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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Long term variability of Cygnus X-1: VII. Orbital variability of the focussed wind in Cyg X-1/HDE 226868 system

Binary systems with an accreting compact object offer a unique opportunity to investigate the strong, clumpy, line-driven winds of early-type supergiants by using the compact object’s X-rays to probe the wind structure. In this paper, we analyze the two-component wind of HDE 226868, the O9.7Iab giant companion of the black hole Cyg X-1, using 4.77 Ms Rossi X-ray Timing Explorer (RXTE) observations of the system taken over the course of 16 years. Absorption changes strongly over the 5.6 d binary orbit, but also shows a large scatter at a given orbital phase, especially at superior conjunction. The orbital variability is most prominent when the black hole is in the hard X-ray state. Our data are poorer for the intermediate and soft state, but show signs for orbital variability of the absorption column in the intermediate state. We quantitatively compare the data in the hard state to a toy model of a focussed Castor-Abbott-Klein wind: as it does not incorporate clumping, the model does not describe the observations well. Finally, a qualitative comparison to a simplified simulation of clumpy winds with spherical clumps shows good agreement in the distribution of the equivalent hydrogen column density for models with a porosity length on the order of the stellar radius at inferior conjunction; we conjecture that the deviations between data and model at superior conjunction could either be due to lack of a focussed wind component in the model or to a more complicated clump structure.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2015

Long Term Variability of Cygnus X-1. VII. Orbital Variability of the Focused Wind in Cyg X-1/HDE 226868 System

Binary systems with an accreting compact object offer a unique opportunity to investigate the strong, clumpy, line-driven winds of early-type supergiants by using the compact object's X-rays to probe the wind structure. We analyze the two-component wind of HDE 226868, the O9.7Iab giant companion of the black hole Cyg X-1, using 4.77 Ms Rossi X-ray Timing Explorer (RXTE) observations of the system taken over the course of 16 years. Absorption changes strongly over the 5.6 d binary orbit, but also shows a large scatter at a given orbital phase, especially at superior conjunction. The orbital variability is most prominent when the black hole is in the hard X-ray state. Our data are poorer for the intermediate and soft state, but show signs for orbital variability of the absorption column in the intermediate state. We quantitatively compare the data in the hard state to a toy model of a focussed Castor-Abbott- Klein wind: as it does not incorporate clumping, the model does not describe the observations well. A qualitative comparison to a simplified simulation of clumpy winds with spherical clumps shows good agreement in the distribution of the equivalent hydrogen column density for models with a porosity length on the order of the stellar radius at inferior conjunction; we conjecture that the deviations between data and model at superior conjunction could either be due to lack of a focussed wind component in the model or to a more complicated clump structure.

binaries↗
DOE OSTI2021

Analysis and prediction of reaction kinetics using the degree of rate control

“Degree of rate control” (DRC) analysis provides a quantitative approach for analysing the kinetics of multi-step reaction mechanisms that has been widely applied to both heterogeneous and homogeneous catalysis research, as well as electrocatalysis. The DRC of any given transition state or intermediate is defined as a partial derivative such that it approximately equals the fractional increase in net rate to the product of interest per differential decrease in its standard-state free energy for that species (÷RT), holding constant the standard-state free energies of all other transition states and intermediates. Even very complex mechanisms usually have only a few species with non-zero DRCs and are thus the species whose interactions with the catalyst most strongly affect the net rate. These key DRC values thus offer a simple and intuitive route to optimize catalyst materials, especially with the assistance of computational methods like density functional theory (DFT). These high-DRC species are also the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. In simple cases with a single “rate-determining step”, the DRC for its transition state (TS) is + 1. Catalyst-bound intermediates, on the other hand, often have negative DRCs equal to a small integer times their fractional occupancy of catalyst sites. The apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all the species (intermediates, transition states and products) in the reaction mechanism, each weighted by its DRC (+RT). It has been shown that the apparent transfer coefficient in electrocatalysis, an inverted form of the Tafel slope, is a weighted average of the number of electrons transferred to generate each intermediate or product species in the mechanism, weighted again by the DRC. Quantitative analysis of kinetic isotope effects (KIEs, or the ratio of net rates for different reactant isotopes) in complex mechanisms has shown that the logarithm of the KIE equals the weighted average over all species in the mechanism of the difference between the two isotopes in their standard-state free energies (÷RT), again weighted by the DRC. The reaction orders with respect to fluid-phase concentrations of reactants, products and intermediates have also been proven to be directly related to DRCs. Thus, there are numerous experimental observables which equate to short linear combinations of DRCs, so that combinations of experimental measurements might provide access to DRC values. Since its invention for transition states in 1994 and its generalization to include intermediates in 2009, the DRC has thus far mainly been calculated for microkinetic models based either entirely on DFT or on DFT with the key energies (i.e., those for high-DRC species) being fine-tuned to match experiments. The relationships summarized in this work provide new opportunities for using experiments earlier in the development and optimization of microkinetic models that require input from computational catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

