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DOE OSTI2025

Wet-radome attenuation in ARM cloud radars and its utilization in radar calibration using disdrometer measurements

Abstract. A relative calibration technique has been developed for the US Department of Energy's (DOE's) Atmospheric Radiation Measurement (ARM) user facility Ka-band ARM Zenith Radars (KAZRs). This method uses the signal attenuation caused by water on the radome to estimate reflectivity factor (Ze) offsets. The wet-radome attenuation (WRA) is assumed to follow a log-linear relationship with rainfall rate during light and moderate rain, as measured by a collocated surface disdrometer. The technique has an uncertainty of approximately 3 dB, due to factors such as disdrometer measurement error, rain variability between radar and disdrometer sample volumes, and the fitting function's uncertainty for the WRA behavior. A practical advantage of this WRA-based approach to shorter-wavelength radar monitoring is that, while it requires a reference disdrometer, it proves feasible for a wider range of collocated disdrometer measurements compared to traditional direct disdrometer comparison at the onset of light rain. This technique thus offers a cost-effective monitoring tool for remote or long-term radar deployments. This calibration technique was applied during the ARM Tracking Aerosol Convection Interactions Experiment (TRACER) from October 2021 through September 2022. The estimated Ze offsets were compared against traditional radar calibration and monitoring methods using available datasets from this campaign. Results show that the WRA-based offsets align closely with mean offsets found between cloud radars and from direct disdrometer comparison near the onset of rain, while also reflecting similar offset and campaign-long trends when compared to collocated, independently calibrated radar wind profilers. Nevertheless, overall, the KAZR Ze offsets estimated during TRACER remained stable at approximately 2 dB lower than the disdrometer estimates from the campaign start until the end of June 2022; afterward, the offsets increased to around 7 dB by the campaign's end. This increase is linked to a drop of about 1 dB in transmitter power toward the end of the project.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Neutrino Transport with Monte Carlo Method. I. Toward Fully Consistent Implementation of Nucleon Recoils in Core-collapse Supernova Simulations

The small energy exchange via nucleon recoils in neutrino–nucleon scattering is now supposed to be one of the important factors for successful explosions of core-collapse supernovae (CCSNe), as they can change neutrino spectra through accumulation of a large number of scatterings. In deterministic methods employed for neutrino transport in CCSN simulations, we normally cannot afford to deploy a large enough number of energy bins needed to resolve this small energy exchange, and subgrid techniques are employed one way or another. In this paper, we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by ~15% for heavy-lepton neutrinos and much smaller amounts for other types of neutrinos in a typical postbounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the deterministic methods. In order to mimic the latter calculation, we redistribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected, depending on the energy resolution. We also discuss the possible implications of our results for the deterministic methods.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

High-throughput functional trait testing for bacterial pathogens

Functional traits are characteristics that affect the fitness and metabolic function of a microorganism. There is growing interest in using high-throughput methods to characterize bacterial pathogens based on functional virulence traits. Traditional methods that phenotype a single organism for a single virulence trait can be time consuming and labor intensive. Alternatively, machine learning of whole-genome sequences (WGS) has shown some success in predicting virulence. However, relying solely on WGS can miss functional traits, particularly for organisms lacking classical virulence factors. We propose that high-throughput assays for functional virulence trait identification should become a prominent method of characterizing bacterial pathogens on a population scale. This work is critical as we move from compiling lists of bacterial species associated with disease to pathogen-agnostic approaches capable of detecting novel microbes. We discuss six key areas of functional trait testing and how advancing high-throughput methods could provide a greater understanding of pathogens.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Online Model-Free Chance-Constrained Distribution System Voltage Control Using DERs

This paper proposes an online data-driven distributed energy resource management system (DERMS) optimization method using chance-constrained formulation to address distribution system voltage regulation. This is achieved via the local sensitivity factor (LSF)-enabled reformulation of the DER control into a linear programming (LP) problem, which is easy and computationally efficient to solve. The LSF is estimated using online measurements and does not need the assumption of node load information. The latter is usually required for existing optimization-based methods but is difficult to obtain in practice. To mitigate measurement uncertainties, a scenario-based chance-constrained formulation is constructed. Compared with other control methods, the results carried out in a realistic distribution system show that the proposed method can effectively eliminate voltage violation issues.

