Accurate Reference Data Research Articles

Accurate reference spectra of HD in an H2–He bath for planetary applications

Context. The hydrogen deuteride (HD) molecule is an important deuterium tracer in astrophysical studies. The atmospheres of gas giants are dominated by molecular hydrogen, and the simultaneous observation of H2 and HD lines provides reliable information on the D/H ratios on these planets. The reference spectroscopic parameters play a crucial role in such studies. Under the thermodynamic conditions encountered in these atmospheres, spectroscopic studies of HD require not only the knowledge of line intensities and positions but also accurate reference data on pressure-induced line shapes and shifts. Aims. Our aim is to provide accurate collision-induced line-shape parameters for HD lines that cover any thermodynamic conditions relevant to the atmospheres of giant planets, namely any relevant temperature, pressure, and perturbing gas composition (the H2–He mixture). Methods. We performed quantum-scattering calculations on our new, highly accurate ab initio potential energy surface (PES), and we used scattering S matrices obtained in this way to determine the collision-induced line-shape parameters. We used cavity ring-down spectroscopy to validate our theoretical methodology. Results. We report accurate collision-induced line-shape parameters for the pure rotational R(0), R(1), and R(2) lines, the most relevant HD lines for investigations of the atmospheres of the giant planets. Besides the basic Voigt-profile collisional parameters (i.e., the broadening and shift parameters), we also report their speed dependences and the complex Dicke parameter, which can influence the effective width and height of the HD lines up to almost a factor of 2 for giant planet conditions. The sub-percent-level accuracy reached in this work is a considerable improvement over previously available data. All the reported parameters (and their temperature dependences) are consistent with the HITRAN database format, hence allowing for the use of the HITRAN Application Programming Interface (HAPI) for generating the beyond-Voigt spectra of HD.

Qinghai-Tibet Plateau Glacier-DEM product derived from the Chinese stereo mapping satellites

Abstract. The Digital Elevation Model (DEM) is an important basic data for glacier research on the Qinghai-Tibet Plateau. With the rapid development of China 's stereo mapping satellite, it is possible to obtain high-precision DEM in the glacier area of the Qinghai-Tibet Plateau. In this study, the stereo images and laser altimetry data of ZY-3 and GF-7 satellites were comprehensively used, and the matching and joint adjustment methods of laser elevation control points and stereo images were proposed. A high-precision DEM product in glacier area was established, and the elevation accuracy of DEM was verified by using UAV data and ICESat-2 data. The results show that the accuracy of GF-7 DEM is better than 1.5 m when the slope is less than 6 degrees, and the overall accuracy is better than 2.8 m. The accuracy of ZY-3 DEM is better than 3.5 m when the slope is less than 6 degrees, and the overall accuracy is better than 5.0 m. Compared with the open source DEM with medium spatial resolution, the DEM elevation accuracy based on domestic stereo mapping satellite images is better, and the grid is finer and more detailed to describe the texture characteristics of the end of the glaciers. Compared with the high spatial resolution data set HMA DEM, the ZY-3 DEM is slightly worse and the GF-7 DEM is better, and both the ZY-3 DEM and GF-7 DEM are better than the HMA DEM in terms of coverage integrity in the Qinghai- Tibet Plateau. Chinese stereo mapping satellites can generate high-precision DEM in the glacier area, and can provide more accurate and reliable terrain reference data than the existing open free data for the study of glaciers in the Qinghai-Tibet Plateau.

Swirling flow field reconstruction and cooling performance analysis based on experimental observations using physics-informed neural networks

