction radii are inputted via a text file. However, the ability to parse mathematical expressions from a text file can be extended to input the analytical expression to calculate other defect properties; including the expressions to calculate the change in the migration barriers of mobile defects due to long-range interaction with extended defects

Nandipati, Giridhar [Pacific Northwest National La↗

DOE OSTI2018

Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals

An approximate analytic expression is derived for the ratio λ of the ascent rate of moist deep convective thermals and the maximum vertical velocity within them; λ is characterized as a function of two nondimensional buoyancy-dependent parameters y and h and is used to express the thermal ascent rate as a function of the buoyancy field. The parameter y characterizes the vertical distribution of buoyancy within the thermal, and h is the ratio of the vertically integrated buoyancy from the surface to the thermal top and the vertical integral of buoyancy within the thermal. Theoretical λ values are calculated using values of y and h obtained from idealized numerical simulations of ascending moist updrafts and compared to λ computed directly from the simulations. The theoretical values of [Formula: see text] 0.4–0.8 are in reasonable agreement with the simulated λ (correlation coefficient of 0.86). These values are notably larger than the [Formula: see text] from Hill’s (nonbuoyant) analytic spherical vortex, which has been used previously as a framework for understanding the dynamics of moist convective thermals. The relatively large values of λ are a result of net positive buoyancy within the upper part of thermals that opposes the downward-directed dynamic pressure gradient force below the thermal top. These results suggest that nonzero buoyancy within moist convective thermals, relative to their environment, fundamentally alters the relationship between the maximum vertical velocity and the thermal-top ascent rate compared to nonbuoyant vortices. Implications for convection parameterizations and interpretation of the forces contributing to thermal drag are discussed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

An improved understanding of the roles of atomic processes and power balance in divertor target ion current loss during detachment

The process of divertor detachment, whereby heat and particle fluxes to divertor surfaces are strongly diminished, is required to reduce heat loading and erosion in a magnetic fusion reactor to acceptable levels. In this paper, the physics leading to the decrease of the total divertor ion current ($I_t$), or ‘roll-over’, is experimentally explored on the TCV tokamak through characterization of the location, magnitude and role of the various divertor ion sinks and sources including a complete analysis of particle and power balance. These first measurements of the profiles of divertor ionisation and hydrogenic radiation along the divertor leg are enabled through novel spectroscopic techniques. Over a range in TCV plasma conditions (plasma current and electron density, with/ without impurity-seeding) the $I_t$ roll-over is ascribed to a drop in the divertor ion source; recombination remains small or negligible farther into the detachment process. Further, the ion source reduction is driven by both a reduction in the power available for ionization, $P_{\text{recl}}$, and concurrent increase in the energy required per ionisation, $E_{\text{ion}}$: this effect of power available on the ionization source is often described as ‘power starvation’ (or ‘power limitation’). The detachment threshold is found experimentally (in agreement with analytic model predictions) to be ~$P_{\text{recl}}/I_tE_{\text{ion}}$ ~ 2, corresponding to a target electron temperature, $T_t ~ E_{\text{ion}}/γ$ where $\gamma$ is the sheath transmission coefficient. The target pressure reduction, required to reduce the target ion current, is driven both by volumetric momentum loss as well as upstream pressure loss. The measured evolution through detachment of the divertor profile of various ion sources/ sinks as well as power losses are quantitatively reproduced through full 2D SOLPS modelling through the detachment process as the upstream density is varied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Large-Scale Trajectory Analysis via Feature Vectors

The explosion of both sensors and GPS-enabled devices has resulted in position/time data being the next big frontier for data analytics. However, many of the problems associated with large numbers of trajectories do not necessarily have an analog with many of the historic big-data applications such as text and image analysis. Modern trajectory analytics exploits much of the cutting-edge research in machine-learning, statistics, computational geometry and other disciplines. We will show that for doing trajectory analytics at scale, it is necessary to fundamentally change the way the information is represented through a feature-vector approach. We then demonstrate the ability to solve large trajectory analytics problems using this representation.