TESTING PHOTOMETRIC DIAGNOSTICS FOR THE DYNAMICAL STATE AND POSSIBLE INTERMEDIATE-MASS BLACK HOLE PRESENCE IN GLOBULAR CLUSTERS

Surface photometry is a necessary tool to establish the dynamical state of star clusters. We produce realistic HST-like images from N-body models of star clusters with and without central intermediate-mass black holes (IMBHs) in order to measure their surface brightness profiles. The models contain {approx}600,000 individual stars, black holes of various masses between 0% and 2% of the total mass, and are evolved for Hubble time. We measure surface brightness and star count profiles for every constructed image in order to test the effect of IMBHs on the central logarithmic slope, the core radius, and the half-light radius. We use these quantities to test diagnostic tools for the presence of central black holes using photometry. We find that the only models that show central shallow cusps with logarithmic slopes between -0.1 and -0.4 are those containing central black holes. Thus, the central logarithmic slope seems to be a good way to choose clusters suspected of containing IMBHs. Clusters with steep central cusps can definitely be ruled out to host an IMBH. The measured r{sub c} /r{sub h} ratio has similar values for clusters that have not undergone core-collapse and those containing a central black hole. We note that observed Galactic globular clusters have a larger span of values for central slope and r{sub c} /r{sub h} than our modeled clusters, and suggest possible reasons that could account for this and contribute to improved future models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Magnetism and the spin state in cubic perovskite CaCo O 3 synthesized under high pressure

Cubic SrCo O 3 with an intermediate spin state can only be stabilized by high pressure and high temperature (HPHT) treatment. It is metallic and ferromagnetic with the highest Curie temperature of the transition-metal perovskites. The chemical substitution by Ca on Sr sites would normally lower crystal symmetry from cubic to orthorhombic as seen in the perovskite family of Ca M O 3 ( M = M 4 + of transition metals, G e 4 + , S n 4 + , and Z r 4 + ) at room temperature. This structural change narrows the bandwidth, so as to further enhance the Curie temperature as the crossover to the localized electronic state is approached. Here, we report a successful synthesis of the perovskite CaCo O 3 with a HPHT treatment. Surprisingly, CaCo O 3 crystallizes in a simple cubic structure that remains stable down to 20 K, the lowest temperature in the structural study. The new perovskite has been thoroughly characterized by a suite of measurements including transport, magnetization, specific heat, thermal conductivity, and thermoelectric power. Furthermore, metallic CaCo O 3 undergoes two successive magnetic transitions at 86 K and 54 K as temperature decreases. The magnetization at 5 K is compatible with the intermediate spin state t 4 e 1 of C o 4 + at the octahedral site. The thermal expansion of the Co-O bond length indicates that the population of high spin state t 3 e 2 increases for T > 100 K . The shortest Co-O bond length in cubic CaCo O 3 is responsible for delocalizing electrons in the π * -band and itinerant-electron ferromagnetism at T < 54 K . In our comprehensive comparison between SrCo O 3 and CaCo O 3 and the justification of their physical properties by first-principles calculation were made in this report. Partially filled π * and σ * bands would make CaCo O 3 suitable to study the Hund's coupling effect in a metal.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Pre-Steady-State Kinetics of Catalytic Intermediates of an [FeFe]-Hydrogenase