The design of thermal protection modules (such as film cooling) for combustion chambers requires a high-fidelity swirling flow field. Although numerical methods provide insights into three-dimensional mechanisms of swirling flow, their predictions of key features such as recirculation zones and swirling jets are often unsatisfactory due to inherent anisotropy and the isotropic nature of the Boussinesq hypothesis. Experimental methods, such as hot wire, laser Doppler velocimetry, and planar particle image velocimetry (PIV), offer more accurate reference data but are limited by sparse or planar observations. In this study, considering the outperformed capability of solving inverse problems, physics-informed neural network (PINN) was adopted to reconstruct the mean swirling flow field based on limited experimental observations from two-dimensional and two-component (2D2C) results. It was found that adding partial information characterizing the swirling flow, such as the swirling jet, could significantly improve the reconstruction of flow field. In addition, film cooling effectiveness was the key variable to evaluate the film cooling performance, which was relatively measurable in the scalar field. To further improve the accuracy of the reconstruction, the multi-source strategy was adopted into the neural network, where the film cooling effectiveness (FCE) of the effusion plate was imported as the scalar source. It was found that the prediction of the flow field near the target plate was improved, where the highest error reduction could reach 76.5%. Finally, through the reconstructed three-dimensional vortex distribution, it was found that swirling flow vortex structures near the swirler exit had a significant impact on cooling effectiveness, causing a non-uniform cooling distribution. This study aims to diagnose the three-dimensional swirling flow field with deep learning by leveraging limited experimental data and deepen the understanding of effusion cooling under swirling flow condition so that obtains a more accurate reference in the design of thermal protection modules.

Accuracy comparison of terrestrial and airborne laser scanning and manual measurements for stem curve-based growth measurements of individual trees

Monitoring forest growth accurately is important for assessing and controlling forest carbon stocks that impact, for example, the atmospheric CO2 concentration and, consequently, the climate change. In prior studies, forest growth monitoring with laser scanning methods has resulted in relatively high errors. However, the contribution of reference measurement error to uncertainty in growth resolution has rarely been analysed, and the reference measurements are usually considered mostly flawless. In this study, a seven-year-long growth of individual trees was estimated using both airborne and terrestrial laser scanning (ALS, TLS) that have emerged as potential candidates for digital forest reference measurements. The growth values were derived for diameter at breast height (DBH) and stem volume between the years 2014 and 2021 using an indirect approach. The values obtained with laser scanning were paired with manual field measurements and also with each other to study pairwise errors. The pairwise comparison showed that even though all the three measurement methods produced good Pearson correlation coefficients for one-time measurements (all above 0.88), the coefficients for growth measurements were significantly lower (0.19–0.44 for DBH and 0.47–0.66 for stem volume). The best correlation and root mean squared deviation (RMSD) for DBH growth (ρ = 0.44, RMSD = 0.98 cm) and stem volume growth (ρ = 0.66, RMSD = 0.052 m3) was observed between the manual field measurements and the ALS-based growth measurement method, in which the tree stem curve was obtained from the 2021 point cloud, and the stem curve was predicted backwards for the year 2014 according to height growth. The ALS method suffered less from outlying values than the TLS-based growth measurement method, in which the growth was computed based on the difference of stem curves derived separately for the years 2014 and 2021. The study showed that observing the stem curve is a potential method for short-period growth monitoring. Using the pairwise comparison results, we further derived estimates for the mean and standard deviation of measurement error of each individual measurement method. For the manual measurements, the standard deviation of error was found to be approximately 0.4 cm for DBH growth and 0.03 m3 for volume growth, which were the lowest of the three methods but not by a large margin. This highlights the need for more accurate reference data as the accuracy of laser scanning-based growth estimation methods continues to approach the accuracy of manual measurements.

Quantum-Chemistry Study of the Hydrolysis Reaction Profile in Borate Networks: A Benchmark.