chance-constrained optimization↗

DOE OSTI2023

Online Model-Free Chance-Constrained Distribution System Voltage Control Using DERs: Preprint

chance-constrained optimization↗

DOE OSTI2023

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew–Burke–Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew–Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. Finally, the quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Analysis of persistent contaminants and personal care products by dispersive liquid-liquid microextraction using hydrophobic magnetic deep eutectic solvents

Here, in this work, hydrophobic magnetic deep eutectic solvents (HMDESs) were used in the development of a simple and rapid dispersive liquid-liquid microextraction (DLLME) approach coupled to high performance liquid chromatography with UV detection (HPLC-UV) for the determination of ten organic contaminants including five polycyclic aromatic hydrocarbons, four UV filters, and a pesticide from water at trace levels. The HMDESs were prepared by mixing a hydrogen bond acceptor, metal halide salt, and hydrogen bond donor in suitable molar ratios. Two HMDESs, 2 tetraoctylammonium bromide ([N 8888 + ][Br - ]): cobalt chloride (CoCl 2 ): 4 octanoic acid (OA) and 3 trioctylphosphine oxide (TOPO): neodymium chloride (NdCl 3 ): 3 OA, offered the highest analyte extraction efficiency overall and were chosen as suitable solvents for validation of the microextraction method. Under optimized extraction conditions, the method required 30 µL of HMDES as extraction solvent, acetone (87.5 µL) as disperser solvent, a NaCl concentration of 30% (w/v), and an extraction time of 120 s at 20°C. Enrichment factors of the analytes ranged from 44.6 for 3-(4-methylbenzylindene) camphor to 66.0 for 2-ethylhexyl-4-(dimethyl)aminobenzoate. The method provided low limits of detection (LODs) ranging from 0.5 to 4.5 µg L -1 , and acceptable precision, with RSD values lower than 9.6%. Furthermore, the validated method was successfully applied for tap and lake water analysis, resulting in relative recoveries of spiked samples ranging between 94.7 and 119.2%.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Iron, magnesium, and titanium isotopic fractionations between garnet, ilmenite, f ayalite, biotite, and tourmaline: Results from NRIXS, ab initio , and study of mineral separates from the Moosilauke metapelite

Interpreting isotopic signatures documented in natural rocks requires knowledge of equilibrium isotopic fractionation factors. Here, we determine equilibrium Fe isotope fractionation factors between several common rock-forming minerals using a comparative approach involving three independent methods: (i) isotopic analyses of natural minerals from a metapelite from Mt. Moosilauke, New Hampshire, for which equilibration temperature and pressure are well constrained to be near the aluminosilicate triple point (T ≃ 500 °C, P ≃ 4 kbar), (ii) Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements of Fe force constants of minerals, and (iii) Density Functional Theory (DFT) ab initio calculations of Fe force constants of minerals. The minerals studied for Fe isotopes include, in increasing order of their β-factors: garnet < ilmenite ≈ fayalite < biotite < tourmaline < muscovite ≈ plagioclase. Some of this ordering is affected by the presence of Fe 3+ in the minerals, which tends to form stiffer bonds and be associated with heavy Fe isotope enrichments relative to Fe 2+ . We are, however, able to assess the magnitude of the effect of the ratio Fe 3+ /ΣFe on equilibrium fractionation factors, notably on the ilmenite-hematite solid solution. Equilibrium Fe isotopic fractionation factors between garnet, ilmenite, biotite, tourmaline and fayalite are determined. We also report Mg and Ti isotopic compositions of selected Moosilauke minerals that allow us to better constrain the equilibrium fractionation factors for garnet-biotite-tourmaline (Mg isotopes) and biotite-ilmenite (Ti isotopes). We show how the newly determined equilibrium fractionation factors can be used to address diverse problems in Earth and planetary sciences, notably (i) Fe and Mg isotopic fractionation during anatexis, (ii) Fe isotopic fractionation in lunar ilmenite, and (iii) Ti isotopic fractionation during fluvial transport of minerals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

AI-Based Protein Interaction Screening and Identification (AISID)