[FeFe]-hydrogenases catalyze the reversible production of hydrogen gas from protons and electrons, but the mechanism of catalysis is still the subject of debate. In this report, we describe a pre-steady-state photoreduction methodology for correlating putative intermediates to the reactivity of an [FeFe]-hydrogenase from Thermotoga maritima . In this method, MV+ is rapidly formed photochemically by pulsed laser excitation and the intermolecular ET and active site dynamics are followed by nanosecond time-resolved visible and infrared spectroscopy, respectively. The results kinetically validate the H ox , H red , and H sred intermediates, strongly supporting a vast body of literature on their involvement in proton reduction.

08 HYDROGEN↗
DOE OSTI2026

Autler-Townes spectroscopy of a Rydberg ladder

Ladder-type two-photon excitation of an atom from a ground state $|g\rangle$, to an intermediate excited state $|e\rangle$, and finally, to a Rydberg state $|r\rangle$ has a variety of uses from quantum information to sensing. A common scheme for detecting this transition optically is through electromagnetically induced transparency (EIT). However, in inverted wavelength schemes, where the ground-to-excited transition wavelength is shorter than the excited-to-Rydberg transition wavelength, the strength of the EIT feature on the lower-leg beam is strongly reduced in a Doppler-broadened medium. Here, in this study, we report on an alternative two-photon spectroscopic feature, which we term the two-photon Autler-Townes resonance, observed on the upper-leg beam. Compared to the EIT signal, this feature's superior signal-to-noise ratio allows one to resolve Rydberg resonances with principal quantum number as high as n=80. We also show that such a feature can be utilized to generate an error signal for stabilizing the frequency of the upper-leg beam.

Xiang, Tai [University of California, Berkeley, CA↗
DOE OSTI2018

Irreversibility in Rolled Tantalum

We investigated the magnetic and thermodynamic properties of rolled tantalum in superconducting state. The magnetization shows a crossover from type I to type II superconductivity as the magnetic field increases beyond the thermodynamic critical field. In both regimes, the sample shows a substantial irreversibility of the magnetization which we attribute to the pinning of the entities that characterize the intermediate and mixed states. Magnetic relaxation data taken in the intermediate state shows an important contribution of the quantum tunnelling below 3.7 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Importance of Dispersion in the Molecular Geometries of Mn(III) Spin-Crossover Complexes

The computational investigation of the molecular geometries of a pair of manganese(III) spin-crossover complexes is reported. For the geometry of the quintet high-spin state, density functionals significantly overestimate Mn–Namine bond distances, although the geometry for the triplet intermediate-spin state is well described. Here, comparisons with several wave function-based methods demonstrate that this error is due to the limited ability of commonly used density functionals to recover dispersion beyond a certain extent. Among the methods employed for geometry optimization, restricted open-shell Møller–Plesset perturbation theory (MP2) appropriately describes the high-spin geometry but results in a slightly shorter Mn–O distance in both spin states. On the other hand, extended multistate complete active space second-order perturbation theory (XMS-CASPT2) provides a good description of the geometry for the intermediate-spin state but also sufficiently recovers dispersion, performing well for the high-spin state. Despite the fact that the electronic structure of both spin states is dominated by one-electron configuration, XMS-CASPT2 offers a balanced approach, leading to molecular geometries with much better agreement with experiment than MP2 and DFT. A scan along the Mn–N amine bond demonstrates that for these complexes coupled cluster methods (i.e., DLPNO-CCSD(T)) also yield bond distances in agreement with experiment while multiconfiguration pair density functional theory (MC-PDFT) is unable to recover dispersion well enough, analogous to single-reference DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

