Search NASA⌕ Search

SEARCH · Search NASA

Results for “Basis function”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,369 records · Page 76
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Observation of Enhanced Long-Range Elliptic Anisotropies Inside High-Multiplicity Jets in p p Collisions at s = 13 TeV

A search for collective effects inside jets produced in proton-proton collisions is performed via correlation measurements of charged particles using the CMS detector at the CERN LHC. The analysis uses data collected at a center-of-mass energy of s = 13 TeV , corresponding to an integrated luminosity of 138 fb − 1 . Jets are reconstructed with the anti- k T algorithm with a distance parameter of 0.8 and are required to have transverse momentum greater than 550 GeV and pseudorapidity | η jet | < 1.6 . Two-particle correlations among the charged particles within the jets are studied as functions of the particles’ azimuthal angle and pseudorapidity separations ( Δ ϕ * and Δ η * ) in a jet coordinate basis, where particles’ η * , ϕ * are defined relative to the direction of the jet. The correlation functions are studied in classes of in-jet charged-particle multiplicity up to N ch j ≈ 100 . Fourier harmonics are extracted from long-range azimuthal correlation functions to characterize azimuthal anisotropy for | Δ η * | > 2 . For low- N ch j jets, the long-range elliptic anisotropic harmonic, v 2 * , is observed to decrease with N ch j . This trend is well described by Monte Carlo event generators. However, a rising trend for v 2 * emerges at N ch j ≳ 80 , hinting at a possible onset of collective behavior, which is not reproduced by the models tested. This observation yields new insights into the dynamics of jet evolution in the vacuum. © 2024 CERN, for the CMS Collaboration 2024 CERN

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

High-temperature electronic structure with the Korringa-Kohn-Rostoker Green's function method [High Temperature Electronic Structure with KKR]

Modeling high-temperature (tens or hundreds of eV), dense plasmas is challenging due to the multitude of non-negligible physical effects including significant partial ionization and multisite effects. These effects cause the breakdown or intractability of common methods and approximations used at low temperatures, such as pseudopotentials or plane-wave basis sets. Here we explore the Korringa-Kohn-Rostoker Green's function method at these high-temperature conditions. The method is all electron, does not rely on pseudopotentials, and uses a spherical harmonic basis set, and so avoids the aforementioned limitations. Finally, it is found to be accurate for solid density aluminum and iron plasmas when compared to a plane-wave method at low temperature, while being able to access high temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Quantum mechanical calculations on cis-2,6-bis(2-chlorophenyl)-3,3-dimethylpiperidin-4-one

Quantum mechanical calculations on cis-2, 6-bis (2-chlorophenyl)-3, 3-dimethylpiperidin-4-one were performed by using HSEH1PBE level of density functional theory (DFT) with 6-311++G (d, p) basis set. Geometric parameters of the title molecule in the ground state were found to be in good agreement with experimental data. The frontier molecular orbitals (HOMO and LUMO) were simulated by the same level. Small energy gap between the HOMO and LUMO is an indicator molecular charge transfer within the title molecule. The electronegativity, chemical hardness and softness were also calculated by using HOMO and LUMO energies. Dipole moment, polarizability and hyperpolarizability parameters were also calculated by using HSEH1PBE level. All calculations were carried out with the GAUSSIAN 09 package program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

