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DOE OSTI2013

ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy

A 10-parameter, range-separated hybrid (RSH), generalized gradient approximation (GGA) density functional with nonlocal correlation (VV10) is presented in this paper. Instead of truncating the B97-type power series inhomogeneity correction factors (ICF) for the exchange, same-spin correlation, and opposite-spin correlation functionals uniformly, all 16 383 combinations of the linear parameters up to fourth order (m = 4) are considered. These functionals are individually fit to a training set and the resulting parameters are validated on a primary test set in order to identify the 3 optimal ICF expansions. Through this procedure, it is discovered that the functional that performs best on the training and primary test sets has 7 linear parameters, with 3 additional nonlinear parameters from range-separation and nonlocal correlation. The resulting density functional, ωB97X-V, is further assessed on a secondary test set, the parallel-displaced coronene dimer, as well as several geometry datasets. Finally and furthermore, the basis set dependence and integration grid sensitivity of ωB97X-V are analyzed and documented in order to facilitate the use of the functional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is a consequence of a complex interplay among the lattice, phonons, and electrons. Interestingly, a large number of NTE materials have been found in various types of functional materials. In the last two decades good progress has been achieved to discover new phenomena and mechanisms of NTE. In the present review article, NTE is reviewed in functional materials of ferroelectrics, magnetics, multiferroics, superconductors, temperature-induced electron configuration change and so forth. Zero thermal expansion (ZTE) of functional materials is emphasized due to the importance for practical applications. The NTE functional materials present a general physical picture to reveal a strong coupling role between physical properties and NTE. There is a general nature of NTE for both ferroelectrics and magnetics, in which NTE is determined by either ferroelectric order or magnetic one. In NTE functional materials, a multi-way to control thermal expansion can be established through the coupling roles of ferroelectricity-NTE, magnetism-NTE, change of electron configuration-NTE, open-framework-NTE, and so on. Chemical modification has been proved to be an effective method to control thermal expansion. Finally, challenges and questions are discussed for the development of NTE materials. There remains a challenge to discover a “perfect” NTE material for each specific application for chemists. The future studies on NTE functional materials will definitely promote the development of NTE materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Benchmarking density functional theory predictions of framework structures and properties in a chemically diverse test set of metal-organic frameworks

We compiled a test set of chemically and topologically diverse Metal–Organic Frameworks (MOFs) with high accuracy experimentally derived crystallographic structure data. The test set was used to benchmark the performance of Density Functional Theory (DFT) functionals (M06L, PBE, PW91, PBE-D2, PBE-D3, and vdW-DF2) for predicting lattice parameters, unit cell volume, bonded parameters and pore descriptors. On average PBE-D2, PBE-D3, and vdW-DF2 predict more accurate structures, but all functionals predicted pore diameters within 0.5 Å of the experimental diameter for every MOF in the test set. The test set was also used to assess the variance in performance of DFT functionals for elastic properties and atomic partial charges. The DFT predicted elastic properties such as minimum shear modulus and Young's modulus can differ by an average of 3 and 9 GPa for rigid MOFs such as those in the test set. Moreover, we calculated the partial charges by vdW-DF2 deviate the most from other functionals while there is no significant difference between the partial charges calculated by M06L, PBE, PW91, PBE-D2 and PBE-D3 for the MOFs in the test set. We find that while there are differences in the magnitude of the properties predicted by the various functionals, these discrepancies are small compared to the accuracy necessary for most practical applications.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Improved spatial resolution for spot sampling in thermal desorption atomic force microscopy – mass spectrometry via rapid heating functions

