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NASA NTRS2004

Efficient Evaluation Functions for Multi-Rover Systems

Evolutionary computation can be a powerful tool in cresting a control policy for a single agent receiving local continuous input. This paper extends single-agent evolutionary computation to multi-agent systems, where a collection of agents strives to maximize a global fitness evaluation function that rates the performance of the entire system. This problem is solved in a distributed manner, where each agent evolves its own population of neural networks that are used as the control policies for the agent. Each agent evolves its population using its own agent-specific fitness evaluation function. We propose to create these agent-specific evaluation functions using the theory of collectives to avoid the coordination problem where each agent evolves a population that maximizes its own fitness function, yet the system has a whole achieves low values of the global fitness function. Instead we will ensure that each fitness evaluation function is both "aligned" with the global evaluation function and is "learnable," i.e., the agents can readily see how their behavior affects their evaluation function. We then show how these agent-specific evaluation functions outperform global evaluation methods by up to 600% in a domain where a set of rovers attempt to maximize the amount of information observed while navigating through a simulated environment.

Agogino, Adrian↗

NASA NTRS2004

Slit Function Measurement of An Imaging Spectrograph Using Fourier Transform Techniques

Knowledge of a spectrograph slit function is necessary to interpret the unresolved lines in an observed spectrum. A theoretical slit function can be calculated from the sizes of the entrance slit, the detector aperture when it functions as an exit slit, the dispersion characteristic of the disperser, and the point spread function of the spectrograph. A measured slit function is preferred to the theoretical one for the correct interpretation of the spectral data. In a scanning spectrometer with a single exit slit, the slit function is easily measured. In a fixed grating/or disperser spectrograph, illuminating the entrance slit with a near monochromatic light from a pre-monochrmator or a tunable laser and varying the wavelength of the incident light can measure the slit function. Even though the latter technique had been used successfully for the slit function measurements, it had been very laborious and it would be prohibitive to an imaging spectrograph or a multi-object spectrograph that has a large field of view. We explore an alternative technique that is manageable for the measurements. In the proposed technique, the imaging spectrograph is used as a detector of a Fourier transform spectrometer. This method can be applied not only to an IR spectrograph but also has a potential to a visible/UV spectrograph including a wedge filter spectrograph. This technique will require a blackbody source of known temperature and a bolometer to characterize the interferometer part of the Fourier Transform spectrometer. This pa?er will describe the alternative slit function measurement technique using a Fourier transform spectrometer.

Park, Hongwoo↗

NASA NTRS2001

Molecular motors and their functions in plants

Molecular motors that hydrolyze ATP and use the derived energy to generate force are involved in a variety of diverse cellular functions. Genetic, biochemical, and cellular localization data have implicated motors in a variety of functions such as vesicle and organelle transport, cytoskeleton dynamics, morphogenesis, polarized growth, cell movements, spindle formation, chromosome movement, nuclear fusion, and signal transduction. In non-plant systems three families of molecular motors (kinesins, dyneins, and myosins) have been well characterized. These motors use microtubules (in the case of kinesines and dyneins) or actin filaments (in the case of myosins) as tracks to transport cargo materials intracellularly. During the last decade tremendous progress has been made in understanding the structure and function of various motors in animals. These studies are yielding interesting insights into the functions of molecular motors and the origin of different families of motors. Furthermore, the paradigm that motors bind cargo and move along cytoskeletal tracks does not explain the functions of some of the motors. Relatively little is known about the molecular motors and their roles in plants. In recent years, by using biochemical, cell biological, molecular, and genetic approaches a few molecular motors have been isolated and characterized from plants. These studies indicate that some of the motors in plants have novel features and regulatory mechanisms. The role of molecular motors in plant cell division, cell expansion, cytoplasmic streaming, cell-to-cell communication, membrane trafficking, and morphogenesis is beginning to be understood. Analyses of the Arabidopsis genome sequence database (51% of genome) with conserved motor domains of kinesin and myosin families indicates the presence of a large number (about 40) of molecular motors and the functions of many of these motors remain to be discovered. It is likely that many more motors with novel regulatory mechanisms that perform plant-specific functions are yet to be discovered. Although the identification of motors in plants, especially in Arabidopsis, is progressing at a rapid pace because of the ongoing plant genome sequencing projects, only a few plant motors have been characterized in any detail. Elucidation of function and regulation of this multitude of motors in a given species is going to be a challenging and exciting area of research in plant cell biology. Structural features of some plant motors suggest calcium, through calmodulin, is likely to play a key role in regulating the function of both microtubule- and actin-based motors in plants.

