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Towards Accurate and Efficient Predictions of Martensitic Transition Temperatures for Shape Memory Alloys from First Principles

Shape memory alloys (SMAs) can remember and recover their original shapes upon heating due to the existence of a reversible martensitic transition (MT) between the high-temperature austenite (A) and low-temperature martensite (M) phases. The martensitic transition temperature (MTT) is a crucial characteristic of an SMA. SMAs have a wide range of potential applications in aerospace, civil engineering, bioengineering, etc., but their operating temperatures are limited by the available SMAs. MTT can be tuned by alloying a binary with other metals, and the multicomponent NiTi-based SMAs have attracted tremendous research efforts recently. It is not efficient to employ the trial-and-error method alone due to the dramatically increased complexity and possibilities in compositions, and thus reliable theory and accurate computations play an indispensable role in creating SMAs with desirable properties.

Zhigang Wu↗

DOE OSTI2019

Unraveling Ferroelectric Polarization and Ionic Contributions to Electroresistance in Epitaxial Hf 0.5 Zr 0.5 O 2 Tunnel Junctions

Tunnel devices based on ferroelectric Hf 0.5 Zr 0.5 O 2 (HZO) barriers hold great promises for emerging data storage and computing technologies. The resistance state of the device can be changed through use of a suitable writing voltage. However, the microscopic mechanisms leading to the resistance change are an intricate interplay between ferroelectric polarization controlled barrier properties and defect-related transport mechanisms. Herein, the fundamental role of the microstructure of HZO films determining the balance between those contributions is demonstrated. The HZO film presents coherent or incoherent grain boundaries, associated to the coexistance of monoclinic and orthorhombic phases, which are dictated by the mismatch with the substrates for epitaxial growth. These grain boundaries are the toggle that allows to obtain either large (up to ≈450%) and fully reversible genuine polarization controlled electroresistance when only the orthorhombic phase is present or an irreversible and extremely large (≈10 3 –10 5 %) electroresistance when both phases coexist.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A molecular dynamics study of domain switching in BiFeO 3 nanofilm under DC electric field

The performance of ferroelectric materials is deeply rooted in the domain switching process triggered by an applied electric field. To understand the effect of controlling factors on the domain switching characteristics, nanoscale studies are essential. In this work, an atomistic-scale computational framework is developed to study the domain switching process of bismuth ferrite (BiFeO 3 ) nanofilms. Through a series of molecular dynamics simulations, the effects of duration and magnitude of an electric field, domain size and nanofilm thickness on the domain switching behavior are investigated. The evolution of domains under different magnitudes and durations of the applied electric field is studied, and the results of unswitched and switched cases are summarized in a switching map. Analysis of various nanofilms reveals that by increasing the film thickness, the switching time is increased. Additionally, the nanofilms with different domain sizes and configurations are examined, and the minimum domain size for complete reversal switching is obtained. Our results are helpful to predict and tune the switching process in ferroelectric materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Discrete-Element and Material-Point Method (DEM and MPM) Based Solvers for Sustainable Technologies

We present the use of discrete element method (DEM) and material point method (MPM) in three relevant green technology applications that include biomass feedstock handling, lithium-ion battery manufacturing, and high-pressure reverse osmosis. Our open-source DEM and MPM solvers are developed using performance portable grid and particle management library, AMReX, thus enabling superior performance on NVIDIA and AMD GPUs with > 100 million particles. Our DEM solver resolves the motion of individual particles in a granular system and includes a bonded sphere method for modeling non-spherical particles along with Hertzian and liquid bridge-based contact models. We simulate highly variable biomass feedstock flows in large-scale hoppers for biofuel production and electrode calendering in battery manufacturing using DEM. Our simulations predict flow blockage in large scale biomass hoppers and electrode microstructure variations, thus providing valuable information for biofuel and battery manufacturers, respectively. The second half of the talk will be on MPM and its application towards pore resolved simulations of reverse osmosis membranes under compressive loads. We present a validation study of our MPM simulations with membrane microscopy imaging thus providing useful insights on membrane stability under high pressure conditions. We also present a spectral stability analysis of using linear hat, quadratic and cubic spline basis in MPM indicating regions of numerical stability.