58 GEOSCIENCES↗

DOE OSTI2022

Isotherm Model for Moisture-Controlled CO 2 Sorption

Moisture-controlled sorption of CO 2 , the basis for moisture-swing CO 2 capture from air, is a novel phenomenon observed in strong-base anion exchange materials. Prior research has shown that Langmuir isotherms provide an approximate fit to moisture-controlled CO 2 sorption isotherm data. However, this fit still lacks a governing equation derived from an analytic model. As such, in this paper we derive an analytic form for an isotherm equation from a bottom-up approach, starting with a fundamental theory for an alkali liquid. In the range of interest relevant to CO 2 capture from air, an isotherm equation for an alkali liquid reduces to a simple analytic form with a single parameter, $K_{\text{eq}}$. In the limit $K_{\text{eq}} \gg 1$, a 2nd order approximation simplifies to a Langmuir isotherm that, however, deviates from experimental data. The isotherm theory for an alkali liquid has been generalized to a strong-base anion exchange material. In a strong-base anion exchange material, water concentration inside a sorbent, [H 2 O], is not large enough to be regarded as constant, which allows us to extend $K_{\text{eq}}$ to $K_{\text{eq(AEM)eff}} = K_{\text{eq(AEM)}} \times$ [H 2 O]$^{–n}$ according to the law of mass action. The final isotherm formula has been validated by experimental data from the literature. For a moisture-controlled CO 2 sorbent, $K_{\text{eq(AEM)eff}}$ varies significantly with moisture content of the sorbent. Depending on moisture level, the observed $K_{\text{eq(AEM)eff}}$ in a specific sorbent ranges from a few times to a few thousand times the value of $K_{\text{eq}}$ of a 2 mol L –1 alkali liquid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Method and system for information retrieval and aggregation from inferred user reasoning

The visual analytic system enables information retrieval within large text collections. Typically, users have to directly and explicitly query information to retrieve it. With this system and process, the reasoning of the user is inferred from the user interaction they perform in a visual analytic tool, and the appropriate information to query, process, and visualize is systematically determined.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2019

Safety Analytics Forecasting and Evaluation Reporting (SAFER)

The SAFER Sandbox is a web application for testing various types of data visualization tools that analyze safety data across national laboratories. By enabling the user to visualize this data through visual and textual analyses, the SAFER Sandbox helps to facilitate the research and support for the National Nuclear Security Administration (NNSA) Office of Safety, Infrastructure and Operations (NA-50). Safety data across the national laboratory complex is not currently analyzed in one location. This prohibits administrators from viewing safety data trends and making large scale decisions based on a holistic view of the data. By implementing data analytics web services such as representative text summary, noun phrase extraction and graph exploration, users can view and explore safety data based on search queries. The data visualizations in the SAFER Sandbox reveal trends and point to items of concern based on safety data. The SAFER Sandbox is a testing ground for these visualizations.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2017

The Impact of Streaming Data on Sensemaking with Mixed-Initative Visual Analytics

Visual data analysis helps people gain insights into data via interactive visualizations. People generate and test hypotheses and questions about data in context of the domain. This process can generally be referred to as sensemaking. Much of the work on studying sensemaking (and creating visual analytic techniques in support of it) has been focused on static datasets. However, how do the cognitive processes of sensemaking change when data are changing? Further, what implication for design does this create for mixed-initiative visual analytics systems? This paper presents the results of a user study analyzing the impact of streaming data on sensemaking. To perform this study, we developed a mixed-initiative visual analytic prototype, the Streaming Canvas, that affords the analysis of streaming text data. We compare the sensemaking process of people using this tool for a static and streaming dataset. We present the results of this study and discuss the implications on future visual analytic systems that combine machine learning and interactive visualization to help people make sense of streaming data.

visualization↗

DOE OSTI2022

Learning Global Proliferation Expertise Evolution Using AI-Driven Analytics and Public Information

Detecting and anticipating global proliferation expertise and capability evolution from unstructured, noisy, and incomplete public data streams is a highly desired, but extremely challenging task. Here, in this article, we present our pioneering data-driven approach to support the non-proliferation mission to detect and explain the evolution of proliferation expertise and capability development globally from terabytes of publicly available information (PAI), focusing on our knowledge extraction pipeline and descriptive analytics. We first discuss how we fuse nine open-source data streams, including multilingual data, to convert 4 TB of unstructured data to structured knowledge and encode dynamically evolving proliferation expertise representations—content and context graphs. For this, we rely on natural language processing (NLP) and deep learning (DL) models to perform information extraction, topic modeling, and distributed text representation (aka embedding) learning. We then present interactive, usable, and explainable descriptive analytics to refine domain knowledge and present it in a human-understandable form. Finally, we introduce future work avenues that will leverage our dynamic knowledge representations and descriptive analytics to enable predictive and prescriptive inferences to achieve real-time domain understanding and contextual reasoning about global proliferation expertise and capability evolution.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

