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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Size-dependent error of the density functional theory ionization potential in vacuum and solution

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.

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

Local and linear chemical reactivity response functions at finite temperature in density functional theory

We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation

The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. Here, we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew for performing self-interaction free calculations in density functional theory based on Fermi-orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction corrected (FLOSIC) method for practical density functional calculations without SIE.

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

Tuning the reactivity of carbon surfaces with oxygen-containing functional groups

Oxygen-containing carbons are promising supports and metal-free catalysts for many reactions. However, distinguishing the role of various oxygen functional groups and quantifying and tuning each functionality is still difficult. Here we investigate the role of Brønsted acidic oxygen-containing functional groups by synthesizing a diverse library of materials. By combining acid-catalyzed elimination probe chemistry, comprehensive surface characterizations, 15N isotopically labeled acetonitrile adsorption coupled with magic-angle spinning nuclear magnetic resonance, machine learning, and density-functional theory calculations, we demonstrate that phenolic is the main acid site in gas-phase chemistries and unexpectedly carboxylic groups are much less acidic than phenolic groups in the graphitized mesoporous carbon due to electron density delocalization induced by the aromatic rings of graphitic carbon. The methodology can identify acidic sites in oxygenated carbon materials in solid acid catalyst-driven chemistry.

Zhou, Jiahua↗
DOE OSTI2015

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

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

Density functional theory of water with the machine-learned DM21 functional

The delicate interplay between functional-driven and density-driven errors in density functional theory (DFT) has hindered traditional density functional approximations (DFAs) from providing an accurate description of water for over 30 years. Recently, the deep-learned DeepMind 21 (DM21) functional has been shown to overcome the limitations of traditional DFAs as it is free of delocalization error. To determine if DM21 can enable a molecular-level description of the physical properties of aqueous systems within Kohn–Sham DFT, we assess the accuracy of the DM21 functional for neutral, protonated, and deprotonated water clusters. Furthermore, we find that the ability of DM21 to accurately predict the energetics of aqueous clusters varies significantly with cluster size. Additionally, we introduce the many-body MB-DM21 potential derived from DM21 data within the many-body expansion of the energy and use it in simulations of liquid water as a function of temperature at ambient pressure. We find that size-dependent functional-driven errors identified in the analysis of the energetics of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength and, consequently, predicting a more ice-like local structure of water at room temperature.

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

Deconstructing the Soil Microbiome into Reduced-Complexity Functional Modules

The soil microbiome is an invaluable component of the biosphere and critical for ecosystem functions, including biogeochemical cycling, soil-atmosphere gas exchange, degradation of toxic compounds, and promotion of plant growth and stress resistance/resilience. An improved understanding of the soil microbiome will help with predicting how these processes respond to external perturbations, and with harnessing beneficial aspects of the soil microbiome for agronomic applications such as crop amendments. However, the extensive taxonomic and functional diversity inherent within the soil microbiome hinders efficient analysis of this system. Microbial biodiversity in soils is orders of magnitude greater than other commonly studied systems such as the human gut microbiome (Blum, Zechmeister-Boltenstern, and Keiblinger 2019; Berendsen, Pieterse, and Bakker 2012). Thousands of microbial taxa may be found in a single gram of soil (Roesch et al. 2007), and high rates of gene flow and mutation further promote microbial diversification (Sergaki et al. 2018). Concomitantly, functional diversity in soil is similarly extensive. Soil is a heterogeneous mixture of microenvironments with defined physical and chemical attributes (Bach et al. 2018), within which numerous microbial guilds of distinct life-strategies and metabolic capacities can be found (Perez-Garcia, Lear, and Singhal 2016; H.-S. Song et al. 2014). Furthermore, the soil microbiome harbors a significant fraction of rare and/or quiescent members (Blagodatskaya and Kuzyakov 2013) that exist below the threshold of detection of current technologies. Such rare taxa may make significant contributions to process rates (Shade and Gilbert 2015; Dawson et al. 2017), but their scarcity complicates their identification and analysis. Finally, the vast amounts of information generated through holistic analyses of soil communities represent an intense computational burden (Scholz, Lo, and Chain 2012; Prosser 2015) that precludes assessment of the complete functional and taxonomic diversity contained in this ecosystem.

