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At least 433 records · Page 24

Charge order in the kagome lattice Holstein model: a hybrid Monte Carlo study

The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for √3 × √3 CDW order at an average electron filling of < n > = 2/3 per site, with an ordering wavevector at the K-points of the Brillouin zone. We estimate a phase transition occurring at T c ≈ t/18, where t is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures T ≥ t/20.

36 MATERIALS SCIENCE↗

Instantaneous mesh load factor ( K γ ) measurements in a wind turbine gearbox using fiber-optic strain sensors

The mesh load factor, K γ , describes how loads are shared between planet gears and has become one of the key design challenges in modern wind turbine gearboxes. Planet load sharing directly impacts tooth root stresses, a critical driver of torque density and gearbox reliability. Experimental evaluation of K γ is typically performed from sun gear tooth root strain gauge measurements, which are complex. Furthermore, such measurements can only provide an average value of load sharing. The present study describes an alternative method to evaluate the mesh load factor in wind turbine gearboxes based on fiber-optic strain sensors installed on the outer surface of the fixed ring gear. We present the results of an extensive measurement campaign to evaluate this novel sensing solution installed on the input planetary stage of a 2-MW wind turbine gearbox at the National Renewable Energy Laboratory's Flatirons Campus (Colorado, USA). The number of strain sensors on the ring gear was selected as an integer multiple of the number of planets, which has enabled an instantaneous evaluation of the mesh load factor. The effect of operating conditions on the planet load-sharing behavior of the gearbox has been investigated. The mesh load factor measured for operating conditions close to rated was below 1.05, well below IEC 61400-4 standard requirements.

17 WIND ENERGY↗

Symmetry breaking forms split-off flat bands in quantum oxides controlling metal versus insulator phases

The crystal structure used as input to electronic structure calculation of conventionally bonded solids consists primarily of the standard crystallographic degrees of freedom. Quantum solids sometimes have additional microscopic degrees of freedom (m-DOF) nested within the crystallographic structure. These might include local motifs including positional (Peierls dimers, deformed octahedra, Jahn-Teller distortions), magnetic (local moment configurations) and dipolar (local ferroelectric configurations). Such motifs can be observed experimentally via local probes that avoid averaging, and theoretically as distinct total energy lowering features relative to more simplified “average crystallographic structures”. Here we examine the ability of electronic structure methods independent of strong correlation physics to explain the broad phenomenology of metal-insulator selectivity in quantum oxides by energy-lowering symmetry breaking. We do this by avoiding the restriction of considering only (i) electron-electron interactions in a fixed unresponsive lattice—as done in Mott strong correlation explanations—allowing, however, (ii) local positional and magnetic motifs that coexist within a crystallographic landscape. We find in a broad range of quantum oxides with different symmetry breaking modes the formation of split-off flat bands that can also control metallic versus insulating characteristics. The split-off band effect is common to magnetic and non-magnetic materials, including both binary and ternary oxides. One finds that when such local symmetry breaking motifs are considered in mean-field-like (e.g. density functional theory) electronic structure calculations of quantum oxides, they explain many of the observed trends in metal vs insulator phases discussed otherwise in prior literature via strong correlation in symmetry unbroken view.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

WHONDRS laboratory time series moisture manipulative experiment from soil core layers across eastern contiguous US: time series aerobic respiration, geochemistry, and aggregates

This dataset supports a broader study examining the effects of wetting and drying on soil layers across the eastern contiguous United States (CONUS). The dataset provides data generated from a laboratory moisture manipulation experiment. The contents include time series aerobic respiration and moisture; dissolved oxygen; sediment geochemistry data; and field metadata. Samples were collected as part of a collaboration between WHONDRS (Worldwide Hydrobiogeochemistry Observation Network for Dynamic River Systems; https://whondrs.pnnl.gov) and MONet (Molecular Observation Network; https://www.emsl.pnnl.gov/monet). The field samples (soil cores) were labeled as MEL_##_COR and subsequent subsamples begin with MEL_##. Additional subsamples were taken for the laboratory experiment and were labeled as EL_##. The labels from the MEL field samples and the EL subsamples can be mapped directly based on the digits following the prefix and underscore (i.e., EL_01 is a subsample from MEL_01). See the critical details section below for more details on sample naming and experimental design.For details on how to navigate this data package, see this infographic from the River Corridor SFA https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About.In addition to this readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions.This dataset is comprised of (1) a folder containing environmental context photos; (2) file-level metadata; (3) data dictionary; (4) field metadata; (5) readme; (6) international generic sample number (IGSN) mapping file; and (7) a subfolder with soil sample data from field samples and the incubation experiment. The sample data subfolder contains (1) effect size; (2) gravimetric moisture from field samples and incubation experiment; (3) respiration rates, raw dissolved oxygen values, and plots; (4) specific conductance, pH, and temperature from the incubation; (5) soil aggregates; (6) a summary containing median values of each data type for each treatment (wet and dry) in the incubation; (7) a summary containing averages for each data type of each soil layer; and (8) methods codes. All files are .csv, .pdf, .jpeg, or .jpg.