The key to advancing materials is to understand and control their structure and chemistry. However, thorough chemical characterization is challenging since existing techniques characterize only a few properties of the specimen, thereby necessitating multiple measurement platforms to acquire the necessary information. The multimodal combination of atomic force microscopy (AFM) and mass spectrometry (MS) transcends existing analytical capabilities for nanometer scale spatially resolved correlation of the chemical and physical properties of a sample surface. One such hybrid system employs heated AFM cantilevers for thermal desorption (TD) sampling of molecules from a surface and subsequent gas phase ionization and detection of the liberated species by MS. Here in this paper, we report on the use of voltage pulse trains to tailor cantilever heating such that spot sampling size was reduced and mass spectral signal was improved compared to constant voltage, static heating of the cantilever. Desorption efficiency (DE), defined as the quotient of the mass spectral signal intensity and the volume of the desorption crater, was used to judge the effectiveness of a particular tailored heating function. To guide the development and optimization of the heating functions and aid in interpreting experimental results, a 1D finite element model was developed that predicted the cantilever response to different heating functions. Three tailored heating functions that used different combinations, magnitudes, and durations of rectangular voltage pulses, were used for surface spot sampling. The resultant sampling spot size and DE were compared to the same metrics obtained with the conventional method that uses a single voltage pulse. Using a model system composed of a thin film of ink containing pigment yellow 74 as a model system, desorption craters shrunk from 2 μm, using the conventional approach, to 310 nm using the optimum tailored heating function. This same pulsed heating function produced a 381× improvement in the DE and an 8× improvement in spatial resolution compared to the conventional heating approach showing that signal/amount of material sampled was improved significantly by this new cantilever heating strategy.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Evidence for non-electrostatic interactions between a pyrophosphate-functionalized uranyl peroxide nanocluster and iron (hydr)oxide minerals

We report the terminal oxygen atoms of the pyrophosphate groups in the uranyl peroxide nanocluster U 24 Pp 12 ([(UO 2 ) 24 (O 2 ) 24 (P 2 O 7 ) 12 ] 48- ) are not fully satisfied by bond valence considerations and can become protonated. This functionality could allow for specific interactions with mineral surfaces, as opposed to the electrostatically-driven interactions observed between non-functionalized uranyl peroxide nanoclusters and mineral surfaces. The sorption of U 24 Pp 12 to goethite and hematite was studied using batch sorption experiments as a function of U 24 Pp 12 concentration, mineral concentration, and pH. A suite of spectroscopic techniques, scanning electron microscopy, and electrophoretic mobility measurements were used to examine the minerals before and after reaction with U 24 Pp 12 , leading to a proposed conceptual model for U 24 Pp 12 interactions with goethite. The governing rate laws were determined and compared to those previously determined for a non-functionalized uranyl peroxide nanocluster. The rate of uranyl peroxide nanocluster sorption depends on the charge density and functionalized component of the uranyl peroxide cage. Electrophoretic mobility and attenuated total reflectance Fourier transform infrared spectroscopy analyses show that an inner-sphere complex forms between the U 24 Pp 12 cluster and the goethite surface through the terminal pyrophosphate groups, leading to a proposed conceptual model in which U 24 Pp 12 interacts with the triply-coordinated reactive sites on the (110) plane of goethite. Finally, these results demonstrate that the behavior of U 24 Pp 12 at the iron (hydr)oxide-water interface is unique relative to interactions of the uranyl ion and non-functionalized uranyl peroxide nanoclusters.

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

Computational insights into the interaction of water with the UiO-66 metal–organic framework and its functionalized derivatives

The UiO-66 metal–organic framework (MOF) has been identified as a promising hydrophilic material for water harvesting. Recent studies show that its water uptake ability at low relative humidity (RH) can be improved by incorporating hydrophilic functional groups into the framework. In this work, we provide computational insights into the adsorption of water in UiO-66 and its functionalized derivatives to reveal the role played by different adsorption sites and functional groups in the adsorption mechanism. We started by developing molecular models for UiO-66, UiO-66-NH 2 , UiO-66-OH, and UiO-66-(OH) 2 compatible with the MB-pol data-driven many-body potential of water. We then benchmarked these models against ab initio data. Here we used these models to perform molecular dynamics simulations and calculate radial distribution functions, IR spectra, and two-dimensional density distribution maps for water in the MOFs. These results consistently show that the μ 3 -OH sites are the preferential interaction sites for water in UiO-66 and all its variants, and the formation of localised water clusters inside the octahedral pores is responsible for the abrupt step in the experimental adsorption isotherms. Furthermore, the presence of functional groups in the framework allows water to cluster in the octahedral pores at lower RH, thus making the MOF a more efficient water harvester. Overall, this study provides molecular-level insights into the pore filling process of UiO-66 and its functionalized derivatives, which are needed for the design of efficient water harvesting materials based on MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Planck 2013 results. IV. Low Frequency Instrument beams and window functions