BIOMASS FUELS,MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Repairing large cracks and reversing fatigue damage in structural metals

Self-healing materials represent a paradigm shift from traditional materials development, enabling intrinsic repair of functionality (such as strength) after a catastrophic failure as opposed to part replacement. Several healing mechanisms have been demonstrated in polymeric and ceramic materials, but few in metallic systems. This study demonstrates a novel liquid-assisted self-healing metal-matrix composite (MMC) designed to be capable of over 90% strength recovery after a healing cycle. The aluminum (Al)-based matrix is reinforced with continuous nickel-titanium (NiTi) shape-memory alloy (SMA) reinforcements. Using a tailored heat treatment for healing, a paired effect of crack closure from the SMA reinforcement and partial liquefaction of the matrix occurs. These effects result in a compressive force across the crack surface, and, coupled with increased diffusion rates from the liquefied matrix, produces consolidation and healing in the composite structure. This work provides experimental and computational evidence for the healing mechanism under both tensile and fatigue conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Computational study on the impact of gasoline-ethanol blending on autoignition and soot/NO x emissions under low-load gasoline compression ignition conditions

Here, in the present work, computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition (GCI) engine are performed to investigate the impact of gasoline-ethanol blending on autoignition, nitrogen oxide (NO x ), and soot emissions under low-load conditions. In order to represent the test gasoline (RD5-87), a four-component toluene primary reference fuel (TPRF)+ethanol (ETPRF) surrogate (with 10% ethanol by volume; E10) is employed. A three-dimensional (3D) engine CFD model employing finite-rate chemistry with a skeletal kinetic mechanism (including NO x sub-mechanism), adaptive mesh refinement (AMR), and hybrid method of moments (HMOM) is adopted to capture the in-cylinder combustion phenomena and soot/NO x emissions. The engine CFD model is validated against experimental data for three gasoline-ethanol blends: E10, E30 and E100, with varying ethanol content by volume. Model validation is carried out for a broad range of start-of-injection (SOI) timings (−21, −27, −36, and −45 crank angle degrees (°CA) after top-dead-center (aTDC)) with respect to in-cylinder pressure, heat release rate, combustion phasing, NO x and soot emissions. For relatively later injection timings (−21 and −27 °CA aTDC), E30 yields higher amount of soot than E10; while the trend reverses for early injection cases (−36 and −45 °CA aTDC ). On the other hand, E100 yields the lowest amount of soot among all fuels irrespective of SOI timing. Further, E10 shows a non-monotonic trend in soot emissions with SOI timing: SOI-36>SOI-45>SOI-21>SOI-27, while soot emissions from E30 exhibit monotonic decrease with advancing SOI timing. NO x emissions from various fuels follow a trend of E10>E30>E100. On the other hand, NO x emissions increase as SOI timing is advanced for all fuels, with an anomaly for E10 and E100 where NO x decreases when SOI is advanced beyond −36 °CA aTDC. Detailed analysis of the numerical results is performed to investigate the soot/NO x emission trends and elucidate the impact of chemical composition and physical properties on autoignition and emissions characteristics.

Computational fluid dynamics↗

DOE OSTI2023

A High‐Rate Li–CO 2 Battery Enabled by 2D Medium‐Entropy Catalyst

Abstract Lithium‐air batteries based on CO 2 reactant (Li–CO 2 ) have recently been of interest because it has been found that reversible Li/CO 2 electrochemistry is feasible. In this study, a new medium‐entropy cathode catalyst, (NbTa) 0.5 BiS 3 , that enables the reversible electrochemistry to operate at high rates is presented. This medium entropy cathode catalyst is combined with an ionic liquid‐based electrolyte blend to give a Li–CO 2 battery that operates at high current density of 5000 mA g −1 and capacity of 5000 mAh g −1 for up to 125 cycles, far exceeding reported values in the literature for this type of battery. The higher rate performance is believed to be due to the greater stability of the multi‐element (NbTa) 0.5 BiS 3 catalyst because of its higher entropy compared to previously used catalysts with a smaller number of elements with lower entropies. Evidence for this comes from computational studies giving very low surface energies (high surface stability) for (NbTa) 0.5 BiS 3 and transmission electron microscopystudies showing the structure being retained after cycling. In addition, the calculations indicate that Nb‐terminated surface promotes Li–CO 2 electrochemistry resulting in Li 2 CO 3 and carbon formation, consistent with the products found in the cell. These results open new direction to design and develop high‐performance Li–CO 2 batteries.