In this study, we presented an AISID method extending AlphaFold-Multimer’s success in structure prediction towards identifying specific protein interactions with an optimized AISIDscore. The method was tested to identify the binding proteins in 18 human TNFSF (Tumor Necrosis Factor superfamily) members for each of 27 human TNFRSF (TNF receptor superfamily) members. For each TNFRSF member, we ranked the AISIDscore among the 18 TNFSF members. The correct pairing resulted in the highest AISIDscore for 13 out of 24 TNFRSF members which have known interactions with TNFSF members. Out of the 33 correct pairing between TNFSF and TNFRSF members, 28 pairs could be found in the top five (including 25 pairs in the top three) seats in the AISIDscore ranking. Surprisingly, the specific interactions between TNFSF10 (TNF-related apoptosis-inducing ligand, TRAIL) and its decoy receptors DcR1 and DcR2 gave the highest AISIDscore in the list, while the structures of DcR1 and DcR2 are unknown. The data strongly suggests that AlphaFold-Multimer might be a useful computational screening tool to find novel specific protein bindings. This AISID method may have broad applications in protein biochemistry, extending the application of AlphaFold far beyond structure predictions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Removing Rotational Variations from Shoulder Thermocouples in Friction Stir Welding

Thick plate and lower temperature friction stir welding results in good post-weld properties by welding at very low tool rotational speeds. Low speeds cause large variations in the measured shoulder temperature, making temperature control difficult. This paper describes a computationally light method to correct for oscillating measured temperatures. Data is collected over the previous two revolutions and used to build a compensation table and calculate a derivative. In simulation, measured temperature variations are reduced by a factor of five to ten. Temperature data is preserved and not cornered, nor is any time delay induced by this method, unlike with filtering methods.

Friction Stir Welding, Temperature↗

DOE OSTI2021

A new method for measuring the 3D turbulent velocity dispersion of molecular clouds

ABSTRACT The structure and star formation activity of a molecular cloud are fundamentally linked to its internal turbulence. However, accurately measuring the turbulent velocity dispersion is challenging due to projection effects and observational limitations, such as telescope resolution, particularly for clouds that include non-turbulent motions, such as large-scale rotation. Here, we develop a new method to recover the 3D turbulent velocity dispersion (σv,3D) from position–position–velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud, and compare its intrinsic σv,3D with three different measures of the velocity dispersion accessible in PPV space: (1) the spatial mean of the 2nd-moment map, σi, (2) the standard deviation of the gradient/rotation-corrected 1st-moment map, σ(c − grad), and (3) a combination of (1) and (2), called the ‘gradient-corrected parent velocity dispersion’, $\sigma _{\mathrm{(p}-\mathrm{grad)}}=(\sigma _{\mathrm{i}}^2+\sigma _{(\mathrm{c}-\mathrm{grad)}}^2)^{1/2}$. We show that the gradient correction is crucial in order to recover purely turbulent motions of the cloud, independent of the orientation of the cloud with respect to the line of sight. We find that with a suitable correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover σv,3D, with method 3 being the most robust and reliable. We determine the correction factor as a function of the telescope beam size for different levels of cloud rotation, and find that for a beam full width at half-maximum f and cloud radius R, the 3D turbulent velocity dispersion can best be recovered from the gradient-corrected parent velocity dispersion via $\sigma _{v,\mathrm{3D}}= \left[(-0.29\pm 0.26)\, f/R + 1.93 \pm 0.15\right] \sigma _{\mathrm{(p}-\mathrm{grad)}}$ for f/R < 1, independent of the level of cloud rotation or LOS orientation.

Stewart, Madeleine↗

DOE OSTI2023

Numerical investigations to identify environmental factors for field-scale reactive transport of pathogens at riverbank filtration sites