In-Situ Magnetic Field Reconstruction in the MAGIS-100 Experiment

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.; Ferm↗

DOE OSTI2018

NBIC Biofeeds: Deploying a New, Digital Tool for Open Source Biosurveillance across Federal Agencies

The National Biosurveillance Integration Center (NBIC) is deploying a scalable, flexible open source data collection, analysis, and dissemination tool to support biosurveillance operations by the U.S. Department of Homeland Security (DHS) and its federal interagency partners.IntroductionNBIC integrates, analyzes, and distributes key information about health and disease events to help ensure the nation’s responses are well-informed, save lives, and minimize economic impact. To meet its mission objectives, NBIC utilizes a variety of data sets, including open source information, to provide comprehensive coverage of biological events occurring across the globe. NBIC Biofeeds is a digital tool designed to improve the efficiency of analyzing large volumes of open source reporting and increase the number of relevant insights gleaned from this dataset. Moreover, the tool provides a mechanism to disseminate tailored, electronic message notifications in near-real time so that NBIC can share specific information of interest to its interagency partners in a timely manner. NBIC intends to implement operational use of the capability in FY 2018. The core components of the system are data collection, curation, and dissemination of information deemed important by NBIC subject matter experts. NBIC Biofeeds has captured information from more than 70,000 unique sources published from around the globe and presents, on average, 9,000 new biosurveillance-relevant articles to users each day. NBIC leverages a variety of data feeds, including third party aggregators like Google and subscription-based feeds such as HealthMap, as well as Really Simple Syndication (RSS) feeds and web-scraping of highly relevant sources. The NBIC biosurveillance taxonomy imbedded in the tool consists of more than 600 metadata targets that cover key information for understanding the significance of an active biological event, including etiologic agents, impact to humans and animals (e.g., infection severity, healthcare workers involved, type of host), social disruption, infrastructure strain, countermeasures engaged, and ‘red flag’ characteristics (e.g., pathogen appearance in a new geographic area, unusual clinical signs). This taxonomy serves as a foundation for data curation and can be tailored by NBIC partners to more directly meet their own mission objectives. At this time, metadata is predominately captured by NBIC analysts, who manually tag information, which triggers the population of three automatically-disseminated products from the tool: 1) the NBIC Daily Biosurveillance Review, 2) immediate and daily summary email notifications, and 3) custom-designed RSS feeds. These products are meant for individual recipients in the federal interagency and for consumption by other biosurveillance information technology systems, such as the Department of Defense, Defense Threat Reduction Agency (DTRA) Biosurveillance Ecosystem (BSVE). NBIC is working in partnership with DTRA to integrate NBIC Biofeeds as an application directly into the BSVE and further develop the BSVE as an all-in-one platform for biosurveillance data analytics. To improve the efficiency and effectiveness of gaining insights using NBIC Biofeeds, developers of the tool at the Pacific Northwest National Laboratory (PNNL) are researching and testing a variety of advanced analytics techniques focused on: 1) article relevancy ratings to improve the review of queried data, 2) significance ratings to elucidate the perceived severity of an event based on reported characteristics, 3) full-text article retrieval and storage for improved machine-tagging, and 4) anomaly detection for emerging threats. Testing and implementation of new analytic capabilities in NBIC Biofeeds is planned for this fiscal year. NBIC Biofeeds was developed to serve as a sophisticated and powerful open source biosurveillance technology of value to the federal government by providing information to stakeholders conducting open source biosurveillance as well as those consuming biosurveillance information. In FY 2018, NBIC Biofeeds will begin operational use by NBIC and an initial set of users in various federal agencies. User accounts for testing purposes will be available to other federal partners, and a broad scope of federal stakeholders can receive products directly from NBIC Biofeeds based on their interests. NBIC Biofeeds is expected to enable more rapid recognition and enhanced analysis of emerging biological events by NBIC analysts. NBIC anticipates other federal agencies with biosurveillance missions will find this technology of value and intends to offer use of the platform to those federal partners that can benefit from access to the tool and information generated from NBIC Biofeeds.