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). Knowledge of the beam profiles is necessary for determining the transfer function to go from the observed to the actual sky anisotropy power spectrum. The main beam distortions affect the beam window function, complicating the reconstruction of the anisotropy power spectrum at high multipoles, whereas the sidelobes affect the low and intermediate multipoles. The in-flight assessment of the LFI main beams relies on the measurements performed during Jupiter observations. By stacking the datafrom multiple Jupiter transits, the main beam profiles are measured down to-20 dB at 30 and 44 GHz, and down to-25 dB at 70 GHz. The main beam solid angles are determined to better than 0.2% at each LFI frequency band. The Planck pre-launch optical model is conveniently tuned to characterize the main beams independently of any noise effects. This approach provides an optical model whose beams fully reproduce the measurements in the main beam region, but also allows a description of the beams at power levels lower than can be achieved by the Jupiter measurements themselves. The agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band. The simulated beams are used for the computation of the window functions for the effective beams. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer bandshapes. The total uncertainties in the effective beam window functions are: 2% and 1.2% at 30 and 44 GHz, respectively (at ℓ ≈ 600), and 0.7% at 70 GHz (at ℓ ≈ 1000).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Structural connectivity in schizophrenia and its impact on the dynamics of spontaneous functional networks

The neuropathology of schizophrenia remains unclear. Some insight has come from modern neuroimaging techniques, which offer an unparalleled opportunity to explore in vivo the structure and function of the brain. Using functional magnetic resonance imaging, it has been found that the large-scale resting-state functional connectivity (rsFC) in schizophrenia — measured as the temporal correlations of the blood-oxygen-level-dependent (BOLD) signal — exhibit altered network topology, with lower small-world index. The origin of these rsFC alterations and link with the underlying structural connectivity remain unclear. In this work, we used a computational model of spontaneous large-scale brain activity to explore the role of the structural connectivity in the large-scale dynamics of the brain in health and schizophrenia. The structural connectomes from 15 adolescent patients with early-onset schizophrenia and 15 age- and gender-matched controls were built from diffusion tensor imaging data to detect the white matter tracts between 90 brain areas. Brain areas, simulated using a reduced dynamic mean-field model, receive excitatory input from other areas in proportion to the number of fibre tracts between them. The simulated mean field activity was transformed into BOLD signal, and the properties of the simulated functional networks were analyzed. Our results suggest that the functional alterations observed in schizophrenia are not directly linked to alterations in the structural topology. Instead, subtly randomized and less small-world functional networks appear when the brain operates with lower global coupling, which shifts the dynamics from the optimal healthy regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Stiffness and strength of oxygen-functionalized graphene with vacancies

The 2D elastic modulus (E{sup 2D}) and strength (σ{sup 2D}) of defective graphene sheets containing vacancies, epoxide, and hydroxyl functional groups are evaluated at 300 K by atomistic simulations. The fraction of vacancies is controlled in the range 0% to 5%, while the density of functional groups corresponds to O:C ratios in the range 0% to 25%. In-plane modulus and strength diagrams as functions of vacancy and functional group densities are generated using models with a single type of defect and with combinations of two types of defects (vacancies and functional groups). It is observed that in models containing only vacancies, the rate at which strength decreases with increasing the concentration of defects is largest, followed by models containing only epoxide groups and those with only hydroxyl groups. The effect on modulus of vacancies and epoxides present alone in the model is similar, and much stronger than that of hydroxyl groups. When the concentration of defects is large, the combined effect of the functional groups and vacancies cannot be obtained as the superposition of individual effects of the two types of defects. The elastic modulus deteriorates faster (slower) than predicted by superposition in systems containing vacancies and hydroxyl groups (vacancies and epoxide groups)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The screening effects of the screened exchange hybrid functional in surface systems: A case study on the CO/Pt(111) problem