While induced bank filtration is a proven method for facilitating sustainable drinking water production, it is at risk from surface water contaminations (e.g., pathogens). Induced bank filtration and pathogen transport in groundwater have been studied extensively. However, long-term studies that consider real-world conditions are missing. These conditions include seasonal changes to environmental conditions and waterworks operations. Therefore, to analyze the effect of seasonal changes on the transport of human pathogenic viruses and their indicators in induced bank filtration, concentrations of adenoviruses and pathogen indicators were monitored over 16 months at an active bank filtration plant at the Rhine River, in Düsseldorf (Germany). Based on this data, a 2D groundwater model was created in PFLOTRAN that simulated flow, heat transport, conservative transport of chloride and the resulting electrical conductivity, reactive transport of oxygen and nitrate, and colloid-based transport of coliforms, somatic coliphages, and adenoviruses. The results show that reduced travel time was the key factor determining periods with a low removal of coliforms and somatic coliphages in the aquifer. Travel time was controlled by river level variations during rainy seasons, and the waterworks extraction rates during dry seasons. Further, for adenovirus transport, travel distance in the subsurface appeared to be the key factor, while travel time had no significant impact. Coliform removal increased when the colmation layer permeability decreased, while coliphage and adenovirus removal was unaffected by the colmation layer permeability. Seasonal changes in temperature and oxygen content did not significantly impact the removal of coliphages and adenoviruses in groundwater. Denitrifying conditions correlated with a lowered coliform removal, but the modelling could not establish a connection between denitrifying conditions and coliform removal. Our study showed that removal of pathogens and pathogen indicators at induced bank filtration plants varies greatly in time and space (e.g., for coliforms from 1 to 4 log-levels at 20m travel distance), and that adenovirus transport differs considerably from transport of coliforms and somatic coliphages.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Machine learning to discover mineral trapping signatures due to CO 2 injection

Mineral trapping is pursued as a geological CO 2 sequestration (GCS) mechanism because it permanently stores CO 2 in solid phases or minerals. However, CO 2 mineral-trapping mechanisms are poorly understood due to (1) lack of sufficient field and laboratory data characterizing these complex processes, and (2) challenges to develop site-specific reactive-transport models coupling fluid flow and geochemical reactions occurring at various temporal (from milliseconds to years) and spatial (from pore (millimeters) to field (kilometers)) scales. Reactive transport with additional complexities such as heterogeneity can make the simulation outputs even more difficult to interpret because of complex nonlinearity and multi-scale interdependencies. Furthermore, the values of model outputs such as concentrations can vary by several orders of magnitude, making it harder to correlate and characterize the impact of the variables via traditional data interpretation techniques such as exploratory data analyses. Recently, machine learning (ML) has shown promise in feature discovery and in highlighting hidden mechanisms that cannot be obtained by existing data-analytics and statistical methods. In this study, we applied an unsupervised ML approach, non-negative matrix factorization with custom -means clustering (NMF) to the data generated by reactive-transport simulations of GCS. The reactive-transport data consisted of 19 attributes, including four physio-chemical variables (pH, porosity, aqueous CO 2 , and sequestered CO 2 ), six chemical species (K + , Na + , HCO, Ca 2+ , Mg 2+ , Fe 2+ ), and four carbonate minerals (calcite, dolomite, siderite, and ankerite), a feldspar mineral (albite), and four clay minerals (illite, clinochlore, kaolinite, and smectite) over a period of 200 years of simulation time. Furthermore, the simulation data used was for Morrow B sandstone at the Farnsworth hydrocarbon unit in Texas. Data are sampled at two locations within the model domain: (1) at the injection well and (2) 200 m west of the injection well. The injection was performed for a period of 10 years. Using NMF, we estimated the temporal interdependencies among the 19 attributes over a span of 200 years. We found that NMF was able to identify four reaction stages and their dominant attributes; these cannot be directly discerned through traditional visualization (e.g., line plots, Pareto analysis, Glyph-based visualization methods) or exploratory data analysis tools of the simulation data. The four stages were: reactions in the injection phase followed by short-, mid-, and long-term reactions. The NMF analysis also revealed that 10 among the 19 attributes are dominant. These dominant attributes for mineral trapping include calcite, dolomite at injection well, siderite at 200 m away from the injection well, clinochlore, kaolinite, Na + , K + , Ca 2+ , Mg 2+ , pH, and aqeuous CO 2 . Finally, at late times (65–200 years), our results showed that calcite plays a major role in mineral trapping with insignificant contribution from siderite, ankerite, and clay minerals. These findings make the proposed unsupervised ML-model attractive for reactive-transport sensing towards real-time GCS monitoring.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Global Sensitivity Analysis of a Reactive Transport Model for Mineral Scale Formation During Hydraulic Fracturing