Non-NASA Center↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

NASA NTRS2005

Quickbird Satellite in-orbit Modulation Transfer Function (MTF) Measurement Using Edge, Pulse and Impulse Methods for Summer 2003

The spatial characteristics of an imaging system cannot be expressed by a single number or simple statement. However, the Modulation Transfer Function (MTF) is one approach to measure the spatial quality of an imaging system. Basically, MTF is the normalized spatial frequency response of an imaging system. The frequency response of the system can be evaluated by applying an impulse input. The resulting impulse response is termed the Point Spread function (PSF). This function is a measure of the amount of blurring present in the imaging system and is itself a useful measure of spatial quality. An underlying assumption is that the imaging system is linear and shift-independent. The Fourier transform of the PSF is called the Optical Transfer Function (OTF) and the normalized magnitude of the OTF is the MTF. In addition to using an impulse input, a knife-edge in technique has also been used in this project. The sharp edge exercises an imaging system at all spatial frequencies. The profile of an edge response from an imaging system is called an Edge Spread Function (ESF). Differentiation of the ESF results in a one-dimensional version of the Point Spread Function (PSF). Finally, MTF can be calculated through use of Fourier transform of the PSF as stated previously. Every image includes noise in some degree which makes MTF of PSF estimation more difficult. To avoid the noise effects, many MTF estimation approaches use smooth numerical models. Historically, Gaussian models and Fermi functions were applied to reduce the random noise in the output profiles. The pulse-input method was used to measure the MTF of the Landsat Thematic Mapper (TM) using 8th order even functions over the San Mateo Bridge in San Francisco, California. Because the bridge width was smaller than the 30-meter ground sample distance (GSD) of the TM, the Nyquist frequency was located before the first zero-crossing point of the sinc function from the Fourier transformation of the bridge pulse. To avoid the zero-crossing points in the frequency domain from a pulse, the pulse width should be less than the width of two pixels (or 2 GSD's), but the short extent of the pulse results in a poor signal-to-noise ratio. Similarly, for a high-resolution satellite imaging system such as Quickbird, the input pulse width was critical because of the zero crossing points and noise present in the background area. It is important, therefore, that the width of the input pulse be appropriately sized. Finally, the MTF was calculated by taking ratio between Fourier transform of output and Fourier transform of input. Regardless of whether the edge, pulse and impulse target method is used, the orientation of the targets is critical in order to obtain uniformly spaced sub-pixel data points. When the orientation is incorrect, sample data points tend to be located in clusters that result in poor reconstruction of the edge or pulse profiles. Thus, a compromise orientation must be selected so that all spectral bands can be accommodated. This report continues by outlining the objectives in Section 2, procedures followed in Section 3, descriptions of the field campaigns in Section 4, results in Section 5, and a brief summary in Section 6.