Naylor, Dan T.↗
DOE OSTI2021

Functionalized Embedded Monometallic Nickel Catalysts for Enhanced Hydrogen Evolution: Performance and Stability

Viable anionic exchange membrane (AEM) electrolysis for H 2 production requires highly active hydrogen evolution reaction (HER) catalysts that are also robust and cost-effective. Traditionally juxtaposition of two transition metals with one being more oxophilic is necessary for easier access to water in the inner Helmholtz plane as a source of protons in the crucial Volmer step for enhanced HER activity. However, they are prone to passivation at anodic potentials or deactivation via the formation of sub-surface metal hydrides at high cathodic overpotentials. Here we report a method of enabling close juxtaposition of Ni-Ni-oxide surfaces by functionalizing Ni-based catalysts via the careful thermal treatment of carbon-supported Ni nano-particles chelated with a select organic chelating compound referred to as cupferron. This functionalization results in an embedded Ni surface with a clear graphitic coating engendering long-term stability for passivation and subsurface hydride formation. The stability and activity of the functionalized Ni catalyst are demonstrated in half-cell RDE and full-cell AEM membrane-based hydrogen pump experiments. In the case of the latter, the functionalized Ni outperforms carbon-supported Pt.

25 ENERGY STORAGE↗
DOE OSTI2016

Statistical measurement of the gamma-ray source-count distribution as a function of energy

Statistical properties of photon count maps have recently been proven as a new tool to study the composition of the gamma-ray sky with high precision. We employ the 1-point probability distribution function of six years of Fermi-LAT data to measure the source-count distribution dN/dS and the diffuse components of the high-latitude gamma-ray sky as a function of energy. To that aim, we analyze the gamma-ray emission in five adjacent energy bands between 1 and 171 GeV. It is demonstrated that the source-count distribution as a function of flux is compatible with a broken power law up to energies of ∼50 GeV. The index below the break is between 1.95 and 2.0. For higher energies, a simple power-law fits the data, with an index of 2.2{sub −0.3}{sup +0.7} in the energy band between 50 and 171 GeV. Upper limits on further possible breaks as well as the angular power of unresolved sources are derived. We find that point-source populations probed by this method can explain 83{sub −13}{sup +7}% (81{sub −19}{sup +52}%) of the extragalactic gamma-ray background between 1.04 and 1.99 GeV (50 and 171 GeV). The method has excellent capabilities for constraining the gamma-ray luminosity function and the spectra of unresolved blazars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Environmental remediation with functional aerogels and xerogels

Several different types of aerogel and/or xerogel scaffolds have been demonstrated as effective sorbents for the capture and immobilization of radionuclides in gaseous form [e.g., iodine gas or I2(g), Xe] as well as ionic form (e.g., Ce4+, Cs+, I–, IO3-, Rb+, Sr2+, 99Tc7+, and U6+). These scaffolds have unique properties, which include high specific surface areas, high pore volumes, varieties of pore sizes, and functionalities that provide methods for binding radionuclides through physisorption, chemisorption, or a combination thereof. This combination of properties and functionalities make these types of materials ideal scaffolds for use as sorbents for capturing radionuclides. The primary base materials that will be discussed in this chapter include Ag0-functionalized silica aerogels, Ag+-impregnated aluminosilicate aerogels, Ag0-functionalized aluminosilicate aerogels, metal-impregnated (non-Ag) aluminosilicate aerogels and xerogels, sulfide-based aerogels, and carbon-based aerogel composites. For the capture of I2(g), the materials reported herein show some of the highest iodine loadings ever reported for inorganic sorbents. For the capture of ionic species, these materials also show promise to be some of the next generations of materials for active radionuclide remediation. This progress report will describe how these materials are fabricated, the general properties of these materials, as well as an overview of how they have been used for different applications in environmental remediation of radionuclides.

aerogel, xerogel, iodine, radionuclide remediation↗
DOE OSTI2020

Electrochemical Oxidation of Organic Molecules at Lower Overpotential: Accessing Broader Functional Group Compatibility with Electron-Proton Transfer Mediators