Injection of water-based hydraulic fracturing fluid (HFF) into tight shale gas/oil formations can increase formation permeability and enhance production rates, but this process frequently causes mineral scale formation that can occlude pore space and hinder flow. To identify the most important factors that control the formation of mineral scales, we applied a novel global sensitivity analysis method—distance-based generalized sensitivity analysis (DGSA)—to a reactive transport model (RTM) that was previously built and calibrated to simulate precipitation of barite [BaSO4] and iron (hydr)oxide [Fe(OH) 3 ] in shale matrices and on fracture surfaces. Reactive transport simulations were run with model parameters randomly sampled based on assigned uncertainties. Modeling results for barite and Fe(OH)3 formation were clustered using machine-learning algorithms. A list of ranked critical input parameters was obtained after statistical quantification of cumulative distribution functions of input parameters. We found that barite formation is most sensitive to the rate of sulfate ion generation, which is determined by the pyrite dissolution rate coefficient and oxidant availability. In addition, barite formation is sensitive to the initial amounts of barite in HFF and shale, followed by barite thermodynamics/kinetics. For Fe(OH) 3 formation, the ranked factors are Fe(OH)3 precipitation rate coefficients, initial HFF pH, initial Fe(OH) 3 amount in HFF, and oxidant availability. Overall, our results provide insights into managing mineral scale formation during hydraulic fracturing to enhance production. Meanwhile, this study serves as an example of global sensitivity analysis of RTMs using the efficient, straightforward, and open-source DGSA method.

58 GEOSCIENCES↗

DOE OSTI2024

UNDERSTANDING THE SEMI-PROBABILISTIC APPROACHES IN STRUCTURAL RELIABILITY USED TO SET DESIGN RELIABILITY TARGETS FOR GRAPHITE COMPONENTS USING ASME BPVC METHODS

Graphite is a quasi-brittle material, resulting in random variability in tensile strength distributions. To account for the random variability in strength, HHA-3000 of the ASME BPVC provides two semi-probabilistic methods for qualifying nuclear graphite components in the design stage, the simplified and full assessments. The full and simplified assessments apply statistical methods to engineering-based design problems. This is often referred to as reliability-based design. Reliability-based design (RBD) is a method to develop reliable designs by accounting for uncertainties and result in small chances of failure when also considering safety factors. RBDs provide reliability targets using semi-probabilistic approaches. RBD is implemented in ASME BPVC HHA-3000 for nuclear graphite components, but is not specific to that application. There has been much confusion around the methods implemented in ASME BPVC HHA-3000 for qualifying nuclear graphite components. To address the confusion, this paper takes a hierarchical approach. First, the general RBD framework is presented. Then, the semi-probabilistic methods and the underlying assumptions implemented in the assessments are presented. The semi-probabilistic methods are separated from the engineering modifications that have been made to the assessments. After building the framework and underlying assumptions, the specific methods in the full and simplified assessments are explained in three steps: inputs, methods, outputs. The methods are applied to an H-451 reflector block. Tensile strength properties for other graphite grades are provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Learning-Accelerated ADMM for Distributed DC Optimal Power Flow

We suggest a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118-and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Learning-Accelerated ADMM for Distributed DC Optimal Power Flow

We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118- and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.

alternating direction method of multipliers↗

DOE OSTI2020

A Filon-like integration strategy for calculating exact exchange in periodic boundary conditions: a plane-wave DFT implementation

An efficient and accurate approach for calculating exact exchange and other two-electron integrals has been developed for periodic electronic structure methods. Traditional approaches used for integrating over the Brillouin zone in band structure calculations, e.g. trapezoidal or Monkhorst-Pack, are not accurate enough for two-electron integrals. This is because their integrands contain multiple singularities over the double integration of the Brillouin zone, which with simple integration methods lead to very inaccurate results. A common approach to this problem has been to replace the Coulomb interaction with a screened Coulomb interaction that removes singularities from the integrands in the two-electron integrals, albeit at the inelegance of having to introduce a screening factor which must precomputed or guessed. Instead of introducing screened Coulomb interactions in an ad hoc way, the method developed in this work derives an effective screened potential using a Filon-like integration approach that is based only on the lattice parameters. This approach overcomes the limitations of traditionally defined screened Coulomb interactions for calculating two-electron integrals, and makes chemistry many-body calculations tractable in periodic boundary conditions. This method has been applied to several systems for which conventional DFT methods do not work well, including the reaction pathways for the addition of H 2 to phenol and Au$^{–}_{20}$ nanoparticle, and the electron transfer of a charge trapped state in the Fe(II) containing mica, annite.

36 MATERIALS SCIENCE↗