Helder, Dennis↗

NASA NTRS2006

Spatial Correlation Function of the Chandra Selected Active Galactic Nuclei

We present the spatial correlation function analysis of non-stellar X-ray point sources in the Chandra Large Area Synoptic X-ray Survey of Lockman Hole Northwest (CLASXS). Our 9 ACIS-I fields cover a contiguous solid angle of 0.4 deg(exp 2) and reach a depth of 3 x 10(exp -15) erg/square cm/s in the 2-8 keV band. We supplement our analysis with data from the Chandra Deep Field North (CDFN). The addition of this field allows better probe of the correlation function at small scales. A total of 233 and 252 sources with spectroscopic information are used in the study of the CLASXS and CDFN fields respectively. We calculate both redshift-space and projected correlation functions in co-moving coordinates, averaged over the redshift range of 0.1 < z < 3.0, for both CLASXS and CDFN fields for a standard cosmology with Omega(sub Lambda) = 0.73,Omega(sub M) = 0.27, and h = 0.71 (H(sub 0) = 100h km/s Mpc(exp -1). The correlation function for the CLASXS field over scales of 3 Mpc< s < 200 Mpc can be modeled as a power-law of the form xi(s) = (S/SO)(exp - gamma), with gamma = 1.6(sup +0.4 sub -0.3) and S(sub o) = 8.0(sup +.14 sub -1.5) Mpc. The redshift-space correlation function for CDFN on scales of 1 Mpc< s < 100 Mpc is found to have a similar correlation length so = 8.55(sup +0.74 sub -0.74) Mpc, but a shallower slope (gamma = 1.3 +/- 0.1). The real-space correlation functions derived from the projected correlation functions, are found to be tau(sub 0 = 8.1(sup +1.2 sub -2.2) Mpc, and gamma = 2.1 +/- 0.5 for the CLASXS field, and tau(sub 0) = 5.8(sup +.1.0 sub -1.5) Mpc, gamma = 1.38(sup +0.12 sub -0.14 for the CDFN field. By comparing the real- and redshift-space correlation functions in the combined CLASXS and CDFN samples, we are able to estimate the redshift distortion parameter Beta = 0.4 +/- 0.2 at an effective redshift z = 0.94. We compare the correlation functions for hard and soft spectra sources in the CLASXS field and find no significant difference between the two groups. We have also found that the correlation between X-ray luminosity and clustering amplitude is weak, which, however, is fully consistent with the expectation using the simplest relations between X-ray luminosity, black hole mass, and dark halo mass. We study the evolution of the AGN clustering by dividing the samples into 4 redshift bins over 0.1 Mpc< z <3.0 Mpc. We find a very mild evolution in the clustering amplitude, which show the same evolution trend found in optically selected quasars in the 2dF survey. We estimate the evolution of the bias, and find that the bias increases rapidly with redshift (b(z = 0.45) = 0.95 +/- 0.15 and b(z = 2.07) = 3.03 +/- 0.83): The typical mass of the dark matter halo derived from the bias estimates show little change with redshift. The average halo mass is found to be log (M(sub halo)/M(sun))approximates 12.1. Subject headings: cosmology: observations - large-scale structure of the universe - x-rays: diffuse background - galaxies: nuclei

Yang, Y.↗

NASA NTRS2012

Methodology to Support Dynamic Function Allocation Policies Between Humans and Flight Deck Automation

Function allocation assigns work functions to all agents in a team, both human and automation. Efforts to guide function allocation systematically have been studied in many fields such as engineering, human factors, team and organization design, management science, cognitive systems engineering. Each field focuses on certain aspects of function allocation, but not all; thus, an independent discussion of each does not address all necessary aspects of function allocation. Four distinctive perspectives have emerged from this comprehensive review of literature on those fields: the technology-centered, human-centered, team-oriented, and work-oriented perspectives. Each perspective focuses on different aspects of function allocation: capabilities and characteristics of agents (automation or human), structure and strategy of a team, and work structure and environment. This report offers eight issues with function allocation that can be used to assess the extent to which each of issues exist on a given function allocation. A modeling framework using formal models and simulation was developed to model work as described by the environment, agents, their inherent dynamics, and relationships among them. Finally, to validate the framework and metrics, a case study modeled four different function allocations between a pilot and flight deck automation during the arrival and approach phases of flight.

Johnson, Eric N.↗

NASA NTRS2004

Functional Groups Based on Leaf Physiology: Are they Spatially and Temporally Robust?

