Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “dependence”

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

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

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Resolving the xi Boo Binary with Chandra, and Revealing the Spectral Type Dependence of the Coronal "Fip Effect"

On 2008 May 2, Chandra observed the X-ray spectrum of xi Boo (G8 V+K4 V), resolving the binary for the first time in X-rays and allowing the coronae of the two stars to be studied separately. With the contributions of ξ Boo A and B to the system's total X-ray emission now observationally established (88.5% and 11.5% respectively), consideration of mass loss measurements for GK dwarfs of various activity levels (including one for xi Boo) leads to the surprising conclusion that xi Boo B may dominate the wind from the binary, with xi Boo A's wind being very weak despite its active corona. Emission measure (EM) distributions and coronal abundances are computed for both stars and compared with Chandra measurements of other moderately active stars with G8-K5 spectral types, all of which exhibit a narrow peak in EM near log T = 6.6, indicating that the coronal heating process in these stars has a strong preference for this temperature. As is the case for the Sun and many other stars, our sample of stars shows coronal abundance anomalies dependent on the first ionization potential (FIP) of the element. We see no dependence of the degree of FIP effect on activity, but there is a dependence on spectral type, a correlation that becomes more convincing when moderately active main-sequence stars with a broader range of spectral types are considered. This clear dependence of coronal abundances on spectral type weakens if the stellar sample is allowed to be contaminated by evolved stars, interacting binaries or extremely active stars with logLX 29, explaining why this correlation has not been recognized in the past.

CHANDRA↗
NASA NTRS2012

Satellite-Based Evidence of Wavelength-Dependent Aerosol Absorption in Biomass Burning Smoke Inferred from Ozone Monitoring Instrument

We provide satellite-based evidence of the spectral dependence of absorption in biomass burning aerosols over South America using near-UV measurements made by the Ozone Monitoring Instrument (OMI) during 2005-2007. In the current near-UV OMI aerosol algorithm (OMAERUV), it is implicitly assumed that the only absorbing component in carbonaceous aerosols is black carbon whose imaginary component of the refractive index is wavelength independent. With this assumption, OMI-derived aerosol optical depth (AOD) is found to be significantly over-estimated compared to that of AERONET at several sites during intense biomass burning events (August-September). Other well-known sources of error affecting the near-UV method of aerosol retrieval do not explain the large observed AOD discrepancies between the satellite and the ground-based observations. A number of studies have revealed strong spectral dependence in carbonaceous aerosol absorption in the near-UV region suggesting the presence of organic carbon in biomass burning generated aerosols. A sensitivity analysis examining the importance of accounting for the presence of wavelength-dependent aerosol absorption in carbonaceous particles in satellite-based remote sensing was carried out in this work. The results convincingly show that the inclusion of spectrally-dependent aerosol absorption in the radiative transfer calculations leads to a more accurate characterization of the atmospheric load of carbonaceous aerosols.

Jethva, H.↗
NASA NTRS2013

Experimental Identification and Simulation of Time and/or Rate Dependent Reversible and Irreversible Deformation Regions for both a Titanium and Nickel Alloy

In this paper time and/or rate dependent deformation regions are experimentally mapped out as a function of temperature. It is clearly demonstrated that the concept of a threshold stress (a stress that delineate reversible and irreversible behavior) is valid and necessary at elevated temperatures and corresponds to the classical yield stress at lower temperatures. Also the infinitely slow modulus, (Es) i.e. the elastic modulus of the material if it was loaded at an infinitely slow strain rate, and the "dynamic modulus", modulus, Ed, which represents the modulus of the material if it is loaded at an infinitely fast rate are used to delineate rate dependent from rate independent regions. As demonstrated at elevated temperatures there is a significant difference between the two modulus values, thus indicating both significant time-dependence and rate dependence. In the case of the nickel-based super alloy, ME3, this behavior is also shown to be grain size specific. Consequently, at higher temperatures viscoelastic behavior exist below k (i.e., the threshold stress) and at stresses above k the behavior is viscoplastic. Finally a multi-mechanism, stress partitioned viscoelastic model, capable of being consistently coupled to a viscoplastic model is characterized over the full temperature range investigated for Ti-6-4 and ME3.