This investigation involved an ab initio and Density Functional Theory (DFT) analysis of the hydrolysis mechanism and energetics in a borate network. The focus was on understanding how water molecules interact with and disrupt the borate network, an area where the experimental data are scarce and unreliable. The modeled system consisted of two boron atoms, bridging oxygen atoms, and varying numbers of water molecules. This setup allows for an exploration of hydrolysis under different environmental conditions, including the presence of OH- or H+ ions to simulate basic or acidic environments, respectively. Our investigation utilized both ab initio calculations at the MP2 and CCSD(T) levels and DFT with a range of exchange-correlation functionals. The findings indicate that the borate network is significantly more susceptible to hydrolysis in a basic environment, with respect to an acidic or to a neutral pH setting. The inclusion of explicit water molecules in the calculations can significantly affect the results, depending on the nature of the transition state. In fact, some transition states exhibited closed-ring configurations involving water and the boron-oxygen-boron network; in these cases, there were indeed more water molecules corresponding to lower energy barriers for the reaction, suggesting a crucial role of water in stabilizing the transition states. This study provides valuable insights into the hydrolysis process of borate networks, offering a detailed comparison between different computational approaches. The results demonstrate that the functionals B3LYP, PBE0, and wB97Xd closely approximated the reference MP2 and CCSD(T) calculated reaction pathways, both qualitatively in terms of the mechanism, and quantitatively in terms of the differences in the reaction barriers within the 0.1-0.2 eV interval for the most plausible reaction pathways. In addition, CAM-B3LYP also yielded acceptable results in all cases except for the most complicated pathway. These findings are useful for guiding further computational studies, including those employing machine learning approaches, and experimental investigations requiring accurate reference data for hydrolysis reactions in borate networks.

Assessment of NA‐CORDEX regional climate models, reanalysis and in situ gridded‐observational data sets against the U.S. Climate Reference Network

AbstractClimate models' capability of reproducing the present climate at both global and regional scales still needs improvements. The assessment of model performance critically depends on the data sets used as comparators/references. Reanalysis and gridded observational data sets have been frequently used for this purpose. However, none of these can be considered an accurate reference data set because of their associated uncertainties and full representativity. This paper, for the first time, uses in‐situ measurements from National Oceanic and Atmospheric Administration U.S. Climate Reference Network (USCRN) spanning the period 2006–2020 to assess daily temperature and precipitation from a suite of dynamically downscaled regional climate models (RCMs; driven by ERA‐Interim) involved in NA‐CORDEX. The assessment is also extended to the most recent and widely used Earth system reanalyses (ERA5, ERA‐Interim, MERRA2 and NARR) and a few in situ‐based gridded data sets (Daymet, PRISM, Livneh and CPC). Results show that biases for the different data sets are seasonally and subregionally dependent. On average, reanalysis and in situ‐based gridded data sets are warmer (with biases exceeding 0.3°C) than USCRN year‐round, while RCMs are colder (warmer) in winter (summer) with biases ranging from −0.5 (0.9)°C for RCMs at 0.44° to −0.2 (1.4)°C for CRCM5‐UQAM‐11. In situ‐based gridded data sets provide the best performance in most of the Contiguous United States (CONUS) regions compared to reanalyses and RCMs, but still have biases in regions such as the Western mountains and the Pacific Northwest. Furthermore, in most US subregions, reanalysis data sets do not outperform reanalysis‐driven RCMs. Likewise, for both reanalysis data sets and RCMs, temperature and precipitation biases vary considerably depending on the local orography, with larger temperature biases for coarser model resolutions and precipitation biases for reanalysis.

Temperature Reliability Investigation for a 400 W Solid-State Power Amplifier under High and Cold Conditions

In order to study the temperature reliability of high-power amplifiers under high cand cold conditions, a 400 W solid-state power amplifier was taken as an example to explore the variation in its performance. The test results showed that its output power, gain, and power-added efficiency increased with the increase in temperature at a fixed frequency. Under a fixed input power, Pout and gain both showed different trends with the rising temperature. Within the frequency band of 2–10 MHz, the higher the temperature, the better the output power and gain. However, within the frequency range of 10–30 MHz, the higher the temperature, the worse the performance. Moreover, with the increasing temperature, its power-added efficiency, the second harmonic and the third harmonic also showed a decreasing trend. Detailed analysis showed that the degradation and inversion of performance parameters are closely related to the zero temperature coefficient and self-heating effect of the lateral double-diffused metal–oxide–semiconductor field-effect transistor. Meanwhile, it is also affected by the circuit structure and thermal design of the PA. In order to ensure stable performance in different environments, performance degradation can be improved by hardware compensation. Therefore, analyzing the working parameters at different temperatures for high-power PAs is the key to achieving temperature control and ensuring their long-term stability and reliability. This can provide relatively accurate reference data for subsequent heat dissipation optimization, greatly improve design efficiency, and even shorten the development cycle and reduce costs.