54 ENVIRONMENTAL SCIENCES↗

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗

A new method for diagnosing effective radiative forcing from aerosol–cloud interactions in climate models

Aerosol–cloud interactions (ACIs) are a leading source of uncertainty in estimates of the historical effective radiative forcing (ERF). One reason for this uncertainty is the difficulty in estimating the ERF from aerosol–cloud interactions (ERFaci) in climate models, which typically requires multiple calls to the radiation code. Most commonly used methods also cannot disentangle the contributions from different processes to ERFaci. Here, we develop a new, computationally efficient method for estimating the shortwave (SW) ERFaci from liquid clouds using histograms of monthly averaged cloud fraction partitioned by cloud droplet effective radius (r e ) and liquid water path (LWP). Multiplying the histograms with SW cloud radiative kernels gives the total SW ERFaci from liquid clouds, which can be decomposed into contributions from the Twomey effect, LWP adjustments, and cloud fraction (CF) adjustments. We test the method with data from five CMIP6-era models, using the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument simulator to generate the histograms. Our method gives similar total SW ERFaci estimates to other established methods in regions of prevalent liquid cloud and indicates that the Twomey effect, LWP adjustments, and CF adjustments have contributed -0.34 ± 0.23, -0.22 ± 0.13, and -0.09 ± 0.11 W m -2 , respectively, to the effective radiative forcing of the climate since 1850 in the ensemble mean (95 % confidence). These results demonstrate that widespread adoption of a MODIS r e –LWP joint histogram diagnostic would allow the SW ERFaci and its components to be quickly and accurately diagnosed from climate model outputs, a crucial step for reducing uncertainty in the historical ERF.

54 ENVIRONMENTAL SCIENCES↗

Getting Warmer: IceCube Nears Freeze Out

IceCube has recently detected a diffuse population of high-energy neutrinos arising from the Milky Way. We use this high-significance detection to place new limits on dark matter (DM) annihilation to neutrinos with two complementary approaches. The first method uses the background-subtracted Galactic longitude distribution of shower events to place a conservative bound on the DM annihilation cross section that does not rely on any assumed Galactic cosmic ray emission model; the resulting limits on the velocity-averaged annihilation cross section improve upon existing bounds by factors of a few. The second method uses the template-dependent neutrino energy spectra from the Inner Galaxy, inferred under different Galactic cosmic ray emission models. This complementary approach shows that the inferred Galactic neutrino intensities are already sensitive to DM contributions near the thermal-relic benchmark for a range of TeV-scale DM masses, though this comparison is more model-dependent. Our results demonstrate that measurements of diffuse Galactic neutrino emission can be used as a powerful probe of DM annihilation into neutrinos. Future observations with IceCube-Gen2 and KM3NeT will substantially extend this sensitivity, potentially allowing a decisive test of the thermal freeze-out mechanism with Galactic neutrino observations.