The screened exchange (sX) hybrid functional has been widely used in computational material science. Although it has widely been studied in bulk systems, less is known about its functional behavior in surface systems which are crucial to many technologies such as materials synthesis and nano-electronic devices. Assessing the screening dependent functional behaviors in the surface systems is therefore important for its application in such systems. In this work, we investigate the screening effects of the sX in CO adsorption on Pt(111) surface. The differences between the sX and Heyd-Scuseria-Ernzerhof (HSE06) hybrid functionals, and the effects of screening parameters are studied. The screening has two effects: first, the HOMO-LUMO gap is screening dependent. This affects the site preference most significantly. In this work, atop adsorption of CO/Pt(111) is predicted by the hybrid functionals with screened exchange potential. The sX(1.44) gives the largest HOMO-LUMO gap for the isolated CO molecule. The adsorption energy difference between the atop and fcc site is also the largest by the sX(1.44) which is explained by the reduced metal d states to the CO 2π* state back-donation, with stronger effect for the fcc adsorption than for the atop adsorption; second, the adsorption energy is screening dependent. This can be seen by comparing the sX(2.38) and HSE06 which have different screening strengths. They show similar surface band structures for the CO adsorption but different adsorption energies, which is explained by the stronger CO 5σ state to the metal d states donation or the effectively screened Pauli repulsion. This work underlines the screening strength as a main difference between sX and HSE06, as well as an important hybrid functional parameter for surface calculation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Weight-lattice discretization of Weyl-orbit functions

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight lattice, so that digitized data on the fundamental region can be Fourier-analyzed. The discretized orbit function has arguments that are redundant if related by the affine Weyl group, while its labels, the Weyl-orbit representatives, invoke the dual affine Weyl group. Here we discretize the orbit functions in a novel way, by using the weight lattice. A cleaner theory results with symmetry between the arguments and labels of the discretized orbit functions. Orthogonality of the new discretized orbit functions is proved, and leads to the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For one type of orbit function, the matrix coincides with the Kac-Peterson modular S matrix, important for Wess-Zumino-Novikov-Witten conformal field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Work function and surface stability of tungsten-based thermionic electron emission cathodes

Materials that exhibit a low work function and therefore easily emit electrons into vacuum form the basis of electronic devices used in applications ranging from satellite communications to thermionic energy conversion. W–Ba–O is the canonical materials system that functions as the thermionic electron emitter commercially used in a range of high-power electron devices. However, the work functions, surface stability, and kinetic characteristics of a polycrystalline W emitter surface are still not well understood or characterized. In this study, we examined the work function and surface stability of the eight lowest index surfaces of the W–Ba–O system using density functional theory methods. We found that under the typical thermionic cathode operating conditions of high temperature and low oxygen partial pressure, the most stable surface adsorbates are Ba–O species with compositions in the range of Ba 0.125 O–Ba 0.25 O per surface W atom, with O passivating all dangling W bonds and Ba creating work function-lowering surface dipoles. Wulff construction analysis reveals that the presence of O and Ba significantly alters the surface energetics and changes the proportions of surface facets present under equilibrium conditions. In conclusion, analysis of previously published data on W sintering kinetics suggests that fine W particles in the size range of 100-500 nm may be at or near equilibrium during cathode synthesis and thus may exhibit surface orientation fractions well described by the calculated Wulff construction.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Structural, electronic, and dynamical properties of liquid water by ab initio molecular dynamics based on SCAN functional within the canonical ensemble

We perform ab initio molecular dynamics (AIMD) simulation of liquid water in the canonical ensemble at ambient conditions using the strongly constrained and appropriately normed (SCAN) meta-generalized-gradient approximation (GGA) functional approximation and carry out systematic comparisons with the results obtained from the GGA-level Perdew-Burke-Ernzerhof (PBE) functional and Tkatchenko-Scheffler van der Waals (vdW) dispersion correction inclusive PBE functional. We analyze various properties of liquid water including radial distribution functions, oxygen-oxygen-oxygen triplet angular distribution, tetrahedrality, hydrogen bonds, diffusion coefficients, ring statistics, density of states, band gaps, and dipole moments. We find that the SCAN functional is generally more accurate than the other two functionals for liquid water by not only capturing the intermediate-range vdW interactions but also mitigating the overly strong hydrogen bonds prescribed in PBE simulations. We also compare the results of SCAN-based AIMD simulations in the canonical and isothermal-isobaric ensembles. Our results suggest that SCAN provides a reliable description for most structural, electronic, and dynamical properties in liquid water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Finding the “lost-time” in detonator function