The functional grouping hypothesis, which suggests that complexity in ecosystem function can be simplified by grouping species with similar responses, was tested in the Florida scrub habitat. Functional groups were identified based on how species in fire maintained Florida scrub regulate exchange of carbon and water with the atmosphere as indicated by both instantaneous gas exchange measurements and integrated measures of function (%N, delta C-13, delta N-15, C-N ratio). Using cluster analysis, five distinct physiologically-based functional groups were identified in the fire maintained scrub. These functional groups were tested to determine if they were robust spatially, temporally, and with management regime. Analysis of Similarities (ANOSIM), a non-parametric multivariate analysis, indicated that these five physiologically-based groupings were not altered by plot differences (R = -0.115, p = 0.893) or by the three different management regimes; prescribed burn, mechanically treated and burn, and fire-suppressed (R = 0.018, p = 0.349). The physiological groupings also remained robust between the two climatically different years 1999 and 2000 (R = -0.027, p = 0.725). Easy-to-measure morphological characteristics indicating functional groups would be more practical for scaling and modeling ecosystem processes than detailed gas-exchange measurements, therefore we tested a variety of morphological characteristics as functional indicators. A combination of non-parametric multivariate techniques (Hierarchical cluster analysis, non-metric Multi-Dimensional Scaling, and ANOSIM) were used to compare the ability of life form, leaf thickness, and specific leaf area classifications to identify the physiologically-based functional groups. Life form classifications (ANOSIM; R = 0.629, p 0.001) were able to depict the physiological groupings more adequately than either specific leaf area (ANOSIM; R = 0.426, p = 0.001) or leaf thickness (ANOSIM; R 0.344, p 0.001). The ability of life forms to depict the physiological groupings was improved by separating the parasitic Ximenia americana from the shrub category (ANOSIM; R = 0.794, p = 0.001). Therefore, a life form classification including parasites was determined to be a good indicator of the physiological processes of scrub species, and would be a useful method of grouping for scaling physiological processes to the ecosystem level.

Foster, Tammy E.↗

NASA NTRS2014

Treadmill Exercise with Increased Body Loading Enhances Post Flight Functional Performance

The goals of the Functional Task Test (FTT) study were to determine the effects of space flight on functional tests that are representative of high priority exploration mission tasks and to identify the key underlying physiological factors that contribute to decrements in performance. Ultimately this information will be used to assess performance risks and inform the design of countermeasures for exploration class missions. We have previously shown that for Shuttle, ISS and bed rest subjects functional tasks requiring a greater demand for dynamic control of postural equilibrium (i.e. fall recovery, seat egress/obstacle avoidance during walking, object translation, jump down) showed the greatest decrement in performance. Functional tests with reduced requirements for postural stability (i.e. hatch opening, ladder climb, manual manipulation of objects and tool use) showed little reduction in performance. These changes in functional performance were paralleled by similar decrements in sensorimotor tests designed to specifically assess postural equilibrium and dynamic gait control. The bed rest analog allows us to investigate the impact of axial body unloading in isolation on both functional tasks and on the underlying physiological factors that lead to decrements in performance and then compare them with the results obtained in our space flight study. These results indicate that body support unloading experienced during space flight plays a central role in postflight alteration of functional task performance. Given the importance of body-support loading we set out to determine if there is a relationship between the load experienced during inflight treadmill exercise (produced by a harness and bungee system) and postflight functional performance. ISS crewmembers (n=13) were tested using the FTT protocol before and after 6 months in space. Crewmembers were tested three times before flight, and on 1, 6, and 30 days after landing. To determine how differences in body-support loading experienced during inflight treadmill exercise impacts postflight functional performance, the loading history for each subject during inflight treadmill (T2) exercise was correlated with postflight measures of performance. Crewmembers who walked on the treadmill with higher pull-down loads had less decrement in postflight postural stability and dynamic locomotor control than those subjects who exercised with lighter loads. These data point to the importance of providing significant body loading during inflight treadmill exercise. This and the addition of specific balance training may further mitigate decrements in critical mission tasks that require dynamic postural stability and mobility. Inflight treadmill exercise provides a multi-disciplinary platform to provide sensorimotor, aerobic and bone mechanical stimuli benefits. Forward work will focus on the development of an inflight training system that will integrate aerobic, resistive and balance training modalities into a single interdisciplinary countermeasure system for exploration class missions.