AP1000{sup R} nuclear power plant safety overview for spent fuel cooling

The AP1000{sup R} plant is an 1100-MWe class pressurized water reactor with passive safety features and extensive plant simplifications that enhance construction, operation, maintenance, safety and costs. The AP1000 design uses passive features to mitigate design basis accidents. The passive safety systems are designed to function without safety-grade support systems such as AC power, component cooling water, service water or HVAC. Furthermore, these passive features 'fail safe' during a non-LOCA event such that DC power and instrumentation are not required. The AP1000 also has simple, active, defense-in-depth systems to support normal plant operations. These active systems provide the first level of defense against more probable events and they provide investment protection, reduce the demands on the passive features and support the probabilistic risk assessment. The AP1000 passive safety approach allows the plant to achieve and maintain safe shutdown in case of an accident for 72 hours without operator action, meeting the expectations provided in the U.S. Utility Requirement Document and the European Utility Requirements for passive plants. Limited operator actions are required to maintain safe conditions in the spent fuel pool via passive means. In line with the AP1000 approach to safety described above, the AP1000 plant design features multiple, diverse lines of defense to ensure spent fuel cooling can be maintained for design-basis events and beyond design-basis accidents. During normal and abnormal conditions, defense-in-depth and other systems provide highly reliable spent fuel pool cooling. They rely on off-site AC power or the on-site standby diesel generators. For unlikely design basis events with an extended loss of AC power (i.e., station blackout) or loss of heat sink or both, spent fuel cooling can still be provided indefinitely: - Passive systems, requiring minimal or no operator actions, are sufficient for at least 72 hours under all possible pool heat load conditions. - After 3 days, several different means are provided to continue spent fuel cooling using installed plant equipment as well as off-site equipment with built-in connections. Even for beyond design basis accidents with postulated pool damage and multiple failures in the passive safety-related systems and in the defense-in-depth active systems, the AP1000 multiple spent fuel pool spray and fill systems provide additional lines of defense to prevent spent fuel damage. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Comparative analysis of atmospheric parameters from high-resolution spectroscopic sky surveys: APOGEE, GALAH, Gaia -ESO

SDSS-IV APOGEE-2, GALAH, and Gaia-ESO are high-resolution, ground-based, multi-object spectroscopic surveys providing fundamental stellar atmospheric parameters and multiple elemental abundance ratios for hundreds of thousands of stars of the Milky Way. Data from these and other surveys contribute to investigations of the history and evolution of the Galaxy. We undertake a comparison between the most recent data releases of these surveys to investigate the accuracy and precision of derived parameters by placing the abundances on an absolute scale. We also discuss the correlations in parameter and abundance differences as a function of main parameters. Uncovering the variants provides a basis to continue the efforts of future sky surveys. Quality samples from the APOGEE-GALAH (15 537 stars), APOGEE-GES (804 stars), and GALAH-GES (441 stars) overlapping catalogs were collected. We investigated the mean variants between the surveys, and linear trends were also investigated. We compared the slope of correlations and mean differences with the reported uncertainties. The average and scatter of v rad , T eff , log g, [M/H], and v micro , along with numerous species of elemental abundances in the combined catalogs, show that in general there is a good agreement between the surveys. We find large radial velocity scatters ranging from 1.3 km s -1 to 4.4 km s -1 when comparing the three surveys. We observe some weak trends (e.g., in ΔT eff vs. Δlog g for the APOGEE-GES stars) and a clear correlation in the v micro - Δv micro planes in the APOGEE-GALAH common sample. For [α/H], [Ti/H] (APOGEE-GALAH giants), and [Al/H] (APOGEE-GALAH dwarfs) potential strong correlations are discovered as a function of the differences in the main atmospheric parameters, and we also find weak trends for other elements. In general we find good agreement between the three surveys within their respective uncertainties. However, there are certain regimes in which strong variants exist, which we discuss. There are still offsets larger than 0.1 dex in the absolute abundance scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Structural Insights into the Mechanisms and Pharmacology of K 2P Potassium Channels

Leak currents, defined as voltage and time independent flows of ions across cell membranes, are central to cellular electrical excitability control. The K 2P (KCNK) potassium channel class comprises an ion channel family that produces potassium leak currents that oppose excitation and stabilize the resting membrane potential in cells in the brain, cardiovascular system, immune system, and sensory organs. Due to their widespread tissue distribution, K 2P s contribute to many physiological and pathophysiological processes including anesthesia, pain, arrythmias, ischemia, hypertension, migraine, intraocular pressure regulation, and lung injury responses. Structural studies of six homomeric K 2P s have established the basic architecture of this channel family, revealed key moving parts involved in K 2P function, uncovered the importance of asymmetric pinching and dilation motions in the K 2P selectivity filter (SF) C-type gate, and defined two K 2P structural classes based on the absence or presence of an intracellular gate. Further, a series of structures characterizing K 2P :modulator interactions have revealed a striking polysite pharmacology housed within a relatively modestly sized (~70 kDa) channel. Binding sites for small molecules or lipids that control channel function are found at every layer of the channel structure, starting from its extracellular side through the portion that interacts with the membrane bilayer inner leaflet. This framework provides the basis for understanding how gating cues sensed by different channel parts control function and how small molecules and lipids modulate K 2P activity. Such knowledge should catalyze development of new K 2P modulators to probe function and treat a wide range of disorders.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Accurate Binding Energies for Lithium Polysulfides and Assessment of Density Functionals for Lithium–Sulfur Battery Research