25 ENERGY STORAGE↗

DOE OSTI2023

Engineering Functionalized 2D Metal-Organic Frameworks Nanosheets with Fast Li + Conduction for Advanced Solid Li Batteries

Solid-state batteries can ensure high energy density and safety in lithium metal batteries, while polymer electrolytes are plagued by slow ion kinetics and low selective transport of Li + . Metal-organic frameworks (MOFs) are proposed as emerging fillers for solid-state poly(ethylene oxide)(PEO) electrolytes, however, developing functionalized MOFs and understanding their roles on ion transfer has proven challenging. Herein, combining computational and experimental results, the functional group regulation in MOFs can effectively change surficial charge distribution and limit anion movement is revealed, providing a potential solution to these issues. Specifically, functionalized 2D MOF sheets are designed through molecular engineering to construct high-performance composite electrolytes, where the electron-donating effect of substituents in 2D-MOFs effectively limits the movement of ClO 4 - and promotes mechanical properties and ion migration numbers (0.36 up to 0.64) of PEO. As a result, Li/Li cells with composite electrolyte exhibit superior cyclability for 1000 h at a current density of 0.2 mA cm -2 . Meanwhile, the solid LiFePO 4 /Li battery delivers highly reversible capacities of 148.8 mAh g -1 after 200 cycles. In conclusion, these findings highlight a new approach for anion confinement through the use of functional group electronic effects, leading to enhanced ionic conductivity, and a feasible direction for high-performance solid-state batteries.

25 ENERGY STORAGE↗

DOE OSTI2025

Phenome‐to‐genome insights for evaluating root system architecture in field studies of maize

Abstract Understanding the genetic basis of root system architecture (RSA) in crops requires innovative approaches that enable both high‐throughput and precise phenotyping in field conditions. In this study, we evaluated multiple phenotyping and analytical frameworks for quantifying RSA in mature, field‐grown maize in three field experiments. We used forward and reverse genetic approaches to evaluate >1700 maize root crowns, including a diversity panel, a biparental mapping population, and maize mutant and wild‐type alleles at two known RSA genes,DEEPER ROOTING 1(DRO1) andRootless1(Rt1). We show the utility of increasing the dimensionality of traditional two‐dimensional (2D) techniques, referred to as the “2D multi‐view” method, to improve the capture of whole root system information for mapping genetic variation influencing RSA. Comparison of univariate and multivariate genome‐wide association study (GWAS) approaches revealed that multivariate traits were effective at dissecting complex RSA phenotypes and identifying pleiotropic quantitative trait loci (QTLs). Overall, three‐dimensional (3D) root models generated from X‐ray computed tomography and digital phenotyping captured a larger proportion of RSA trait variations compared to other methods of root phenotyping, as evidenced by both genome‐wide and single‐gene analyses. Among the individual root traits, root pulling force emerged as a highly heritable estimate of RSA that identified the largest number of shared QTLs with 3D phenotypes. Our study shows that integrating complementary phenotyping technologies helps to provide a more comprehensive understanding of the genetic architecture of RSA in field‐grown maize.