CONSPECTUS: Electrochemical organic oxidation reactions are highly appealing because protons are often effective terminal electron acceptors, thereby avoiding undesirable stoichiometric oxidants. These reactions are often plagued by high overpotentials, however, that greatly limit their utility. Single-electron transfer (SET) from organic molecules generates high energy radical-cations. Formation of such intermediates often requires electrode potentials far above the thermodynamic potentials of the reaction and frequently causes decomposition and/or side reactions of ancillary functional groups. In this Account, we show how electrocatalytic electron-proton transfer mediators (EPTMs) address this challenge. EPTMs bypass the formation of radical-cation intermediates by supporting mechanisms that operate at electrode potentials much lower (=1 V) than analogous direct electrolysis reactions. The stable aminoxyl radical TEMPO (2,2,6,6-tetramethylpiperidine N-oxyl) is an effective mediator for electrochemical alcohol oxidation, and we have employed such processes for applications ranging from pharmaceutical synthesis to biomass conversion. A complementary electrochemical alcohol oxidation method employs a cooperative Cu/TEMPO mediator system that operates at 0.5 V lower electrode potential than the TEMPO-only mediated process. This difference, which arises from a different catalytic mechanism, rationalizes the broad functional group tolerance of Cu/TEMPO-based aerobic alcohol oxidation catalysts. Aminoxyl mediators address long-standing challenges in the "Shono oxidation", an important method for a-C–H oxidation of tertiary amides and carbamates. Shono oxidations are initiated by a high-potential SET step that limits their utility. Aminoxyl-mediated Shono-type oxidations have been developed that operate at much lower potentials and tolerate diverse functional groups. Analogous reactivity underlies a-C–H cyanation of secondary cyclic amines, a new method that enables efficient diversification of piperidine-based pharmaceutical building blocks and preparation of non-natural amino acids. Electrochemical oxidations of benzylic C–H bonds are commonly initiated by SET to generate radical cations, but such methods are again plagued by large overpotentials. Mediated electrolysis methods that promote hydrogen-atom-transfer (HAT) from benzylic C–H bonds to Fe-oxo species and phthalimide N-oxyl (PINO) support C–H oxygenation, iodination, and oxidative-coupling reactions. A complementary method merges photochemistry with electrochemistry to achieve amidation of C(sp3)–H bonds. This unique process operates at much lower overpotentials compatible with diverse functional groups. These results have broad implications for organic electrochemistry, highlighting the importance of "overpotential" considerations and the prospects for expanding synthetic utility by using mediators to bypass high-energy outer-sphere electron-transfer mechanisms. Principles demonstrated here for oxidation are equally relevant to electrochemical reductions.

Wang, Fei↗
DOE OSTI2013

Conjugate flow action functionals

We present a new general framework to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations relative to a diffeomorphic flow of curvilinear coordinates which is assumed to be functionally dependent on the solution field. Such flow, which will be called the conjugate flow, evolves in space and time similarly to a physical fluid flow of classical mechanics and it can be selected in order to symmetrize the Gâteaux derivative of the field equations with respect to suitable local bilinear forms. This is equivalent to requiring that the governing equations of the field theory can be derived from a principle of stationary action on a Lie group manifold. By using a general operator framework, we obtain the determining equations of such manifold and the corresponding conjugate flow action functional. In particular, we study scalar and vector field theories governed by second-order nonlinear partial differential equations. The identification of transformation groups leaving the conjugate flow action functional invariant could lead to the discovery of new conservation laws in fluid dynamics and other disciplines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Growth and characterization of Al{sub 2}O{sub 3} films on fluorine functionalized epitaxial graphene

Intelligent engineering of graphene-based electronic devices on SiC(0001) requires a better understanding of processes used to deposit gate-dielectric materials on graphene. Recently, Al{sub 2}O{sub 3} dielectrics have been shown to form conformal, pinhole-free thin films by functionalizing the top surface of the graphene with fluorine prior to atomic layer deposition (ALD) of the Al{sub 2}O{sub 3} using a trimethylaluminum (TMA) precursor. In this work, the functionalization and ALD-precursor adsorption processes have been studied with angle-resolved photoelectron spectroscopy, low energy electron diffraction, and X-ray photoelectron spectroscopy. It has been found that the functionalization process has a negligible effect on the electronic structure of the graphene, and that it results in a twofold increase in the adsorption of the ALD-precursor. In situ TMA-dosing and XPS studies were also performed on three different Si(100) substrates that were terminated with H, OH, or dangling Si-bonds. This dosing experiment revealed that OH is required for TMA adsorption. Based on those data along with supportive in situ measurements that showed F-functionalization increases the amount of oxygen (in the form of adsorbed H{sub 2}O) on the surface of the graphene, a model for TMA-adsorption on graphene is proposed that is based on a reaction of a TMA molecule with OH.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