Lithium–sulfur batteries have high theoretical energy density, but a better knowledge of their intimate structural details will be helpful in improving their conductivity and long-term cycling behavior. In order to identify the stationary configurations of lithium polysulfides (Li 2 S n , 2 ≤ n ≤ 8) formed in the charging and discharging processes of the lithium–sulfur batteries, ab initio molecular dynamics was employed to sample the configuration space of Li 2 S n , followed by optimization of structures by CCSD(T)-F12b/aug-cc-pVDZ. Here, using the optimized stationary points, we have created the LiSAE38 benchmark database of atomization energies (AEs) of 38 lithium polysulfide isomers by using the higher-level WMS and W3X-L methods. In addition, the performances of 39 density functionals have been assessed against the benchmark AEs and the relative stabilities of Li 2 S n isomers. On the basis of the assessments with the def2-QZVP basis set, the PW6B95, B97-1, B3LYP-D3, TPSS, and DSD-PBEP86 density functionals are the most accurate for the AEs, whereas the mPW2-PLYP-D, DSD-PBEP86, PW6B95, HSE06, and PBEQIDH functionals are most accurate for the relative energies. Local functionals are of special interest because of their lower cost (faster timings in terms of computer resources) for large systems; among the tested local functionals, MN15-L and revM06-L are the most accurate for the calculations of relative stabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

The structural basis of flagellin detection by NAIP5: A strategy to limit pathogen immune evasion

Robust innate immune detection of rapidly evolving pathogens is critical for host defense. Nucleotide-binding domain leucine-rich repeat (NLR) proteins function as cytosolic innate immune sensors in plants and animals. However, the structural basis for ligand-induced NLR activation has so far remained unknown. NAIP5 (NLR family, apoptosis inhibitory protein 5) binds the bacterial protein flagellin and assembles with NLRC4 to form a multiprotein complex called an inflammasome. Here we report the cryo–electron microscopy structure of the assembled ~1.4-megadalton flagellin-NAIP5-NLRC4 inflammasome, revealing how a ligand activates an NLR. Six distinct NAIP5 domains contact multiple conserved regions of flagellin, prying NAIP5 into an open and active conformation. We show that innate immune recognition of multiple ligand surfaces is a generalizable strategy that limits pathogen evolution and immune escape.

Tenthorey, Jeannette L.↗
DOE OSTI2022

Tuning Enzyme Thermostability via Computationally Guided Covalent Stapling and Structural Basis of Enhanced Stabilization

Enhancing the thermostability of enzymes without impacting their catalytic function represents an important yet challenging goal in protein engineering and biocatalysis. We recently introduced a novel method for enzyme thermostabilization that relies on the computationally guided installation of genetically encoded thioether “staples” into a protein via cysteine alkylation with the noncanonical amino acid O-2-bromoethyl tyrosine (O2beY). Here, we demonstrate the functionality of an expanded set of electrophilic amino acids featuring chloroacetamido, acrylamido, and vinylsulfonamido side-chain groups for protein stapling using this strategy. Using a myoglobin-based cyclopropanase as a model enzyme, our studies show that covalent stapling with pchloroacetamido-phenylalanine (pCaaF) provides higher stapling efficiency and enhanced stability (thermodynamic and kinetic) compared to the other stapled variants and the parent protein. Interestingly, molecular simulations of conformational flexibility of the cross-links show that the pCaaF staple allows fewer energetically feasible conformers than the other staples, and this property may be a broader indicator of stability enhancement. Using this strategy, pCaaF-stapled variants with significantly enhanced stability against thermal denaturation (ΔT m ' = +27 °C) and temperature-induced heme loss (ΔT 50 = +30 °C) were obtained while maintaining high levels of catalytic activity and stereoselectivity. Crystallographic analyses of singly and doubly stapled variants provide key insights into the structural basis for stabilization, which includes both direct interactions of the staples with protein residues and indirect interactions through adjacent residues involved in heme binding. This work expands the toolbox of protein stapling strategies available for protein stabilization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