Exploding bridgewire (EBW) detonators were invented during the Manhattan Project over 75 years ago. Initially developed for precise timing and reproducibility, they continue to be used in many applications. Despite widespread use and reliability, their mechanism for function remains controversial. They provide precision timing, yet their function is described in terms of a “lost time” accounting for nearly half of the function time. Buried in understanding the EBW function is the mystery of how an incoherent impulse such as powering a bridgewire yields the coherent energy output of a detonation. Even the general phenomena by which release of chemical energy in a crystalline organic explosive becomes associated with the sonic plane of a steady detonation wave remain uncertain. Here, we investigate the EBW function with a suite of diagnostics and show that stationary heating occurs during the “lost-time.” We use x-ray radiography to observe the propagation of a shock wave from bridgewire vaporization and establish that the origin of the radially emanating detonation wave is spatially separated from the initial shock. Utilizing the observed temperature as a boundary condition in our explosive response models yields a thermal ignition consistent with the “lost-time” and detonation location consistent with previous work. With these findings, we define a direct thermal initiation mechanism for the EBW function consistent with previous integral observations and explain the displacement of initiation from the bridgewire burst in time and space.

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

Plasma thermal transport with a generalized 8-moment distribution function

Moment equations that model plasma transport require an ansatz distribution function to close the system of equations. The resulting transport is sensitive to the specific closure used, and several options have been proposed in the literature. Two different 8-moment distribution functions can be generalized to form a single-parameter family of distribution functions. The transport coefficients resulting from this generalized distribution function can be expressed in terms of this free parameter. This provides the flexibility of matching the 8-moment model to some validating result at a given magnetization value, such as Braginskii’s transport, or the more recent results of Davies et al. [Physics of Plasma, 28, 012305 (2021)]. Here, this process can be thought of as solving for the 8-moment distribution function that matches the value of a transport coefficient given by a Chapman-Enskog expansion, while retaining the improved physical properties, such as finite propagation speeds and time dependence which belong to the hyperbolic moment models. Since the presented generalized distribution function only has a single free parameter, only a single transport coefficient can be matched at a time. However, this generalization process may be extended to provide multiple free parameters. The focus of this Brief Communication is on the dramatically improved thermal conductivity of the proposed model compared to the two base moment models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Understanding the effect of density functional choice and van der Waals treatment on predicting the binding configuration, loading, and stability of amine-grafted metal organic frameworks

Metal organic frameworks (MOFs) are crystalline, three-dimensional structures with high surface areas and tunable porosities. Made from metal nodes connected by organic linkers, the exact properties of a given MOF are determined by node and linker choice. MOFs hold promise for numerous applications, including gas capture and storage. M2(4,4′-dioxidobiphenyl-3,3′-dicarboxylate)—henceforth simply M2(dobpdc), with M = Mg, Mn, Fe, Co, Ni, Cu, or Zn—is regarded as one of the most promising structures for CO2 capture applications. Further modification of the MOF with diamines or tetramines can significantly boost gas species selectivity, a necessity for the ultra-dilute CO2 concentrations in the direct-air capture of CO2. There are countless potential diamines and tetramines, paving the way for a vast number of potential sorbents to be probed for CO2 adsorption properties. The number of amines and their configuration in the MOF pore are key drivers of CO2 adsorption capacity and kinetics, and so a validation of computational prediction of these quantities is required to suitably use computational methods in the discovery and screening of amine-functionalized sorbents. In this work, we study the predictive accuracy of density functional theory and related calculations on amine loading and configuration for one diamine and two tetramines. In particular, we explore the Perdew–Burke–Ernzerhof (PBE) functional and its formulation for solids (PBEsol) with and without the Grimme-D2 and Grimme-D3 pairwise corrections (PBE+D2/3 and PBEsol+D2/3), two revised PBE functionals with the Grimme-D2 and Grimme-D3 pairwise corrections (RPBE+D2/3 and revPBE+D2/3), and the nonlocal van der Waals correlation (vdW-DF2) functional. We also investigate a universal graph deep learning interatomic potential’s (M3GNet) predictive accuracy for loading and configuration. These results allow us to identify a useful screening procedure for configuration prediction that has a coarse component for quick evaluation and a higher accuracy component for detailed analysis. Our general observation is that the neural network-based potential can be used as a high-level and rapid screening tool, whereas PBEsol+D3 gives a completely qualitatively predictive picture across all systems studied, and can thus be used for high accuracy motif predictions. We close by briefly exploring the predictions of relative thermal stability for the different functionals and dispersion corrections.