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

Electromagnetic and neutral-weak response functions of 4 He and 12 C

A major goal of nuclear theory is to understand the strong interaction in nuclei as it manifests itself in terms of two- and many-body forces among the nuclear constituents, the protons and neutrons, and the interactions of these constituents with external electroweak probes via one- and many-body currents. The objective of the present work is to calculate the quasielastic electroweak response functions in light nuclei within the realistic dynamical framework outlined above. These response functions determine the inclusive cross section as function of the lepton momentum and energy transfers. Their ab initio calculation is a very challenging quantum many-body problem, since it requires summation over the entire excitation spectrum of the nucleus and inclusion in the electroweak currents of one- and many-body terms. Green's functions Monte Carlo methods allow one to circumvent both difficulties by computing the response in imaginary time (the so-called Euclidean response) and hence summing implicitly over the bound and continuum states of the nucleus, and by implementing specific algorithms designed to deal with the complicated spin-isospin structure of nuclear many-body operators. Theoretical predictions for 4 He and 12 C, confirmed by experiment in the electromagnetic case, show that two-body currents generate excess transverse strength from threshold to the quasielastic to the dip region and beyond. In conclusion, these results challenge the conventional picture of quasielastic inclusive scattering as being largely dominated by single-nucleon knockout processes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Predicting objective function weights from patient anatomy in prostate IMRT treatment planning

Purpose: Intensity-modulated radiation therapy (IMRT) treatment planning typically combines multiple criteria into a single objective function by taking a weighted sum. The authors propose a statistical model that predicts objective function weights from patient anatomy for prostate IMRT treatment planning. This study provides a proof of concept for geometry-driven weight determination. Methods: A previously developed inverse optimization method (IOM) was used to generate optimal objective function weights for 24 patients using their historical treatment plans (i.e., dose distributions). These IOM weights were around 1% for each of the femoral heads, while bladder and rectum weights varied greatly between patients. A regression model was developed to predict a patient's rectum weight using the ratio of the overlap volume of the rectum and bladder with the planning target volume at a 1 cm expansion as the independent variable. The femoral head weights were fixed to 1% each and the bladder weight was calculated as one minus the rectum and femoral head weights. The model was validated using leave-one-out cross validation. Objective values and dose distributions generated through inverse planning using the predicted weights were compared to those generated using the original IOM weights, as well as an average of the IOM weights across all patients. Results: The IOM weight vectors were on average six times closer to the predicted weight vectors than to the average weight vector, usingl{sub 2} distance. Likewise, the bladder and rectum objective values achieved by the predicted weights were more similar to the objective values achieved by the IOM weights. The difference in objective value performance between the predicted and average weights was statistically significant according to a one-sided sign test. For all patients, the difference in rectum V54.3 Gy, rectum V70.0 Gy, bladder V54.3 Gy, and bladder V70.0 Gy values between the dose distributions generated by the predicted weights and IOM weights was less than 5 percentage points. Similarly, the difference in femoral head V54.3 Gy values between the two dose distributions was less than 5 percentage points for all but one patient. Conclusions: This study demonstrates a proof of concept that patient anatomy can be used to predict appropriate objective function weights for treatment planning. In the long term, such geometry-driven weights may serve as a starting point for iterative treatment plan design or may provide information about the most clinically relevant region of the Pareto surface to explore.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2019

The Aemulus Project. II. Emulating the Halo Mass Function

Existing models for the dependence of the halo mass function on cosmological parameters will become a limiting source of systematic uncertainty for cluster cosmology in the near future. We present a halo mass function emulator and demonstrate improved accuracy relative to state-of-the-art analytic models. In this work, mass is defined using an overdensity criteria of 200 relative to the mean background density. Our emulator is constructed from the AEMULUS simulations, a suite of 40 N-body simulations with snapshots from z = 3 to z = 0. These simulations cover the flat wCDM parameter space allowed by recent cosmic microwave background, baryon acoustic oscillation and SNe Ia results, varying the parameters w, Omega(m), Omega(b), sigma(8), N-eff, n(s), and H-0. We validate our emulator using five realizations of seven different cosmologies, for a total of 35 test simulations. These test simulations were not used in constructing the emulator, and were run with fully independent initial conditions. We use our test simulations to characterize the modeling uncertainty of the emulator, and introduce a novel way of marginalizing over the associated systematic uncertainty. We confirm nonuniversality in our halo mass function emulator as a function of both cosmological parameters and redshift. Our emulator achieves better than 1% precision over much of the relevant parameter space, and we demonstrate that the systematic uncertainty in our emulator will remain a negligible source of error for cluster abundance studies through at least the LSST Year 1 data set.

large-scale structure of universe↗
DOE OSTI2015

Fractional charge and spin errors in self-consistent Green’s function theory

We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