NBIC↗

DOE OSTI2024

The VIBES Are Shifting: Assessing Emergent Capabilities in Multi-Modal Models

Researchers assessing open-source domains such as the internet, and particularly those studying information conflict, often have no single prescribed workflow. In the course of their research, they may need to perform a diverse array of tasks far beyond simply identifying an ever-changing set of objects. These analytical tasks can include ascertaining the provenance of images, understand an image in the context of accompanying text-based data, or identifying indicators of digital image manipulation. They must further be able to do this at the scale of tens of thousands of images or more. Traditional machine vision models have typically lacked the flexibility and breadth of performance sufficient for these needs. The research team from Pacific Northwest National Laboratory assessed the performance of a single baseline CLIP ViT-L model against a series of analytical tasks relevant for the study of online information conflict.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Clean Energy Innovation Ecosystems Discovery - Measuring Innovation Through Data Analytics (MIDAS)

As part of the Mission Innovation rollout at the Paris COP 21, 20 countries announced to double their R&D budgets over 5 years to accelerate lab-to-market clean energy innovations. These innovations must address technical urgency and navigate complex institutional, social and financial environments. To inform budget and program development, policymakers need to understand existing clean energy innovation ecosystems (IE) and their characteristics at the local, state, and regional levels within the US. Researchers at ORNL have implemented a ground-breaking application of natural language processing, link analysis, and other computational techniques to transform text and numerical data into metrics on clean energy innovation activity and geography. The 'Measuring Innovation through Data Analytics' (MIDAS) application uses data to determine where clean energy innovation ecosystems exist and the underlying scoring algorithm "ranks" the strength of the ecosystem for several clean energy technologies. The selection of the data sources is driven by the fact that a clean energy IE can be identified as an intersection of nascent clean technology efforts and financing mechanisms and related large companies located in a geographically concentrated area with an enabling environment to encourage commercialization and networking assets to facilitate communication. MIDAS is a machine-assisted methodology that provides the user with a replicable method to rapidly identify, quantify and characterize clean energy innovation ecosystems. This software application and the underlying datasets have the potential to address many important policy questions. The initial broad list of U.S. clean energy ecosystems, with geographic area, technology focus, and list and types of involved organizations can help describe regional tech activities and capabilities. Other potential applications include understanding the effect of private sector investments on ecosystem activity, and trends analysis.

Chinthavali, Supriya↗

DOE OSTI2021

Online Interactive Platform for COVID-19 Literature Visual Analytics: Platform Development Study

Background Papers on COVID-19 are being published at a high rate and concern many different topics. Innovative tools are needed to aid researchers to find patterns in this vast amount of literature to identify subsets of interest in an automated fashion. Objective We present a new online software resource with a friendly user interface that allows users to query and interact with visual representations of relationships between publications. Methods We publicly released an application called PLATIPUS (Publication Literature Analysis and Text Interaction Platform for User Studies) that allows researchers to interact with literature supplied by COVIDScholar via a visual analytics platform. This tool contains standard filtering capabilities based on authors, journals, high-level categories, and various research-specific details via natural language processing and dozens of customizable visualizations that dynamically update from a researcher’s query. Results PLATIPUS is available online and currently links to over 100,000 publications and is still growing. This application has the potential to transform how COVID-19 researchers use public literature to enable their research. Conclusions The PLATIPUS application provides the end user with a variety of ways to search, filter, and visualize over 100,00 COVID-19 publications.</:p>

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2023

Graphically Contracted Function Construction with the Recursive Pairwise Merge Algorithm

A new implementation of a recursive pairwise merge algorithm to construct a GCF from a list of CSF expansion coefficients is presented. The essential new feature is the preallocation of some work arrays used within the intermediate steps of the merge procedure. This results in roughly an order of magnitude improvement in overall efficiency and also approximately eliminates a factor of n, the molecular orbital dimension, from the original implementation. Initial application of this merge procedure to a series of H m molecules shows that the GCF wave functions can be represented well both with delocalized canonical Hartree-Fock orbitals and with localized molecular orbitals. Finally, for a given wave function complexity, as measured by the average facet count, $\bar{\text {f}}$, the delocalized Hartree-Fock orbitals show smaller errors for small $\bar{\text {f}}$ values, while the localized orbitals show smaller errors for larger $\bar{\text {f}}$ values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