Mukhopadhyay, Mainak [Fermilab; Chicago U., KICP; ↗

Determining Cs-137 Background body burdens for Wild Pigs At Savannah River Site

Savannah River Site (SRS) is a unique U.S. Department of Energy facility in that most of the 310-square miles of land has not be industrialized since operations began in 1953. This has allowed abundant, undisturbed vegetation structure to exists as well as an increase in herd sizes among wildlife populations onsite. Cs-137 is widespread across SRS due to the production of nuclear materials, but is mostly from global atmospheric fallout from nuclear weapons testing. Due to most of SRS being undisturbed land, the concentrations of Cs-137 are higher on site than off site. The SRS began conducting annual deer harvests that were open to the public beginning in 1965. All animals harvested during these hunts are monitored for Cs-137, which is measured using a Sodium Iodide detector. There has been an effective method for calculating the background Cs-137 body burden for the deer population at the SRS, developed by Gaines and Novak using data collected during hunts and gamma overflight data to determine the areas contaminated by site activities. For animals that have a Cs-137 concentration above the established background level, a dose is assigned to the hunter. By applying the same method for wild pigs using data collected from hunts, gamma overflight, and developing a site-specific home range of wild pigs, we were able to calculate the Cs-137 background body burden concentrations of wild pigs on site. Objectives: Develop site-specific home range for wild pigs at SRS; Determine the average concentrations of Cs-137 in wild pigs from background; Use Gaines and Novak method for determining background Cs-137 body burdens wild pigs on SRS. Methods and Materials: Development of site-specific home range of wild pigs was determined to be 2.5 miles using: Four studies conducted between 1969 and 1992 for the SRS wild pig population. (Mayer and Brisbin) The background compartments were determined using: Gamma overflight data showing contaminated areas; Site-specific home range of the wild pigs. Results and Conclusion: All data were generated through the JMP software to provide a histogram and summary statistics. The estimate of an upper tolerance limit for the background contamination with 95% confidence is 1.965 pCi/g for the wild pigs. This means that for wild pigs on SRS from the background compartments are expected to have Cs-137 concentrations of less than 1.965 pCi/g. The current background for the deer is 2.59 pCi/g. For the background compartments Cs-137 concentrations from 2012-2018: Mean: 0.815 pCi/g, Maximum: 2.341 pCi/g, Minimum: -0.704 pCi/g.

07 ISOTOPE AND RADIATION SOURCES↗

Flame aerosol synthesis of hollow alumina nanoshells for application in thermal insulation

Commercial implementation of hollow nanoshell materials is often limited by difficult scale-up and high cost. Here we present a scalable, continuous, and potentially low-cost route to hollow nanostructured materials using a High Temperature Reducing Jet flame aerosol reactor. The key advantage of this process over traditional flame aerosol synthesis methods is separation of flame chemistry and particle formation, which allows production of hollow nanoshells from an aqueous salt solution without any template or surfactant. We produced amorphous hollow alumina with an average diameter of 181 nm and shell thickness below 10 nm, and demonstrated the generality of the method by also producing hollow SiO 2 , ZrO 2 , Ga 2 O 3 , and Co 2 O 3 . We characterized the morphology, phase transition, thermal stability, and thermal conductivity of the flame-made hollow alumina by electron microscopy, x-ray diffraction, and thermal analysis methods. As a prototypical application, we incorporated hollow alumina into thermal insulation, combining it with common fiberglass insulation to reduce the thermal conductivity by 30% relative to pure fiberglass, to 0.028 W m -1 K -1 while maintaining robust fire-resistance and elasticity.

36 MATERIALS SCIENCE↗

Model-Free Approach for Profiling of Polydisperse Soft Matter Using Small Angle Scattering

A strategy for determining the size polydispersity of systems from their small angle coherent scattering is outlined. Here, using the method of moment expansion, we show that the various central moments representing the average particle size, variance of particle size, and skewness of size distribution function (SDF) for polydisperse systems can be extracted from spectral analysis without bias. When the degree of polydispersity is moderate, SDF can be further reconstructed based on the maximum entropy principle. Numerical benchmarking of a model study over a wide range of size nonuniformity demonstrates the validity of this analytical approach for quantifying the size distribution of general soft matter systems in a model-free manner. Furthermore, the efficacy of this method was validated by successfully applying it to the fitting of small-angle neutron scattering data obtained from L64 Pluronic micelles using various form factor models. The numerical and experimental verification underscores the reliability and versatility of this method in accurately characterizing the size distribution of complex soft matter systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A novel approach to partitioning evapotranspiration into evaporation and transpiration in flooded ecosystems