Arnold, Steven M.↗
NASA NTRS2015

The Time-Dependent Chemistry of Cometary Debris in the Solar Corona

Recent improvements in solar observations have greatly progressed the study of sungrazing comets. They can now be imaged along the entirety of their perihelion passage through the solar atmosphere, revealing details of their composition and structure not measurable through previous observations in the less volatile region of the orbit further from the solar surface. Such comets are also unique probes of the solar atmosphere. The debris deposited by sungrazers is rapidly ionized and subsequently influenced by the ambient magnetic field. Measuring the spectral signature of the deposited material highlights the topology of the magnetic field and can reveal plasma parameters such as the electron temperature and density. Recovering these variables from the observable data requires a model of the interaction of the cometary species with the atmosphere through which they pass. The present paper offers such a model by considering the time-dependent chemistry of sublimated cometary species as they interact with the solar radiation field and coronal plasma. We expand on a previous simplified model by considering the fully time-dependent solutions of the emitting species' densities. To compare with observations, we consider a spherically symmetric expansion of the sublimated material into the corona and convert the time-dependent ion densities to radial profiles. Using emissivities from the CHIANTI database and plasma parameters derived from a magnetohydrodynamic simulation leads to a spatially dependent emission spectrum that can be directly compared with observations. We find our simulated spectra to be consistent with observation.

sun: corona↗
NASA NTRS2014

External Dependencies-Driven Architecture Discovery and Analysis of Implemented Systems

A method for architecture discovery and analysis of implemented systems (AIS) is disclosed. The premise of the method is that architecture decisions are inspired and influenced by the external entities that the software system makes use of. Examples of such external entities are COTS components, frameworks, and ultimately even the programming language itself and its libraries. Traces of these architecture decisions can thus be found in the implemented software and is manifested in the way software systems use such external entities. While this fact is often ignored in contemporary reverse engineering methods, the AIS method actively leverages and makes use of the dependencies to external entities as a starting point for the architecture discovery. The AIS method is demonstrated using the NASA's Space Network Access System (SNAS). The results show that, with abundant evidence, the method offers reusable and repeatable guidelines for discovering the architecture and locating potential risks (e.g. low testability, decreased performance) that are hidden deep in the implementation. The analysis is conducted by using external dependencies to identify, classify and review a minimal set of key source code files. Given the benefits of analyzing external dependencies as a way to discover architectures, it is argued that external dependencies deserve to be treated as first-class citizens during reverse engineering. The current structure of a knowledge base of external entities and analysis questions with strategies for getting answers is also discussed.

Ganesan, Dharmalingam↗
NASA NTRSDate not supplied

TROPOMI Geometry-dependent Lambertian-Equivalent surface Reflectivity (GLER) Product for Improved Trace-Gas Retrieval

Accurate information about the reflectivity of the Earth's surface is required for most satellite retrievals of atmospheric composition, and this information is generally taken from monthly surface reflectivity climatology that neglects angular dependence. Previously we introduced Geometry-dependent Lambertian-equivalent surface reflectivity (GLER) which captures solar and satellite viewing angle dependence as well as daily and seasonal changes. GLER is calculated from simulations of Rayleigh-only top-of-atmosphere (TOA) radiances over non-Lambertian surfaces. We use NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) bidirectional reflectance distribution function (BRDF) product over land and the wind-dependent Cox–Munk wave-facet slope distribution including water-leaving radiance over water to accounts for surface BRDF. We have developed global GLER product, previously for the Ozone Monitoring Instrument (OMI) and recently for Sentinel-5 Precursor (S5P) TROPOspheric Monitoring Instrument (TROPOMI) with several new improvements and updates. We have implemented the near real time daily V006 MODIS MCD43C1 BRDF data and gap-filled with a daily BRDF coefficient climatology created from 2002-2017 V006 MCD43GF data. The NASA’s Global Modelling Initiative hourly 0.25 x 0.25 deg Replay simulations are used for more accurate determination of pixel specific terrain pressure. To improve detection of seasonal snow/ice scenes, we use the 4-km snow cover product from the Interactive Multi-sensor Snow and Ice Mapping System (IMS). Finally, we use an improved version of the vector linearized discrete ordinate radiative transfer (VLIDORT) for update of the top-of-atmosphere (TOA) radiance look-up-tables (LUTs). We demonstrate how the use of GLER is beneficial to TROPOMI’s high spatial resolution (up to 3.5 km x 3.5 km) measurements to monitor atmospheric trace gas pollutants down to the sub-city scale.