Genetics & Heredity↗

DOE OSTI2013

MiR-34a targets GAS1 to promote cell proliferation and inhibit apoptosis in papillary thyroid carcinoma via PI3K/Akt/Bad pathway

Highlights: •MiR-34a is up- and GAS1 is down-regulated in papillary thyroid carcinoma. •GAS1 is a direct target for miR-34a. •MiR-34a promotes PTC cells proliferation and inhibits apoptosis through PI3K/Akt/Bad pathway. -- Abstract: MicroRNAs (miRNAs) are fundamental regulators of cell proliferation, differentiation, and apoptosis, and are implicated in tumorigenesis of many cancers. MiR-34a is best known as a tumor suppressor through repression of growth factors and oncogenes. Growth arrest specific1 (GAS1) protein is a tumor suppressor that inhibits cancer cell proliferation and induces apoptosis through inhibition of RET receptor tyrosine kinase. Both miR-34a and GAS1 are frequently down-regulated in various tumors. However, it has been reported that while GAS1 is down-regulated in papillary thyroid carcinoma (PTC), miR-34a is up-regulated in this specific type of cancer, although their potential roles in PTC tumorigenesis have not been examined to date. A computational search revealed that miR-34a putatively binds to the 3′-UTR of GAS1 gene. In the present study, we confirmed previous findings that miR-34a is up-regulated and GAS1 down-regulated in PTC tissues. Further studies indicated that GAS1 is directly targeted by miR-34a. Overexpression of miR-34a promoted PTC cell proliferation and colony formation and inhibited apoptosis, whereas knockdown of miR-34a showed the opposite effects. Silencing of GAS1 had similar growth-promoting effects as overexpression of miR-34a. Furthermore, miR-34a overexpression led to activation of PI3K/Akt/Bad signaling pathway in PTC cells, and depletion of Akt reversed the pro-growth, anti-apoptotic effects of miR-34a. Taken together, our results demonstrate that miR-34a regulates GAS1 expression to promote proliferation and suppress apoptosis in PTC cells via PI3K/Akt/Bad pathway. MiR-34a functions as an oncogene in PTC.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Switching speed limits in electrically driven VO 2 structural Mott–Peierls transition

Mott materials are archetypal quantum systems actively explored as next-generation electronic and photonic platforms, with potential applications spanning non-Von Neumann computing, robotics, energy storage, and microwave technologies. Among these, vanadium dioxide (VO 2 ) has emerged as one of the most intensively studied compounds, owing to its sharp, near-room-temperature insulator-to-metal phase transition. VO 2 also serves as a benchmark system for testing cutting-edge theories and experimental techniques. Here, we directly visualize the electrically driven transition dynamics in VO 2 using a microwave-driven, frequency-tunable pulsed transmission electron microscope that combines nanometer spatial and picosecond temporal resolution. Under high-frequency (MHz–GHz) excitation, we capture the ultrafast nucleation, propagation, and dissolution of metallic domains within an operating device over millions of reversible cycles. We observe the ultrafast formation of consistent metallic nuclei beneath the electrodes, followed by the propagation of a structural phase front at 4.54 nm/ns. Our experiments show that phonon-mediated structural recovery ultimately limits reversible switching of VO 2 at GHz frequencies, and that a tunable regime for reversible operation spans from kHz to GHz through device engineering. Beyond VO 2 , our approach provides a powerful framework for probing non-equilibrium structural transformations in correlated and functional materials under realistic electrical stimuli.