ACCRETION FLOW DYNAMICS OF MAXI J1836-194 DURING ITS 2011 OUTBURST FROM TCAF SOLUTION

The Galactic transient X-ray binary MAXI J1836-194 was discovered on 2011 August 29. Here we make a detailed study of the spectral and timing properties of its 2011 outburst using archival data from the RXTE Proportional Counter Array instrument. The evolution of accretion flow dynamics of the source during the outburst through spectral analysis with Chakrabarti–Titarchuk’s two-component advective flow (TCAF) solution as a local table model in XSPEC. We also fitted spectra with combined disk blackbody and power-law models and compared it with the TCAF model fitted results. The source is found to be in hard and hard-intermediate spectral states only during the entire phase of this outburst. No soft or soft-intermediate spectral states are observed. This could be due to the fact that this object belongs to a special class of sources (e.g., MAXI J1659-152, Swift J1753.5-0127, etc.) that have very short orbital periods and that the companion is profusely mass-losing or the disk is immersed inside an excretion disk. In these cases, flows in the accretion disk are primarily dominated by low viscous sub-Keplerian flow and the Keplerian rate is not high enough to initiate softer states. Low-frequency quasi-periodic oscillations (QPOs) are observed sporadically although as in normal outbursts of transient black holes, monotonic evolutions of QPO frequency during both rising and declining phases are observed. From the TCAF fits, we find the mass of the black hole in the range of 7.5–11 M{sub ⊙}, and from time differences between peaks of the Keplerian and sub-Keplerian accretion rates we obtain a viscous timescale for this particular outburst, ∼10 days.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Carotenoid Nuclear Reorganization and Interplay of Bright and Dark Excited States

We report here quantum chemical calculations using multireference perturbation theory (MRPT) with the density matrix renormalization group (DMRG) plus photothermal deflection spectroscopy measurements to investigate the manifold of carotenoid excited states and establish their energies relative to the bright state (S 2 ) as a function of nuclear reorganization. We conclude that the primary photophysics and function of carotenoids are determined by interplay of only the bright (S 2 ) and lowest-energy dark (S 1 ) states. The lowest-lying dark state, far from being energetically distinguishable from the lowest-lying bright state along the entire excited-state nuclear reorganization pathway, is instead computed to be either the second or first excited state depending on what equilibrium geometry is considered. This finding suggests that, rather than there being a dark intermediate excited state bridging a non-negligible energy gap from the lowest-lying dark state to the lowest-lying bright state, there is in fact no appreciable energy gap to bridge following photoexcitation. Instead, excited-state nuclear reorganization constitutes the bridge from S 2 to S 1 , in the sense that these two states attain energetic degeneracy along this pathway.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2013

Crystal structure, magnetism and transport properties of Ce{sub 3}Ni{sub 25.75}Ru{sub 3.16}Al{sub 4.1}B{sub 10}