TROPOMI↗
DOE OSTI2022

TECHNICAL BACKGROUND FOR THE UPDATE AND EXTENSION OF THE TIME-DEPENDENT ALLOWABLE STRESSES OF TYPE 304H AND 316H STAINLESS STEELS

Type 304H and 316H stainless steels are codified in the ASME Boiler and Pressure Vessel Code for Section III, Division 5, Class A construction for up to 1500F (816C) and 300,000 hours. Extension of the design lifetimes to 500,000 hours has been undertaken by various research projects and by the ASME Section III, Division 5 Code Committees. Due to a long-standing issue related to non-classical creep behavior on the use of the time to the onset of tertiary creep as one of the time-dependent allowable stress criteria, little progress was made in the extension of the time-dependent allowable stresses for Type 304H and 316H stainless steels. A recent effort by Dabrow and Nestell (Impact of Tertiary Creep on Time Dependent Allowable Stresses for Type 304H and 316H Stainless Steels, Report 0300-0003-RPT-001, MPR Associates, Alexandria, VA, 2020) has provided a rational method for the treatment of the highly variable data for the time to onset of tertiary creep. In this paper, the background formulas for determining the time-dependent allowable stress values of Type 304H and 316H stainless steels, as assembled from relevant project work, are presented. These updates and extensions are being recommended to the ASME Code committees for approval, and are subject to change upon feedback from ASME Section III Code committees.

304/316 life extension↗
DOE OSTI2024

Evaluation of Thermal Scattering Law for U 3 Si 2 Using Temperature-Dependent Phonon Density of States

The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Temperature and illumination dependence of silicon heterojunction solar cells with a wide range of wafer resistivities

Abstract Recently, the significant improvements in the surface and contact passivation of silicon (Si) solar cells as well as their bulk quality have shifted their operating point to higher injections. Hence, they are less dependent on wafer doping. This shift opens an opportunity of using high‐resistivity wafers for practical photovoltaic applications, introducing a promising approach to push the cell efficiency towards the intrinsic limit and to improve the module reliability by increasing the cell breakdown voltage. Therefore, insights into the performance of Si solar cells using high‐resistivity wafers at various operating temperatures are of significant interest. In this study, we investigate the temperature‐ and illumination‐dependent performance of Si heterojunction (SHJ) solar cells using a wide range of wafer resistivities (between 3 and 1000 Ω⋅cm). Although a reduction in the passivation quality of the passivating contacts is observed at elevated temperature, the impact on the temperature coefficient of the open‐circuit voltage (TC V oc )—the dominant contributor to the temperature coefficient (TC) of the cell efficiency—is very limited. Their TC V oc are still dominated by the temperature dependence of the effective intrinsic carrier concentration. Furthermore, we also find that the investigated cells are more sensitive to temperature variation at lower illumination intensities. It is noteworthy that the efficiency of the cells fabricated using high‐resistivity wafers is comparable to that of the reference cells at any given temperature, highlighting the potential of using high‐resistivity wafers for solar cells.

14 SOLAR ENERGY↗
DOE OSTI2026

Directional dependence of equilibrated TLD-400 chips in multiple radiation fields

Fielding of thermoluminescent dosimeters (TLDs) for measurement of photon radiation dose in experiments is the standard practice for γ-irradiation facilities, pulsed power x-ray facilities, and reactor facilities at Sandia National Laboratories (SNL). Due to the high-dose experimental conditions and the mixed ( 1 n, γ) fields in these facilities, SNL radiation metrologists have historically used CaF 2 :Mn TLDs (also known as TLD-400). Recent inquiries to the radiation metrology staff have raised concerns that the aluminum-equilibrated TLD-400 chips may exhibit a directionally dependent response. The metrologists were asked whether the dose measured by the chip may be impacted by the angle of incidence on the equilibrated TLD. To provide a thorough answer to this query, a set of adjoint Monte Carlo radiation transport calculations was performed for three different equilibrated TLDs as well as bare TLD chips using the Integrated Tiger Series (ITS) code. The key feature of the adjoint calculations performed in this study is that each photon escaping the modeled geometry was tallied into angular bins to provide information on both the energy and angular dependence of the equilibrated chip. After the adjoint Monte Carlo calculations were completed, the resulting energy-dependent response function for each angular bin was convolved with multiple photon energy spectra representing various radiation facilities at SNL. The radiation facilities selected for analysis span a range of photon energies from approximately 1 keV up to approximately 20 MeV. Thus, the presented results are applicable to a wide variety of radiation facilities around the world. Although the bare TLD-400 chip was expected to display the largest variation due to the photon angle of impact on the dosimeter, the dosimeter with the thinnest aluminum equilibrator (SNL thin equilibrated TLD-400) was determined to have the biggest differential between the impact angle with the maximum dose ( D max ) and the impact angle with the minimum dose ( D min ). However, the SNL normal equilibrated TLD-400 chip demonstrated a dramatic reduction in that differential between maximum and minimum dose angles. The reduction in this differential is one of the dominant factors in experimenters’ choice to field these dosimeters at SNL radiation facilities. The results from the PNNL (Hanford) energy-flattening field capsule are consistent with the previous publications. The differential dose responses due to the photon impact angle indicate that experimenters should strive to field their TLD-400 dosimeters in a consistent manner to avoid additional uncertainty in the measurements based on dosimeter orientation.