Bloomberg, J. J.↗

NASA NTRS2014

The Evolution of the Galaxy Rest-Frame Ultraviolet Luminosity Function Over the First Two Billion Years

We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity function at z = 4 to 8. We use deep Hubble Space Telescope imaging over the CANDELS/GOODS fields, the Hubble Ultra Deep Field and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1- 2403 clusters. The combination of these surveys provides an effective volume of 0.6-1.2 ×10(exp 6) Mpc(exp 3) over this epoch, allowing us to perform a robust search for bright (M(sub UV) less than −21) and faint (M(sub UV) = −18) galaxies. We select galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 galaxies at 3.5 less than z less than 8.5, with more than 1000 galaxies at z of approximately 6 - 8. We measure both a stepwise luminosity function for galaxies in our redshift samples, as well as a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright galaxies at z of greater than or equal to 6. Our bestfit value of the characteristic magnitude M* is consistent with −21 at z of greater than or equal to 5, different than that inferred based on previous trends at lower redshift. At z = 8, a single power-law provides an equally good fit to the UV luminosity function, while at z = 6 and 7, an exponential cutoff at the bright-end is moderately preferred. We compare our luminosity functions to semi-analytical models, and find that the lack of evolution in M* is consistent with models where the impact of dust attenuation on the bright-end of the luminosity function decreases at higher redshift, though a decreasing impact of feedback may also be possible. We measure the evolution of the cosmic star-formation rate (SFR) density by integrating our observed luminosity functions to M(sub UV) = −17, correcting for dust attenuation, and find that the SFR density declines proportionally to (1 + z)((exp −4.3)(+/-)(0.5)) at z greater than 4, consistent with observations at z greater than or equal to 9. Our observed luminosity functions are consistent with a reionization history that starts at redshift of approximately greater than 10, completes at z greater than 6, and reaches a midpoint (x(sub HII) = 0.5) at 6.7 less than z less than 9.4. Finally, using a constant cumulative number density selection and an empirically derived rising star-formation history, our observations predict that the abundance of bright z = 9 galaxies is likely higher than previous constraints, though consistent with recent estimates of bright z similar to 10 galaxies.

Galaxy↗

NASA NTRSDate not supplied

Custom Integration of Multiple Medical Functionalities

INTRODUCTION: Previous spaceflight experience and results from probabilistic risk assessment of spaceflight medical risk have highlighted the need for vital sign measurements, medical scopes, and clinical imaging tools for managing medical conditions during spaceflight. The Human Research Program’s Exploration Medical Capability (ExMC) Element and the Mars Campaign Office’s Exploration Medical Integrated Product Team (XMIPT) have performed ground-based evaluations of two Commercial-off-the-Shelf (COTS) Multi-functional Integrated Medical (MIM) devices, which integrate various medical capabilities together in one device. The key findings from these evaluations are presented in a complementary presentation, leaving this presentation to focus on forward recommendations for customized integration of multiple medical functionalities. KEY COMPONENTS: The key features of a custom integration of multiple medical functionalities includes devices and capabilities that optimally reduce medical risk. The COTS MIM devices incorporated functionality for best supporting Earth-based, emergency, pre-hospital care. Our custom integration will use probabilistic risk assessment tools, such as the Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT), to determine the optimal functionality to include based on medical risk minimization. An additional feature of custom integration includes the ability to adapt to different requirements within different vehicles and/or missions. The COTS MIM devices store data in patient specific records, however, the format of the records is not modifiable, and data are not easily transferred from the MIM device to a central data architecture outside of the manufacturer’s established system. Our concept for custom integration will use devices that have an open application programming interface, which can easily connect to independent data architectures and third-party visualization software. The ultrasound capabilities included within the COTS MIM devices did not satisfy many of the Artemis Research and Operations Working Group’s ultrasound functional needs, and therefore, incorporation of higher quality ultrasound capabilities within a customized integration will be beneficial. The COTS MIM devices included minimal procedural guidance and clinical decision support tools. Supplemental tools of this type would need to be supplied along with the COTS MIM devices if they were to be used operationally, so another advantage of customization is the ability to integrate these support tools along with the medical functionality, for a more streamlined user experience. CONCLUSION: Investigation of a customized integration of medical functionality provides a method for further understanding the needs of a long-term exploration spaceflight medical system. The crew members of these exploration missions will need to operate more and more independently from Earth-based ground support. Therefore, having an optimized, streamlined medical system, which contains the functionality and supporting information needed, while remaining within mission and vehicle constraints, will help to maintain crew health and performance, which is necessary for achieving high levels of mission success.