Single crystals of Ce{sub 3}Ni{sub 25.75}Ru{sub 3.16}Al{sub 4.1}B{sub 10} were obtained from a process in which a polycrystalline sample of CeRu{sub 2}Al{sub 2}B was annealed in an excess of a Ni–In flux. The initial phase, CeRu{sub 2}Al{sub 2}B, does not recrystallize, instead, crystals of a new phase, Ce{sub 3}Ni{sub 25.75}Ru{sub 3.16}Al{sub 4.1}B{sub 10}, could be isolated once the flux was removed. The title compound crystallizes in the tetragonal space group P4/nmm (No. 129) with a=1139.02(8), c=801.68(6) pm (c/a=0.70) in the Nd{sub 3}Ni{sub 29}Si{sub 4}B{sub 10} structure type. Electrical resistivity measurements reveal metallic behavior with a minimum of 700 µΩ cm and a small residual resistivity ratio of RRR=1.4 indicating a large amount of disorder scattering. The cerium atoms are either in the 4+ or an intermediate valence state with a valence fluctuation temperature far above room temperature. - Graphical abstract: Single crystals of Ce{sub 3}Ni{sub 25.75}Ru{sub 3.16}A{sub l4.1}B{sub 10} were obtained using a process in which a polycrystalline sample of CeRu{sub 2}Al{sub 2}B was annealed in an excess of a Ni–In flux. Electrical resistivity measurements reveal metallic behavior with a minimum of 700 μΩ cm and a small residual resistivity ratio of RRR=1.4 indicating a large amount of disorder scattering. The cerium atoms are either in the 4+ or an intermediate valence state with a valence fluctuation temperature far above room temperature. Display Omitted - Highlights: • Flux synthesis of high quality single crystals of Ce{sub 3}Ni{sub 25.75}Ru{sub 3.16}Al{sub 4.1}B{sub 10} is presented along with the crystal structure, magnetic and transport properties. • The compound is isostructural to Nd{sub 3}Ni{sub 29}Si{sub 4}B{sub 10} but is first of this structure type showing mixed occupancies of d-elements. • This is an intermetallic phase with Ce in either the 4+ or an intermediate valence state. • The fact that this structure with mixed occupied transition metal sites exists suggests that more compounds of this type should be accessible and the physical properties tuned.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Ferroelectric Domain Wall Engineering Enables Thermal Modulation in PMN–PT Single Crystals

Acting like thermal resistances, ferroelectric domain walls can be manipulated to realize dynamic modulation of thermal conductivity ( k ), which is essential for developing novel phononic circuits. Despite the interest, little attention has been paid to achieving room-temperature thermal modulation in bulk materials due to challenges in obtaining a high thermal conductivity switching ratio ( k high / k low ), particularly in commercially viable materials. Here, room-temperature thermal modulation in 2.5 mm-thick Pb(Mg 1/3 Nb 2/3 )O 3 – x PbTiO 3 (PMN– x PT) single crystals is demonstrated. With the use of advanced poling conditions, assisted by the systematic study on composition and orientation dependence of PMN– x PT, a range of thermal conductivity switching ratios with a maximum of ≈1.27 is observed. Further, simultaneous measurements of piezoelectric coefficient (d 33 ) to characterize the poling state, domain wall density using polarized light microscopy (PLM), and birefringence change using quantitative PLM reveal that compared to the unpoled state, the domain wall density at intermediate poling states (0< d 33 33,max ) is lower due to the enlargement in domain size. At optimized poling conditions (d 33,max ), the domain sizes show increased inhomogeneity that leads to enhancement in the domain wall density. This work highlights the potential of commercially available PMN– x PT single crystals among other relaxor-ferroelectrics for achieving temperature control in solid-state devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Computational Investigation of the Chemical Bond between An(III) Ions and Soft-Donor Ligands

The chemical bonding of actinide ions with arene and borohydride ligands is explored via quantum chemical methods to understand how the transuranium elements interact with softdonor ligands. Specifically, the [An(C 6 Me 6 )(BH 4 ) 3 ] complexes (An = U, Np, and Pu) and their reduced congeners are studied. Density functional theory (DFT) shows that the metal–ligand interactions in the neutral complexes are governed by electrostatic interactions. Both DFT and complete active space (CASSCF) results show that as one moves from U to Pu, the 5f-orbitals are stabilized leading to a poorer energy match with the ligand orbitals. This contributes to progressively weaker metal-arene and metal-borohydride interactions across the series due to a decrease in energy-driven covalency. A reduction in orbital contributions to bonding is obtained for the transuranium-arene interactions as well. Upon reduction, the arene is reduced, forming a δ-bond. This causes the An–arene distances to contract by 0.1–0.2 Å compared to the neutral complexes. The ground state is assigned as the intermediate-spin state where the arene radical is antiferromagnetically coupled to the metal-centered f-electrons in Np and Pu. On the other hand, the ferromagnetically and antiferromagnetically coupled states are close in energy in the uranium complex, but do not mix when spin– orbit coupling is included using a state-interaction approach (SO-CASPT2). The population of the CASSCF δ*-antibonding natural orbital increases from U to Pu consistent with the increased An–arene distances, weaker interactions, and decreasing covalency across the series. Although the An–B distance increases by ca. 0.06 Å upon reduction, both the neutral and reduced species involve an An(III)–borohydride bond and as such are qualitatively similar. The Np complexes can be assigned to have slightly weaker bonding than the uranium analogs but are overall “uranium-like”. The Pu complexes are predicted to have less covalent contributions to bonding in both the Pu–arene and Pu–borohydride interactions; however, the Pu–arene interaction is predicted to be particularly weak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Molecular photoelectron angular distribution rotations in multi-photon resonant ionization of H{sub 2}{sup +} by circularly polarized ultraviolet laser pulses