Chemistry↗
DOE OSTI2016

Functional remediation components: A conceptual method of evaluating the effects of remediation on risks to ecological receptors

Governmental agencies, regulators, health professionals, tribal leaders, and the public are faced with understanding and evaluating the effects of cleanup activities on species, populations, and ecosystems. While engineers and managers understand the processes involved in different remediation types such as capping, pump and treat, and natural attenuation, there is often a disconnect between (1) how ecologists view the influence of different types of remediation, (2) how the public perceives them, and (3) how engineers understand them. The overall goal of the present investigation was to define the components of remediation types (= functional remediation). Objectives were to (1) define and describe functional components of remediation, regardless of the remediation type, (2) provide examples of each functional remediation component, and (3) explore potential effects of functional remediation components in the post-cleanup phase that may involve continued monitoring and assessment. Functional remediation components include types, numbers, and intensity of people, trucks, heavy equipment, pipes, and drill holes, among others. Several components may be involved in each remediation type, and each results in ecological effects, ranging from trampling of plants, to spreading invasive species, to disturbing rare species, and to creating fragmented habitats. In some cases remediation may exert a greater effect on ecological receptors than leaving the limited contamination in place. A goal of this conceptualization is to break down functional components of remediation such that managers, regulators, and the public might assess the effects of timing, extent, and duration of different remediation options on ecological systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

The luminosity function at z ∼ 8 from 97 Y-band dropouts: Inferences about reionization

We present the largest search to date for Y-band dropout galaxies (z ∼ 8 Lyman break galaxies, LBGs) based on 350 arcmin{sup 2} of Hubble Space Telescope observations in the V, Y, J, and H bands from the Brightest of Reionizing Galaxies (BoRG) survey. In addition to previously published data, the BoRG13 data set presented here includes approximately 50 arcmin{sup 2} of new data and deeper observations of two previous BoRG pointings, from which we present 9 new z ∼ 8 LBG candidates, bringing the total number of BoRG Y-band dropouts to 38 with 25.5 ≤ m{sub J} ≤ 27.6 (AB system). We introduce a new Bayesian formalism for estimating the galaxy luminosity function, which does not require binning (and thus smearing) of the data and includes a likelihood based on the formally correct binomial distribution as opposed to the often-used approximate Poisson distribution. We demonstrate the utility of the new method on a sample of 97 Y-band dropouts that combines the bright BoRG galaxies with the fainter sources published in Bouwens et al. from the Hubble Ultra Deep Field and Early Release Science programs. We show that the z ∼ 8 luminosity function is well described by a Schechter function over its full dynamic range with a characteristic magnitude M{sup ⋆}=−20.15{sub −0.38}{sup +0.29}, a faint-end slope of α=−1.87{sub −0.26}{sup +0.26}, and a number density of log{sub 10} ϕ{sup ⋆}[Mpc{sup −3}]=−3.24{sub −0.24}{sup +0.25}. Integrated down to M = –17.7, this luminosity function yields a luminosity density log{sub 10} ϵ[erg s{sup −1} Hz{sup −1} Mpc{sup −3}]=25.52{sub −0.05}{sup +0.05}. Our luminosity function analysis is consistent with previously published determinations within 1σ. The error analysis suggests that uncertainties on the faint-end slope are still too large to draw a firm conclusion about its evolution with redshift. We use our statistical framework to discuss the implication of our study for the physics of reionization. By assuming theoretically motivated priors on the clumping factor and the photon escape fraction we show that the UV luminosity density from galaxy samples down to M = –17.7 can ionize only 10%-50% of the neutral hydrogen at z ∼ 8. Full reionization would require extending the luminosity function down to M = –15. The data are consistent with a substantial fraction of neutral hydrogen at z > 7, in agreement with recent suggestions based on deep spectroscopy of z ∼ 8 LBGs.

79 ASTRONOMY AND ASTROPHYSICS↗