Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “APPROXIMATIONS”

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 1,405 records · Page 78

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C 2 singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B 2 , C 2 , O 2 , and F 2 in the local spin density approximation (LSDA), the Perdew–Burke–Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C 2 . Here, this work shows that spin symmetry breaking in singlet C 2 , which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermofield Theory for Finite-Temperature Electronic Structure

Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. Furthermore, they also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

G 0 W 0 Ionization Potentials of First-Row Transition Metal Aqua Ions

Here, we report computations of the vertical ionization potentials within the GW approximation of the near-complete series of first-row transition metal (V–Cu) aqua ions in their most common oxidation states, i.e., V 3+ , Cr 3+ , Cr 2+ , Mn 2+ , Fe 3+ , Fe 2+ , Co 2+ , Ni 2+ , and Cu 2+ . The d-orbital occupancy of these systems spans a broad range from d 2 to d 9 . All of the structures were first optimized at the density functional theory level using a large cluster of explicit water molecules that are embedded in a continuum solvation model. Vertical ionization potentials were computed with the one-shot G 0 W 0 approach on a range of transition metal ion clusters (6, 18, 40, and 60 explicit water molecules), wherein the convergence with respect to the basis set size was evaluated using the systems with 40 water molecules. We assess the results using three different density functional approximations as starting points for the vertical ionization potential calculations, namely, G 0 W 0 @PBE, G 0 W 0 @PBE0, and G 0 W 0 @r 2 SCAN. While the predicted ground-state structures are similar to all three exchange-correlation functionals, the vertical ionization potentials were in closer agreement with experiment when using the G 0 W 0 @PBE0 and G 0 W 0 @r 2 SCAN approaches, with the r 2 SCAN-based calculations being significantly less expensive. Computed bond distances and vertical ionization potentials for all structures are in good agreement with available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗

X‑ray Coherent Diffractive Imaging of Large Helium Nanodroplets Doped with Small Molecules

We report the first X-ray coherent diffractive imaging experiment on molecule-doped helium nanodroplets. It complements previous work, where we reported single-shot X-ray coherent diffractive imaging studies of Xe dopant clusters formed in 4He and 3He droplets. These noble gas clusters were used to visualize the impact of rotational excitation of the droplets on the spatial distribution of atomic dopants within the droplets, and to study the differences and connections between quantum and classical droplet rotational motion. Here, we expand our studies to the molecular dopants CF4, CHF3, CH3CN, and SF6, imaged with 1.5 keV photons. We find multiple Bragg spots in the diffraction patterns of molecule-doped droplets with radii of approximately 600 nm, which provide evidence that molecules form elongated clusters with preferential alignment along the angular momentum axis of the 4He droplets, in agreement with our previous results on the aggregation of Xe clusters on quantum vortices. Real-space reconstructions of molecular dopant cluster density profiles are obtained for droplets with smaller radii of approximately 300 nm. The diffuse images suggest the formation of low-density, potentially porous, molecular clusters upon aggregation at T = 0.4 K in 4He droplets. In the normal fluid 3He droplets, molecules aggregate into loose clusters on the droplets' equator, similar to previous observations for Xe atoms. Time-of-flight mass spectra reveal that the doped helium nanodroplet moieties fragment extensively into constituent atomic ions, producing only a small fraction of molecular fragment ions. The findings are discussed in the context of previously proposed schemes to use He droplets as potential tamper materials for ultrafast X-ray imaging experiments.

Feinberg, AlexandraJ↗

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First-Principles-Based Machine Learning Models for Phase Behavior and Transport Properties of CO 2

In this work, we construct distinct first-principles-based machine-learning models of CO 2 , reproducing the potential energy surface of the PBE-D3, BLYP-D3, SCAN and SCAN-rvv10 approximations of density functional theory. Here we employ the Deep Potential methodology to develop the models and consequently achieve a significant computational efficiency over ab initio molecular dynamics (AIMD) that allows for larger system sizes and time scales to be explored. Although our models are trained only with liquid phase configurations, they are able to simulate a stable interfacial system and predict vapor-liquid equilibrium properties, in good agreement with results from the literature. Because of the computational efficiency of the models, we are also able to obtain transport properties, such as viscosity and diffusion coefficients. We find that the SCAN-based model presents a temperature shift in the position of the critical point, while the SCAN-rvv10-based model shows improvement but still exhibits a temperature shift that remains approximately constant for all properties investigated in this work. We find that the BLYP-D3-based model generally performs better for liquid phase and vapor-liquid equilibrium properties, but the PBE-D3-based model is better suited for predicting transport properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Water Uptake by Silica Nanopores: Impacts of Surface Hydrophilicity and Pore Size