Adjoint radiation transport↗
DOE OSTI2022

Excitation Intensity- and Size-Dependent Halide Photosegregation in CsPb(I 0.5 Br 0.5 ) 3 Perovskite Nanocrystals

Although broad consensus exists that photoirradiation of mixed-halide lead perovskites leads to anion segregation, no model today fully rationalizes all aspects of this near ubiquitous phenomenon. In this work, we quantitatively compare experimental, CsPb(I 0.5 Br 0.5 ) 3 nanocrystal (NC) terminal anion photosegregation stoichiometries and excitation intensity thresholds to a band gap-based, thermodynamic model of mixed-halide perovskite photosegregation. Mixed-halide NCs offer strict tests of theory given physical sizes, which dictate local photogenerated carrier densities. We observe that mixed-anion perovskite NCs exhibit significant robustness to photosegregation, with photosegregation propensity decreasing with decreasing NC size. Observed size- and excitation intensity-dependent photosegregation data agree with model predicted size- and excitation intensity-dependent terminal halide stoichiometries. Established correspondence between experiment and theory, in turn, suggests that mixed-halide perovskite photostabilities can be predicted a priori using local gradients of (empirical) Vegard’s law expressions of composition-dependent band gaps.

36 MATERIALS SCIENCE↗
DOE OSTI2026

California Trees Seasonally Use Augmented Water Sources: Water Isotope Tracking in a Groundwater‐Dependent Ecosystem

Sustainable groundwater management must account for the needs of groundwater dependent ecosystems. To understand the relationship of ecosystems and seasonal water use, we studied the stable isotope composition (δ 18 O and δ 2 H) of water in streamside trees in a semi-arid streamside environment (Livermore, California, USA). We sampled seven trees at two sites every other month from April 2024 through April 2025 for tree xylem stable water isotope signatures. These data were compared to potential source waters: precipitation, imported surface water, soil water and regional groundwaters. Large daily precipitation events were found to be isotopically similar to regional groundwater and were thus treated as one water source. A Bayesian mixing model using stable water isotopes was used to determine the ratios of these three potential source waters (small daily precipitation events, groundwater/large daily precipitation events and imported water) present in tree xylem water. On average, tree water sources include 32% imported water (SD = 9%), 35% small daily precipitation events (SD = 10%) and 33% groundwater (SD = 3%), with significant seasonal variation (t summer-winter = 30.8, p < 0.01), particularly drawing more imported water (more than 55%) in the summer. While small daily precipitation events contribute only 10% of the total precipitation in our dataset, it represents a third of water used by trees. In addition, while these ecosystems are designated as groundwater dependent ecosystems, the trees use approximately one third imported water and even more during dry summer months. This approach provides water managers with a practical tool for quantifying ecosystem water needs, supporting data-driven decisions and regulatory compliance. While California's Sustainable Groundwater Management Act emphasizes supporting groundwater dependent ecosystems, it allows flexibility in demonstrating benefits. In conclusion, our methodology provides a way to document that management actions (such as managed aquifer recharge with imported water) deliver measurable co-benefits to GDEs.

Geosciences↗
DOE OSTI2021

Skeletal model reduction with forced optimally time dependent modes

Skeletal model reduction based on local sensitivity analysis of time dependent systems is presented in which sensitivities are modeled by forced optimally time dependent (f-OTD) modes. The f-OTD factorizes the sensitivity coefficient matrix into a compressed format as the product of two skinny matrices, i.e. f-OTD modes and f-OTD coefficients. The modes create a low-dimensional, time dependent, orthonormal basis which capture the directions of the phase space associated with most dominant sensitivities. These directions highlight the instantaneous active species, and reaction paths. Evolution equations for the f-OTD modes and coefficients are derived, and the implementation of f-OTD for skeletal reduction is described. For demonstration, skeletal reduction is conducted of the constant pressure ethylene-air burning in a zero-dimensional reactor, and new reduced models are generated. The laminar flame speed, the ignition delay, and the extinction curve as predicted by the models are compared against some existing skeletal models in literature for the same detailed model. Finally, the results demonstrate the capability of f-OTD to eliminate unimportant reactions and species in a systematic, efficient and accurate manner.