Reliable partitioning of micrometeorologically measured evapotranspiration (ET) into evaporation (E) and transpiration (T) would greatly enhance our understanding of the water cycle and its response to climate change related shifts in local-to-regional climate conditions and rising global levels of vapor pressure deficit (VPD). While some methods on ET partitioning have been developed, their underlying assumptions make them difficult to apply more generally, especially in sites with large contributions of E. Here, we report a novel ET partitioning method using artificial neural networks (ANNs) in combination with a range of environmental input variables to predict daytime E from nighttime ET measurements. The study uses eddy covariance data from four restored wetlands in the Sacramento-San Joaquin Delta, California, USA, as well as leaf-level T data for validation. The four wetlands vary in their vegetation make-up and structure, representing a range of ET conditions. The ANNs were built with increasing complexity by adding the input variable that resulted in the next highest average value of model testing R 2 across all sites. The order of variable inclusion (and importance) was: VPD > gap-filled sensible heat flux (H_gf) > air temperature (T air ) > friction velocity (u * ) > other variables. The model using VPD, H_gf, T air , and u * showed the best performance during validation with independent data and had a mean testing R 2 value of 0.853 (averaged across all sites, range from 0.728 to 0.910). In comparison to other methods, our ANN method generated T/ET partitioning results which were more consistent with CO 2 exchange data especially for more heterogeneous sites with large E contributions. Further, our method improves the understanding of T/ET partitioning. While it may be particularly suited to flooded ecosystems, it can also improve T/ET partitioning in other systems, increasing our knowledge of the global water cycle and ecosystem functioning.

59 BASIC BIOLOGICAL SCIENCES↗

Improving Peptide-Level Mass Spectrometry Analysis via Double Competition

A critical statistical task in the analysis of shotgun proteomics data involves controlling the false discovery rate (FDR) among the reported set of discoveries. This task is most commonly solved at the peptide-spectrum match (PSM) level by using target-decoy competition (TDC), in which a set of observed spectra are searched against a database containing a mixture of real (target) and decoy peptides. The PSM-level procedure can be adapted to the peptide level by selecting the top-scoring PSM per peptide prior to FDR estimation. Here, we investigate both PSM-level and peptide-level FDR control methods and come to two conclusions. First, although the TDC procedure is provably correct under certain assumptions, we observe that one of these assumptions - that incorrect PSMs are independent of one another - is frequently violated. Hence, we empirically demonstrate that TDC-based PSM-level FDR estimates can be liberally biased. Further, we propose that researchers avoid PSM-level results and instead focus on peptide-level analysis. Second, we investigate three ways to carry out peptide level TDC and show that the most common method ("PSM-only") offers the lowest statistical power in practice. The most powerful method, peptide-level FDR with PSM competition ("PSM-and-peptide"), carries out competition first at the PSM level and then again at the peptide level. In our experiments, this approach yields an average increase of 17% more discovered peptides at a1% FDR threshold relative to the PSM-only method.

59 BASIC BIOLOGICAL SCIENCES↗

Integrated Metrics for County-Level Resilience Ranking Using Entropy and TOPSIS

In the face of atypical weather events, power infrastructure failures, and limited resources for resilience investment, energy decision-makers need data-driven metrics to allocate resilience investments and maximize the reduction of power outage impacts. For state-level planning, for instance, ranking the resilience of each county is key to ensuring effective distribution of resources. In such cases, resilience for each spatial unit is multifaceted and is captured by a set of indicators (i.e., metrics) that can be combined into an overall score that reduces the complexity of power outage dynamics to a single decision metric. However, weighting of these indicators is often addressed by simplifying assumptions (i.e., equal weights) or semi-subjective methods that rely on user-defined weights that can introduce biases (e.g., weighted average score). Within the disaster risk reduction and resilience engineering community, a recurring challenge in multicriteria decision-making is the objective weighting of indicators for composite indices. To address this issue, we have leveraged a Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) combined with an entropy-based weighting approach to calculated the integrated scores. This method objectively determines the importance of each metric, better discerns between spatial units (i.e., counties), and offers a more reliable ranking of counties according to their relative resilience attributes. By improving methods for integrating resilience indicators, our approach helps planners and decision-makers prioritize resources more effectively for more efficient resilience investments.

Bhusal, Narayan [Oak Ridge National Laboratory (OR↗

Stability boundary and optimal operating parameter identification in milling using Bayesian learning

Here, this paper describes a novel Bayesian learning approach for stability boundary and optimal parameter identification in milling without the knowledge of the underlying tool dynamics or material cutting force coefficients. The paper is divided into two parts. First, a Bayesian learning method for stability lobe identification using test results is described. Each axial depth and spindle speed combination is characterized by a probability of stability which is updated using Bayes’ rule when a test result (stable or unstable) is made available. A novel likelihood function is defined which incorporates knowledge of the stability behavior. Numerical results show convergence to the analytical stability lobe diagram. Second, an adaptive experimental strategy to identify optimal operating parameters that maximize material removal rate is described. Numerical evaluation shows convergence to the optimal operating point with error less than 15 % within ten tests on average. The approach is validated using experimental results. Results show that the proposed method is an efficient and robust learning method to identify the stability lobe diagram and optimal operating parameters with a limited number of tests/data points.