B E Lewandowski↗

DOE OSTI2013

Dynamical model for longitudinal wave functions in light-front holographic QCD

We construct a Schrödinger-like equation for the longitudinal wave function of a meson in the valence qq{sup -bar} sector, based on the ’t Hooft model for large-N two-dimensional QCD, and combine this with the usual transverse equation from light-front holographic QCD, to obtain a model for mesons with massive quarks. The computed wave functions are compared with the wave function ansatz of Brodsky and de Téramond and used to compute decay constants and parton distribution functions. The basis functions used to solve the longitudinal equation may be useful for more general calculations of meson states in QCD. -- Highlights: •Provide relativistic quark model based on light-front holographic QCD. •Incorporate dependence on quark mass. •Consistent with the Brodsky–de Téramond quark-wave-function ansatz. •Compute meson decay constants and parton distribution functions. •Illustrate use of basis functions that could be convenient for more general numerical calculations in light-front QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

Results of Perdew–Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, where the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol for small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F 2 molecule being a notable outlier.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

The density matrix functional approach to electron correlation: Dynamic and nondynamic correlation along the full dissociation coordinate

For chemistry an accurate description of bond weakening and breaking is vital. The great advantage of density matrix functionals, as opposed to density functionals, is their ability to describe such processes since they naturally cover both nondynamical and dynamical correlation. This is obvious in the Löwdin-Shull functional, the exact natural orbital functional for two-electron systems. We present in this paper extensions of this functional for the breaking of a single electron pair bond in N-electron molecules, using LiH, BeH{sup +}, and Li{sub 2} molecules as prototypes. Attention is given to the proper formulation of the functional in terms of not just J and K integrals but also the two-electron L integrals (K integrals with a different distribution of the complex conjugation of the orbitals), which is crucial for the calculation of response functions. Accurate energy curves are obtained with extended Löwdin-Shull functionals along the complete dissociation coordinate using full CI calculations as benchmark.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Multicomponent density functional theory embedding formulation

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

The primary goal of Kohn–Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao–Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE), Tao–Perdew–Staroverov–Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree–Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Lastly, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Comparative study of Minnesota functionals performance on ferroelectric BaTiO 3 and PbTiO 3

Density functional theory based simulations are the leading tool for the computational investigation of ferroelectrics and the parametrization of their classical potentials. However, the predictions often depend strongly on the exchange correlation functional. The most popular choices, LDA and GGA, tend to underestimate or overestimate some structural, electric, and energy properties. These impede development of highly accurate classical potentials that extend the reach of first-principles simulations to finite temperatures and realistic sizes. In this work, we investigate the performance of recently developed Minnesota exchange correlation functionals on prototypical ferroelectrics BaTiO 3 , and PbTiO 3 , in comparison with some popular ones. We find that there exists strong correlation between predictions for some properties (tetragonality, phase energy difference, and polarization) by different functionals. Along the correlation line, we find a range of functionals (including some from the Minnesota suite) whose predictions fall in between those of LDA and GGA and, therefore, offer an improvement. A way to relatively rank functional performance with respect to chosen benchmarks is proposed and applied to identify the top performers for BaTiO 3 and PbTiO 3 . Here, the performance is found to be material dependent. Therefore, we propose that the performance assessment carried out in this work is employed to "screen" functionals prior to their use on ferroelectrics. Quick and computationally inexpensive, it is likely to lead to improved descriptions, especially for classical potential parametrization. The Minnesota functional suite is found to be suitable for this task.

36 MATERIALS SCIENCE↗