42 ENGINEERING↗
DOE OSTI2020

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Spectrally-dependent positive and negative photo-plastic effects in CdZnTe and CdZnTeSe

We studied the Vickers microhardness HV0.025 of CdZnTe and CdZnTeSe samples upon illumination with quasi-monochromatic light with wavelengths ranging between 750 and 1540 nm. We observed that light with a wavelength close to or above the bandgap of the samples results in a positive photo-plastic effect (hardening), and light in the spectral range well below the band gap can lead both to positive or negative effects depending on the parameters of deep levels in the bandgap. We performed measurements of spectrally dependent photoconductivity and compared them with HV0.025. Based on the analysis, we propose a complex qualitative model explaining the spectral dependence of HV0.025 by the charging and neutralization of deep levels by optical transitions between the valence and conduction bands and between the bands and deep levels in the band gap. Tuning of parameters of deep levels could be used to control the sign and magnitude of the photo-plastic effect.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Pressure-dependent kinetics of cyclopentene consumption

Recent experiments have uncovered deficiencies in the ability of current kinetic models for cyclopentane combustion to predict species profiles as a function of O2 concentration. One likely source of these discrepancies flows from the limited availability of relevant kinetic data for key functionalized intermediates, requiring the use of distant analogies to estimate their rates. This work fills this gap for cyclopentene, the most prominent C5 intermediate in low-temperature cyclopentane combustion. Ab initio transition-state-theory based master equation methods are used to calculate pressure-dependent rate constants across four potential energy surfaces (C5H8 + OH, C5H8 + HO2, C5H7, and C5H7 + O2). Potential energy surfaces are characterized at the CCSD(T)-F12/cc-pVDZ-F12//revDSD-PBEP86-D3BJ/def2-TZVPP level of theory. Pressure-dependent rate constants and branching fractions are determined via 1D master equation calculations. The results are used to analyze the competition for radicals between cyclopentene and cyclopentane in the intermediate temperature region, and to identify the dominant pathways flowing from these initiation channels. On the OH initiation surface, we find good agreement with recently published experimental rate constants at high temperature, and we elucidate the complex temperature dependence below 800 K, where 𝜋𝜋 addition becomes prominent. On the HO2 initiation surface, we find an interesting alternative route to bicyclic ether formation via well-skipping over the HO2 adduct well. On the cyclopentenyl radical surface, the major product is cyclopentadiene plus H. On the cyclopentenyl + O2 surface, we find that resonance stabilization largely prevents the allylic radical from undergoing oxidation, whereas the alkylic radical has a somewhat elevated propensity for oxidation pathways relative to cyclopentyl.

ab initio calculations↗
DOE OSTI2025

The Temperature Dependence of the Langmuir Adsorption Model for a Single-Site Metal–Organic Framework

The single-site Langmuir adsorption model, also known as the Langmuir isotherm equation, is one of the simplest possible descriptions of adsorption phenomena, and yet finds widespread applicability across a range of disciplines. In its simplest form, it is deployed to treat adsorption equilibria at constant temperature (i.e., along isotherms); however, at the heart of its derivation is a more general class of models that each incorporate an explicit temperature dependence, subject to assumptions about the spatial/translational degrees of freedom of the adsorbed species. In this work, measurements of the temperature dependence of supercritical adsorption of H 2 on a single-site metal-organic framework (MOF) are presented, and fitted using a range of Langmuir models with distinct treatments of degrees of freedom in the adsorbed phase. Surprisingly, all of the models can be used to adequately represent the measured data, despite yielding significantly different values for binding energy and the temperature dependence of the isosteric enthalpy of adsorption (i.e., the isosteric heat, qst). Furthermore, a critical finding is that the mean-temperature isosteric enthalpy of adsorption remains consistent across all models within experimental error, highlighting its reliability for evaluating adsorption thermodynamics.

08 HYDROGEN↗
DOE OSTI2022

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