Bayesian machine learning↗

Selective One-Dimensional 13 C– 13 C Spin-Diffusion Solid-State Nuclear Magnetic Resonance Methods to Probe Spatial Arrangements in Biopolymers Including Plant Cell Walls, Peptides, and Spider Silk

Two-dimensional (2D) and 3D through-space 13 C– 13 C homonuclear spin-diffusion techniques are powerful solid-state nuclear magnetic resonance (NMR) tools for extracting structural information from 13 C-enriched biomolecules, but necessarily long acquisition times restrict their applications. In this work, we explore the broad utility and underutilized power of a chemical shift-selective one-dimensional (1D) version of a 2D 13 C– 13 C spin-diffusion solid-state NMR technique. The method, which is called 1D dipolar-assisted rotational resonance (DARR) difference, is applied to a variety of biomaterials including lignocellulosic plant cell walls, microcrystalline peptide fMLF, and black widow dragline spider silk. 1D 13 C– 13 C spin-diffusion methods described here apply in select cases in which the 1D 13 C solid-state NMR spectrum displays chemical shift-resolved moieties. Furthermore, this is analogous to the selective 1D nuclear Overhauser effect spectroscopy (NOESY) experiment utilized in liquid-state NMR as a faster (1D instead of 2D) and often less ambiguous (direct sampling of the time domain data, coupled with increased signal averaging) alternative to 2D NOESY. Selective 1D 13 C– 13 C spin-diffusion methods are more time-efficient than their 2D counterparts such as proton-driven spin diffusion (PDSD) and dipolar-assisted rotational resonance. The additional time gained enables measurements of 13 C– 13 C spin-diffusion buildup curves and extraction of spin-diffusion time constants TSD, yielding detailed structural information. Specifically, selective 1D DARR difference buildup curves applied to 13 C-enriched hybrid poplar woody stems confirm strong spatial interaction between lignin and acetylated xylan polymers within poplar plant secondary cell walls, and an interpolymer distance of ~0.45–0.5 nm was estimated. Additionally, Tyr/Gly long-range correlations were observed on isotopically enriched black widow spider dragline silks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Application of a Chemical Index to Aerosol Mass Spectrometry: Delta Plots and Functional Group Distributions

A better understanding of the chemical properties of organic aerosol (OA) particles will improve our ability to characterize their sources and predict their lifetime. The high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) is widely used to measure OA in real time using thermal vaporization followed by electron ionization (EI). EI creates fragment ions that can be assigned to functional groups using delta analysis, a method of classifying mass spectra according to the presence of different chemically related ion series. In this study, we demonstrate the application of delta analysis to characterize molecular structures using a new visualization method. We also use delta analysis to quantify the functional group distribution with an average absolute error of ∼5–6% for individual standard molecules, comparable to the error observed for OA mixtures from biomass and coal combustion fit with Fourier transform infrared spectroscopy. Finally, we apply delta functional group analysis to AMS positive matrix factorization (PMF) factors across seven different field campaigns and find a similar composition across the more oxidized factors with about 55% acid and 26% alcohol groups. The analysis method described here can be applied to any HR-ToF-AMS data set to provide quantitative relative functional group distributions for OA mixtures.

aerosol↗

Perspective on Kramers symmetry breaking and restoration in relativistic electronic structure methods for open-shell systems

Without rigorous symmetry constraints, solutions to approximate electronic structure methods may artificially break symmetry. In the case of the relativistic electronic structure, if time-reversal symmetry is not enforced in calculations of molecules not subject to a magnetic field, it is possible to artificially break Kramers degeneracy in open shell systems. This leads to a description of excited states that may be qualitatively incorrect. Despite this, different electronic structure methods to incorporate correlation and excited states can partially restore Kramers degeneracy from a broken symmetry solution. For single-reference techniques, the inclusion of double and possibly triple excitations in the ground state provides much of the needed correction. Formally, however, this imbalanced treatment of the Kramers-paired spaces is a multi-reference problem, and so methods such as complete-active-space methods perform much better at recovering much of the correct symmetry by state averaging. Using multi-reference configuration interaction, any additional corrections can be obtained as the solution approaches the full configuration interaction limit. A recently proposed “Kramers contamination” value is also used to assess the magnitude of symmetry breaking.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Generality of the GUGA MRCI Approach in COLUMBUS for Treating Complex Quantum Chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