Lagrangian Z-vector approach to Bethe-Salpeter analytic gradients: Assessing approximations.

We present an implementation of excited-state analytic gradients within the Bethe-Salpeter equation formalism using an adapted Lagrangian Z-vector approach with a cost independent of the number of perturbations. We focus on excited-state electronic dipole moments associated with the derivatives of the excited-state energy with respect to an electric field. In this framework, we assess the accuracy of neglecting the screened Coulomb potential derivatives, a common approximation in the Bethe-Salpeter community, as well as the impact of replacing the GW quasiparticle energy gradients by their Kohn-Sham analogs. The pros and cons of these approaches are benchmarked using both a set of small molecules for which very accurate reference data are available and the challenging case of increasingly extended push-pull oligomer chains. The resulting approximate Bethe-Salpeter analytic gradients are shown to compare well with the most accurate time-dependent density-functional theory (TD-DFT) data, curing in particular most of the pathological cases encountered with TD-DFT when a nonoptimal exchange-correlation functional is used.

Comprehensive measurement of the near-infrared refractive index of GaAs at cryogenic temperatures.

The refractive index is a critical parameter in optical and photonic device design. However, due to the lack of available data, precise designs of devices working in low temperatures are still frequently limited. In this work, we have built a homemade spectroscopic ellipsometer (SE) and measured the refractive index of GaAs at a matrix of temperatures (4 K < T < 295 K) and photon wavelengths (700 nm < λ < 1000 nm) with a system error of ∼0.04. We verified the credibility of the SE results by comparing them with afore-reported data at room temperature and with higher precision values measured by vertical GaAs cavity at cryogenic temperatures. This work makes up for the lack of the near-infrared refractive index of GaAs at cryogenic temperatures and provides accurate reference data for semiconductor device design and fabrication.

The sustainability agenda and its implications for post-trade technology adoption

Environmental, social and governance (ESG), referring to the process of integrating ESG factors into investment decisions, and sustainable and impact investing, referring to the intent to deliver an environmental or social outcome on top of financial performance, are growing very rapidly. BNY Mellon and Aviva Investors reflected on implications for post-trade technology adoption. Rapid growth in demand is accompanied by increased expectations from a range of parties including regulators with a focus on disclosures and labelling, international institutions seeking greater alignment and lobbying groups asking for more data. All of this is affecting data to be sourced, controlled and reported, and reporting is complicated by lack of consensus on ESG definitions and difficulty in comparing data and incorporating investors' preferences across jurisdictions. Each party in the post-trade custody chain depends on reference data and needs access to the same accurate sustainability ESG reference data. Missing, different and inaccurate reference data creates errors and discrepancies. Sustainability data acquisition is thus becoming an emerging area of focus for post-trade servicing teams, particularly finding, formatting, correcting and monitoring updates and maintaining asset coverage, creating a shift in operating model. Technology is a critical enabler given the growing volume of data, lack of a single ESG definition and the need to prove product claims and support clients' preferences throughout the custody chain

Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT.

NMR spectroscopy undoubtedly plays a central role in determining molecular structures across different chemical disciplines, and the accurate computational prediction of NMR parameters is highly desirable. In this work, a new Δ-machine learning approach is presented to correct DFT-computed NMR chemical shifts using input features from the calculation and in addition highly accurate reference data at the CCSD(T)/pcSseg-2 level of theory with a basis set extrapolation scheme. The model is trained on a data set containing 1000 optimized and geometrically distorted structures of small organic molecules comprising most elements of the first three periods and containing data for 7090 1H and 4230 13C NMR chemical shifts. Applied to the PBE0/pcSseg-2 method, the mean absolute deviation (MAD) on the internal NMR shift test set is reduced by 81% for 1H and 92% for 13C at virtually no additional computational cost. For 12 different DFT functional and basis set combinations, the MAD of the ML-corrected NMR shifts ranges from 0.021 to 0.039 ppm (1H) and from 0.38 to 1.07 ppm (13C). Importantly, the new method consistently outperforms the simple and widely used linear regression correction technique. This behavior is reproduced on three different external benchmark sets, confirming the generality and robustness of the correction scheme, which can easily be applied in DFT-based spectral simulations.