We study effects of pulse durations on molecular photoelectron angular distributions (MPADs) in ultrafast circular polarization ultraviolet resonant ionization processes. Simulations performed on aligned H{sub 2}{sup +} by numerically solving time dependent Schrödinger equations show rotations of MPADs with respect to the molecular symmetry axes. It is found that in multi-photon resonant ionization processes, rotation angles are sensitive to pulse durations, which we attribute to the coherent resonant excitation between the ground state and the intermediate excited electronic state induced by Rabi oscillations. Multi-photon nonresonant and single photon ionization processes are simulated and compared which exhibit a constant rotation angle. An asymmetry parameter is introduced to describe the pulse duration sensitivity by perturbation theory models. Influence of pulse frequency detunings on MPADs is also investigated where oscillations of rotations are absent at long pulse durations due to nonresonance excitation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Preparation of high orbital angular momentum Rydberg states by optical-millimeter-wave STIRAP

Rydberg states of molecules are intrinsically challenging to study due to the presence of fast non-radiative decay pathways, such as predissociation. However, selectively exciting Rydberg states with values of the orbital angular momentum (ℓ) ℓ ≳ 3 is a productive strategy to minimize this rapid decay and to populate molecular Rydberg states with lifetimes that approach those of atoms. Here, in this proof-of-principle demonstration, we transfer population to an nf Rydberg state of the calcium atom by stimulated Raman adiabatic passage, in which an optical and a millimeter-wave field couple the initial and final states via an intermediate nd Rydberg state. Numerical simulations reproduce the observed time and frequency dependences of the population transfer and suggest the utility of this scheme to populate high-ℓ Rydberg states of molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Rovibrationally resolved Rayleigh and Raman scattering cross sections for molecular hydrogen

Accurate Rayleigh and Raman scattering cross sections, tensor components, depolarization ratios, and reversal coefficients for all rovibrational transitions within the X1Σg+ ground electronic state of H2 have been calculated. Raman spectra have been generated using these data. A method for calculating Raman scattering cross sections is formulated that is valid below the ionization threshold and in the region containing resonances, which explicitly accounts for all bound and dissociative vibrational levels of the bound intermediate electronic states and approximately accounts for the ionization continuum. A representative set of cross sections is presented for incident photon energies below 15 eV and compared with existing results in the literature where possible. Convergence of our results with an increasing number of bound intermediate electronic states is demonstrated. The accuracy of the Placzek–Teller approximation is discussed. The effect of accounting for the intermediate ionization continuum is investigated. Local thermal equilibrium cross sections are calculated for Rayleigh and Raman scattering. This work represents the most accurate and complete treatment of Raman scattering for molecular hydrogen to date. A total of 9582 Rayleigh and Raman scattering cross sections have been generated and are openly available on Zenodo under an open-source Creative Commons Attribution license at https://zenodo.org/doi/10.5281/zenodo.13441471.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree–Fock exchange. Furthermore, these results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