36 MATERIALS SCIENCE↗

DOE OSTI2015

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

For many problems in computational science and engineering, the so-called forward problem-solution of the underlying mathematical model to yield output quantities of interest, given input parameters--is difficult enough for frontier complex models, which are often characterized by coupled multiphysics and possibly stochastic behavior over a wide range of length and time scales. However, we face the need to move beyond the forward problem, to address what is often the ultimate goal of CS&E: decision-making. This requires us to tackle a spectrum of mathematical problems that subsume, and are thus even more difficult than, the forward problem. First, given experimental data, we wish to estimate unknown parameters characterizing a model of a natural or engineered system by solving an inverse problem. Second, we seek the optimal con figuration of the system (or experiments) by solving an optimal design problem. Third, the optimal operation of the system must be determined by solving an optimal control problem. And fourth, we must quantify uncertainties as they propagate through all of the preceding problems, from data to model inference to prediction and finally to optimal design and control. Optimal mathematical methods and algorithms for such end-to-end, data-to-decisions modeling and simulation of complex problems--requiring integrated solution of forward, inverse, optimization, and UQ problems for large, multiphysics, multiscale models--entails challenges of the highest order, while also presenting great opportunities for applied mathematics research. Unfortunately, research on forward, inverse, optimization, and UQ problems has all-too-often progressed in isolation. This has led to mathematical methods that perform well when considering the forward simulation in isolation, but are prohibitive or suboptimal or unstable when combined with other methods within the framework of inversion, optimization, or UQ. The reverse is also true: general-purpose methods developed within the inversion, optimization, and UQ fields often become prohibitive when applied to complex CS&E problems since they do not exploit their structure. DiaMonD is a multi-institutional DOE MMICC effort that aims to address the challenges of end-to-end, data-to-decisions modeling and simulation for complex CS&E problems in a unifi ed, systematic, and integrated fashion. Institutions involved are Colorado State, Florida State, Los Alamos, MIT, Oak Ridge, Stanford, and UT-Austin. The goals of DiaMonD are (1) to develop advanced mathematical methods and analysis for multimodel, multiphysics, multiscale model problems driven by frontier DOE applications, including those in subsurface energy and environmental flows, materials for energy storage and conversion, and ice sheet dynamics; (2) to create theory and algorithms for integrated inversion, optimization, and uncertainty quantification for these complex problems; and (3) to disseminate the philosophy of an integrated end-to-end, data-to-decisions approach to modeling and simulation of complex problems to the broader applied math and computational science communities through workshops and other outreach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

B 2 H 6 splitting on catalytic surfaces and role of BH 3 towards hydrogen spillover

A fundamental understanding of the spillover mechanism is an open and challenging problem and plays an important role in catalysis. In particular, bond-exchange spillover mechanism is considered to be effective for reversible storage and release of hydrogen at near ambient conditions. For this, three critical steps are needed: finding the right support (acceptor), the right catalyst to split H 2 , and ensuring that once H 2 is split, the H atoms can migrate on the surface with the help of secondary catalysts and eventually hydrogenate the entire material. In this paper we address these challenges using density functional theory. Here we show that BH 3 , a secondary catalyst, can be produced by symmetrically splitting its stable precursor, B 2 H 6 , on doped metal-free surfaces such as graphene and h-BN as well as on MOF5. In addition, to reduce computational cost, we develop structural descriptor and predictive model equation to effectively screen potential BH 3 binding sites. Symmetrical splitting of B 2 H 6 on different types of materials can address the hydrogen spillover challenge, making efficient storage of hydrogen possible.

08 HYDROGEN↗

NASA NTRS2021

Multiobjective Multidisciplinary Optimization of Low-Boom Supersonic Transports Using Multifidelity Models

A multidisciplinary optimization (MDO) method has been developed to design a computational fluid dynamics (CFD) based low-boom configuration that can be obtained from a Pareto solution of a low-fidelity multiobjective MDO problem with mission constraints. This paper refines the developed MDO method by using multifidelity models for CFD-based multiobjective MDO and a better method for the system-level trade between the target low boom ground noise level and the overland range. The refined MDO method can generate a low-boom configuration that satisfies the mission requirements, has the lowest takeoff gross weight and the longest range for the low-boom mission, trims the low-boom cruise flight with fuel redistributions, and has a reversed equivalent area distribution closely matching a low-boom target with ground noise level below 70 PLdB. The validity of the refined MDO method is demonstrated by a design study of a low-boom supersonic transport that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.7 and range of 3500 nm, and cruises overwater at Mach 1.8 with range of 3882 nm. Moreover, the refined MDO method eliminates the difference between the assumed cruise weight for CFD-based low-boom inverse design optimization and the estimated cruise weight of the optimal inverse design solution with respect to the mission requirements.