Density-Corrected Density Functional Theory for Molecular Properties.

Density-corrected (DC) density functional theory (DFT) has been proposed to overcome difficulties related to the self-interaction error. The procedure uses the Hartree-Fock electron density (matrix) non-self-consistently in conjunction with an approximate functional. DC-DFT has so far mainly been tested for total energy differences, whereas other types of molecular properties have not been evaluated systematically. This work focuses on the performance of DC-DFT for molecular properties, namely, dipole moments, static polarizabilities, and electric field gradients (EFGs) at atomic nuclei. Accurate reference data were generated from coupled-cluster theory to assess the performance of DC and self-consistent DFT calculations for twelve molecules, including diatomics with transition metals. DC-DFT does no harm in dipole moment calculations, but it negatively impacts the polarizability in at least one case. DC-DFT performs well for EFGs, even for the difficult case of CuCl.

A semilocal machine-learning correction to density functional approximations.

Machine learning (ML) has demonstrated its potential usefulness for the development of density functional theory methods. In this work, we construct an ML model to correct the density functional approximations, which adopts semilocal descriptors of electron density and density derivative and is trained by accurate reference data of relative and absolute energies. The resulting ML-corrected functional is tested on a comprehensive dataset including various types of energetic properties. Particularly, the ML-corrected Becke's three parameters and the Lee-Yang-Parr correlation (B3LYP) functional achieves a substantial improvement over the original B3LYP on the prediction of total energies of atoms and molecules and atomization energies, and a marginal improvement on the prediction of ionization potentials, electron affinities, and bond dissociation energies; whereas, it preserves the same level of accuracy for isomerization energies and reaction barrier heights. The ML-corrected functional allows for fully self-consistent-field calculation with similar efficiency to the parent functional. This study highlights the progress of building an ML correction toward achieving a functional that performs uniformly better than B3LYP.

Deep Learning–Based Prediction of Kuroshio Path South of Japan

Abstract Variation of the Kuroshio path south of Japan has an important impact on weather, climate, and ecosystems due to its distinct features. Motivated by the ever-popular deep learning methods using neural network architectures in areas where more accurate reference data for oceanographic observations and reanalysis are available, we build four deep learning models based on the long short-term memory (LSTM) neural network, combined with the empirical orthogonal function (EOF) and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), namely, the LSTM, EOF–LSTM, CEEMDAN–LSTM, and EOF–CEEMDAN–LSTM. Using these models, we conduct long-range predictions (120 days) of the Kuroshio path south of Japan based on 50-yr ocean reanalysis and nearly 15 years of satellite altimeter data. We show that the EOF–CEEMDAN–LSTM performs the best among the four models, by attaining approximately 0.739 anomaly correlation coefficient and 0.399° root-mean-square error for the 120-day prediction of the Kuroshio path south of Japan. The hindcasts of the EOF–CEEMDAN–LSTM are successful in reproducing the observed formation and decay of the Kuroshio large meander during 2004/05, and the formation of the latest large meander in 2017. Finally, we present predictions of the Kuroshio path south of Japan at 120-day lead time, which suggest that the Kuroshio will remain in the state of the large meander until November 2022.

Optimizing forest canopy structure retrieval from smartphone‐based hemispherical photography

Abstract Hemispherical photography (HP) is a long‐standing tool for forest canopy characterization. Currently, there are low‐cost fisheye lenses to convert smartphones into highly portable HP equipment (smartphone‐based HP, hereafter SHP). However, there is an obstacle to having a close‐to‐ideal method for citizen science and large‐scale or opportunistic sampling: the known sensitivity of HP to illumination conditions. The purpose of this paper is to test a ready‐to‐use approach based on previous research and to contribute to quantifying the errors associated with choosing SHP in non‐recommended light conditions over well‐established HP practices. In 30 locations distributed in broadleaf and coniferous woodlands, a total of 1080 photographs were taken with two smartphone models, manipulating the exposure, and under varied sky conditions. After image binarization, accurate reference data was employed to evaluate the reliability of extracting canopy parameters from SHP. The proposed methodology can reliably quantify canopy openness (RMSE ~0.04) and plant area index (RMSE ~0.4). Results suggest that SHP, when used following the recommendations of the present study, allows retrieval of reliable canopy metrics independently of sky conditions and forest type.