THE MASSIVE SATELLITE POPULATION OF MILKY-WAY-SIZED GALAXIES

Several occupational distributions for satellite galaxies more massive than m{sub *} Almost-Equal-To 4 Multiplication-Sign 10{sup 7} M{sub Sun} around Milky-Way (MW)-sized hosts are presented and used to predict the internal dynamics of these satellites as a function of m{sub *}. For the analysis, a large galaxy group mock catalog is constructed on the basis of (sub)halo-to-stellar mass relations fully constrained with currently available observations, namely the galaxy stellar mass function decomposed into centrals and satellites, and the two-point correlation functions at different masses. We find that 6.6% of MW-sized galaxies host two satellites in the mass range of the Small and Large Magellanic Clouds (SMC and LMC, respectively). The probabilities of the MW-sized galaxies having one satellite equal to or larger than the LMC, two satellites equal to or larger than the SMC, or three satellites equal to or larger than Sagittarius (Sgr) are Almost-Equal-To 0.26, 0.14, and 0.14, respectively. The cumulative satellite mass function of the MW, N{sub s} ({>=}m{sub *}) , down to the mass of the Fornax dwarf is within the 1{sigma} distribution of all the MW-sized galaxies. We find that MW-sized hosts with three satellites more massive than Sgr (as the MW) are among the most common cases. However, the most and second most massive satellites in these systems are smaller than the LMC and SMC by roughly 0.7 and 0.8 dex, respectively. We conclude that the distribution N{sub s} ({>=}m{sub *}) for MW-sized galaxies is quite broad, the particular case of the MW being of low frequency but not an outlier. The halo mass of MW-sized galaxies correlates only weakly with N{sub s} ({>=}m{sub *}). Then, it is not possible to accurately determine the MW halo mass by means of its N{sub s} ({>=}m{sub *}); from our catalog, we constrain a lower limit of 1.38 Multiplication-Sign 10{sup 12} M{sub Sun} at the 1{sigma} level. Our analysis strongly suggests that the abundance of massive subhalos should agree with the abundance of massive satellites in all MW-sized hosts, i.e., there is not a missing (massive) satellite problem for the {Lambda}CDM cosmology. However, we confirm that the maximum circular velocity, v{sub max}, of the subhalos of satellites smaller than m{sub *} {approx} 10{sup 8} M{sub Sun} is systematically larger than the v{sub max} inferred from current observational studies of the MW bright dwarf satellites; different from previous works, this conclusion is based on an analysis of the overall population of MW-sized galaxies. Some pieces of evidence suggest that the issue could refer only to satellite dwarfs but not to central dwarfs, then environmental processes associated with dwarfs inside host halos combined with supernova-driven core expansion should be on the basis of the lowering of v{sub max}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Structural Basis For Antigenic Peptide Precursor Processing by the Endoplasmic Reticulum Aminopeptidase ERAP1

ERAP1 trims antigen precursors to fit into MHC class I proteins. To fulfill this function, ERAP1 has unique substrate preferences, trimming long peptides but sparing shorter ones. To identify the structural basis for ERAP1's unusual properties, we determined the X-ray crystal structure of human ERAP1 bound to bestatin. The structure reveals an open conformation with a large interior compartment. An extended groove originating from the enzyme's catalytic center can accommodate long peptides and has features that explain ERAP1's broad specificity for antigenic peptide precursors. Structural and biochemical analyses suggest a mechanism for ERAP1's length-dependent trimming activity, whereby binding of long rather than short substrates induces a conformational change with reorientation of a key catalytic residue toward the active site. ERAP1's unique structural elements suggest how a generic aminopeptidase structure has been adapted for the specialized function of trimming antigenic precursors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