MDO↗

NASA NTRS2022

Isotropization and Evolution of Energy-Containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1

We examine the radial evolution of correlation lengths perpendicular (l^ C) and parallel (  lC) to the magnetic-field direction, computed from solar wind magnetic-field data measured by Parker Solar Probe (PSP) during its first eight orbits, Helios 1, Advanced Composition Explorer (ACE), WIND, and Voyager 1 spacecraft. Correlation lengths are grouped by an interval’s alignment angle; the angle between the magnetic-field and solar wind velocity vectors (ΘBV). Parallel and perpendicular angular channels correspond to angles 0° < ΘBV < 40° and 50° < ΘBV < 90°, respectively. We observe an anisotropy in the inner heliosphere within 0.40 au, with  l l »^ 0.75 C C at 0.10 au. This anisotropy reduces with increasing heliocentric distance and the correlation lengths roughly isotropize within 1 au. Results from ACE and WIND support a reversal of the anisotropy, such that  l l »^ 1.29 C C at 1 au. The ratio does not appear to change significantly beyond 1 au, although the small number of parallel intervals in the Voyager data set precludes unambiguous conclusions from being drawn. This study provides insights regarding the radial evolution of the large, most energetic interacting turbulent fluctuations in the heliosphere. We also emphasize the importance of tracking the changes in sampling direction in PSP measurements as the spacecraft approaches the Sun, when using these data to study the radial evolution of turbulence. This can prove to be vital in understanding the more complex dynamics of the solar wind in the inner heliosphere and can assist in improving related simulations.

Manuel Enrique Cuesta↗

DOE OSTI2014

The Negative Ion Photoelectron Spectrum of meta -Benzoquinone Radical Anion (MBQ •– ): A Joint Experimental and Computational Study

Negative ion photoelectron (NIPE) spectra of the radical anion of meta-benzoquinone (MBQ, m-OC6H4O) have been obtained at 20 K, using both 355 and 266 nm lasers for electron photodetachment. The spectra show well-resolved peaks and complex spectral patterns. The electron affinity of MBQ is determined from the first resolved peak to be 2.875 ±17 0.010 eV. Single-point, CASPT2/aug-cc-pVTZ//CASPT2/ aug-cc-pVDZ calculations predict accurately the positions of the 0-0 bands in the NIPE spectrum for formation of the four lowest electronic states of neutral MBQ from the 2A2 state of MBQ•-. In addition, the Franck-Condon factors that are computed from the CASPT2/aug-cc-pVDZ optimized geometries,vibrational frequencies, and normal mode vectors, successfully simulate the intensities and frequencies of the vibrational peaks in the NIPE spectrum that are associated with each of these electronic states. The successful simulation of the NIPE spectrum of MBQ•- allows the assignment of 3B2 as the ground state of MBQ, followed by the 1B2 and 1A1 electronic states, respectively 9.0 ± 0.2 and 16.6 ± 0.2 kcal/mol higher in energy than the triplet. These experimental energy differences are in good agreement with the calculated values of 9.7 and 15.7 kcal/mol. The relative energies of these two singlet states in MBQ confirm the previous prediction that their relative energies would be reversed from those in meta-benzoquinodimethane (MBQDM, m-CH2C6H4CH2).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2011

The Radical Stabilization Energy of a Substituted Carbon-centered Free Radical Depends both on the Functionality of the Substituent and the Ordinality of the Radical

Chemical intuition suggests that the stabilization of a carbon-centered free radical by a substituent X would be the greatest for a prim and least for a more stable tert radical because of saturation. However, analysis of a comprehensive recent set of bond dissociation energies computed by Coote and coworkers (Phys. Chem. Chem. Phys. 2010 12 9597) and transformed into radical stabilization energies (RSE) suggests that this supposition is often violated. The RSE for a given X depends not only on the nature of X but also on the ordinality (i.e., prim, sec, or tert) of the radical onto which it is substituted. For substituents that stabilize by electron delocalization but also contain electron-withdrawing centers, such as the carbonyl function, the stabilization of XCMe2 compared with HCMe2 is greater than for XCH2 compared with HCH2 . However, for substituents that stabilize by lone-pair electron donation, such as N or O centers, the order is strongly reversed. This contrast can be qualitatively rationalized by considering charge-separated VB contributors to the radical structure (R2C+ X- and R2C- X+ ) and the contrasting effects of methyl substituents on them. This conclusion is not dependent on the particular definition used for RSE.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