Reduced specificity for the local lymph node assay for lipophilic chemicals: Implications for the validation of new approach methods for skin sensitization

Meaningful and accurate reference data are crucial for the validation of New Approach Methodologies (NAMs) in toxicology. For skin sensitization, multiple reference datasets are available including human patch test data, guinea pig data and data from the mouse local lymph node assay (LLNA). When assessed against the LLNA, a reduced sensitivity has been reported for in vitro and in chemico assays for lipophilic chemicals with a LogP ≥3.5, resulting in reliability restrictions within the h-CLAT OECD test guideline.Here we address the question of whether LLNA data are an appropriate reference for chemicals in this physicochemical range. Analysis of LLNA vs human reference data indicates that the false-discovery rate of the LLNA is significantly higher for chemicals with LogP ≥3.5. We present a mechanistic hypothesis whereby irritation caused by testing lipophilic chemicals at high test doses leads to unspecific cell proliferation. The accompanying analysis indicates that for lipophilic chemicals with negative calls in in vitro and in chemico assays, resorting to the LLNA is not necessarily a better option. These results indicate that the validation of NAMs in this particular LogP range should be based on a more holistic evaluation of the reference data and not solely upon LLNA data.

Ab initio quantum scattering calculations for the CO-O2 system and a new CO-O2 potential energy surface: O2 and air broadening of the R(0) line in CO.

We present ab initio calculations of the collisional broadening of the R(0) pure rotational line in CO (at 115GHz) perturbed by O2. Our calculations are done in a fully quantum way by solving close-coupling quantum-scattering equations without any approximations. We also report a new, highly accurate CO-O2 potential energy surface on which we did the quantum-scattering calculations. The calculated collisional broadening agrees with the available experimental data in a wide temperature range. The calculated collisional shift is negligible compared to the broadening, which is also consistent with the experimental data. We combine this result with our previous calculations for the same line in CO perturbed by N2 [Jóźwiak et al., J. Chem. Phys. 154, 054314 (2021)]; the obtained air-perturbed broadening of the R(0) pure rotational line in CO and its temperature dependence perfectly agree with the HITRAN database. This result constitutes an important step toward developing a methodology for providing accurate ab initio reference data on spectroscopic collisional line-shape parameters for molecular systems relevant to the Earth's atmosphere and for populating spectroscopic line-by-line databases.

Reference Data Accuracy Impacts Burned Area Product Validation: The Role of the Expert Analyst

Accurate reference data to validate burned area (BA) products are crucial to obtaining reliable accuracy metrics for such products. However, the accuracy of reference data can be affected by numerous factors; hence, we can expect some degree of deviation with respect to real ground conditions. Since reference data are usually produced by semi-automatic methods, where human-based image interpretation is an important part of the process, in this study, we analyze the impact of the interpreter on the accuracy of the reference data. Here, we compare the accuracy metrics of the FireCCI51 BA product obtained from reference datasets that were produced by different analysts over 60 sites located in tropical regions of South America. Additionally, fire severity, tree cover percentage, and canopy height were selected as explanatory sources of discrepancies between interpreters’ reference BA classifications. We found significant differences between the FireCCI51 accuracy metrics obtained with the different reference datasets. The highest accuracies (highest Dice coefficient) were obtained with the reference dataset produced by the most experienced interpreter. The results indicated that fire severity is the main source of discrepancy between interpreters. Disagreement between interpreters was more likely to occur in areas with low fire severity. We conclude that the training and experience of the interpreter play a crucial role in guaranteeing the quality of the reference data.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods.

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

ATOMIC-2 Protocol for Thermochemistry.

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2um analyses.