First principles DFT study of dye-sensitized CdS quantum dots

Dye-sensitized quantum dots (QDs) are considered promising candidates for dye-sensitized solar cells. In order to maximize their efficiency, detailed theoretical studies are important. Here, we report a first principles density functional theory (DFT) investigation of experimentally realized dye - sensitized QD / ligand systems, viz., Cd{sub 16}S{sub 16}, capped with acetate molecules and a coumarin dye. The hybrid B3LYP functional and a 6−311+G(d,p)/LANL2dz basis set are used to study the geometric, energetic and electronic properties of these clusters. There is significant structural rearrangement in all the clusters studied - on the surface for the bare QD, and in the positions of the acetate / dye ligands for the ligated QDs. The density of states (DOS) of the bare QD shows states in the band gap, which disappear on surface passivation with the acetate molecules. Interestingly, in the dye-sensitised QD, the HOMO is found to be localized mainly on the dye molecule, while the LUMO is on the QD, as required for photo-induced electron injection from the dye to the QD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Optical sensor comprising diffraction gratings with functionalized pores and method of detecting analytes using the sensor

Diffraction gratings comprising a substrate with protrusions extending therefrom. In one embodiment, the protrusions are made of a porous material, for example porous silicon with a porosity of greater than about 10%. The diffraction grating may also be constructed from multiple layers of porous material, for example porous silicon with a porosity of greater than about 10%, with protrusion of attached thereto. In some embodiments the protrusions may be made from photoresist or another polymeric material. The gratings are the basis for sensitive sensors. In some embodiments, the sensors are functionalized with selective binding species, to produce sensors that specifically bind to target molecules, for example chemical or biological species of interest.

Weiss, Sharon M.↗
DOE OSTI2016

Hydrogen trapping at neutron irradiation produced defects in recrystallized alpha annealed Zircaloy-4 - 2016-0060

Hydrogen is absorbed into zirconium alloy-clad fuel elements and structural components as a result of water-side corrosion in both pressurized water reactor (PWR) and boiling water reactor (BWR) environments. Increasing hydrogen concentrations in the zirconium alloy affect both its mechanical properties and dimensional stability. It is well known that hydrogen can diffuse relatively rapidly through zirconium base alloys (in relation to the lifetime of the components) in response to solid solution concentration, temperature, and stress gradients. Migration of hydrogen within a component through its life must be considered to reliably predict the performance of the component through life and even post-service life. Many of the physical properties needed to describe this process, such as the solubility of hydrogen in zirconium alloys, diffusion coefficients of hydrogen through zirconium alloys, and the Soret effect within zirconium alloys, already have been published. Many of these measurements have been made outside of the reactor core environment on nonirradiated zirconium alloys. This paper presents in-reactor, isothermal hydrogen diffusion data that show an effect of the in-reactor radiation environment on the final measured hydrogen concentrations. Samples used are similar to the hydrogen diffusion couples used by several investigators in the past to measure the hydride dissolution solvus as a function of temperature. The experimental results are interpreted on the basis of a physical model for hydrogen trapping that hypothesizes that hydrogen in solid solution in the zirconium lattice comes into thermodynamic equilibria with the hydride phase as well as into a steady-state equilibrium with trapping at irradiation-induced defects within the lattice. In agreement with the model, the irradiation effect on final measured concentrations is seen to be a decreasing function of the irradiation temperature between ∼271 deg. C and 354 deg. C, with any effect essentially eliminated by an irradiation temperature of 354 deg. C. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2025

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of Non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of “how difficult the problem is” (like the well-known T 1 diagnostic), but its variation with the level of theory also gives information about “how well this particular method works”, irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be 2 ). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis

This paper presents the first converged frequency-dependent HF polarizability results for general molecules, on a set of 89 closed-shell atoms and molecules. The solver employs multiresolution analysis (MRA) in a multiwavelet basis to compute both ground and response states to a guaranteed precision, which are validated against independent numerical grid calculations on atoms and linear molecules. The MRA ground-state energies and response properties are used to evaluate results in correlation-consistent basis sets up to 5Z augmented with either single or double diffuse functions and core-polarization functions. Systematic trends are revealed through consideration of chemical composition as well as the use of machine learning to cluster convergence trends, the latter suggesting the possibility of learning and correcting basis-set error.

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

Implementation of density functional embedding theory within the projector-augmented-wave method and applications to semiconductor defect states

We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green’s function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green’s function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green’s function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green’s function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green’s function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