Water uptake at 298 K by two mesoporous silicas with different pore sizes was studied using volumetric vapor sorption. Here, through variation of sample pretreatment temperature and time, the number of surface hydroxyl groups was varied, leading to marked changes in the water sorption behavior. With increasing surface hydroxyl density, the adsorption of water to the pore surfaces increases, leading to formation of a thicker and denser water sorption layer. The BET model was used to measure surface hydroxyl density from low pressure parts of water adsorption isotherms. Adsorption of water molecules scales with the number density of surface hydroxyl groups, and monolayer coverage is reached at reduced pressure of ca. 0.3. The onset of adsorption pore condensation of water shifts to lower reduced pressure with increasing surface hydroxyl density, indicating growing thickness of adsorption layers. However, the water pore condensation step of the desorption branch shifts to smaller reduced pressure with increasing surface hydroxylation, reducing the adsorption-desorption hysteresis width. An adsorbed phase model is utilized to calculate the distribution of pore water molecules between adsorbed and pore condensation phases, and characterize the density and thickness of the water sorption phase. In the smaller pores, the adsorbed phase forms a sparse monolayer, while approximately a bilayer is formed in the wider pores. The previously reported silica nanopore underfilling by water is confirmed and rationalized by a significantly reduced water density in the adsorbed phase with respect to bulk, while the pore core is filled with water of approximately bulk density.

36 MATERIALS SCIENCE↗

Mechanistic understanding of catalytic conversion of ethanol to 1-butene over 2D-pillared MFI zeolite

Ethanol is an important C2 platform molecule for producing value-added chemicals and distillate hydrocarbon fuels (e.g., jet and diesel). Among these, catalytic upgrading of ethanol to butenes can generate valuable commodity chemicals (e.g., 1-butene) and provide C4 olefin intermediates that can be further upgraded to jet/diesel fuels. 2D zeolites offer hierarchical mesoporous structures, leading to improved mass transport and reduced diffusion length, which can help to address the coking challenges faced by ethanol conversion to hydrocarbons over 3D zeolites. In this study, we investigate the acid-catalyzed conversion of ethanol to 1-butene over the Brønsted acid sites (BAS) in 2D-pillared MFI zeolite (2D-PMFI) using ab initio molecular dynamics (AIMD) simulations, in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), and calorimetric measurements. A detailed thermodynamic analysis, using quasi-harmonic approximation (QHA), on the Gibbs free energy pathway of ethanol conversion shows that the consideration of entropy is critical to accurately capture the detailed thermodynamic profiles. The formation of bulky ethoxy-ethene complex is found to be a potential rate-determining step (RDS), proceeding via stepwise mechanism. The reactivity of 2D-PMFI can be further tuned by manipulating RDS through a careful control of number of BAS and operating temperatures. The accuracy of computational model is confirmed through the comparison of calculated vibrational density of states (VDOS) against the experimental DRIFTS measurements. Overall, our study provides mechanistic insights into ethanol upgrading over the 2D-PMFI and shows the importance of evaluating entropic effects in such confined system.

Ethanol conversion, 2D-pillared zeolite, MFI, Anha↗

Extremely Slow Trap-Mediated Hole Relaxation in Room-Temperature InP/ZnSe/ZnS Quantum Dots

Time-resolved photoluminescence (PL) and transient absorption (TA) spectroscopy have been used to elucidate the hole relaxation dynamics in high-quality InP/ZnSe/ZnS quantum dots (QDs) at room temperature. In QDs having an In/P ratio close to 1:1, hole cooling is fast compared to the ~40 ps time-correlated photon-counting instrument response. However, in QDs that luminesce at wavelengths greater than around 600 nm and have excess indium, a significant fraction of the PL exhibits a slower rise time. In this case, the PL rises over a range of timescales varying from close to the instrument response to approximately 300–400 ps. The time constant of the slowest component increases with increasing InP core size and the fraction of the PL that has the slow rise time increases with excess indium in the particle. In all cases, a slow rise time and any spectral evolution on that timescale are absent in the TA results, indicating that the slow dynamics may be assigned to relaxation in the valence band. QDs emitting at wavelengths below 560 nm show very different dynamics, exhibiting a barely detectable <50 ps rise time. Based on these results and measured elemental compositions, the slow hole relaxation is assigned to the transient population of indium-based traps in the ZnSe shell that are above the valence band edge only for the larger, red-emitting QDs. Here, the relative trap to band edge relaxation rates can be understood in terms of effective mass approximation hole wave function calculations, which show that the relaxation rate is largely determined by the extent to which the hole wave function in the lowest exciton penetrates into the ZnSe shell, overlapping the trapped-hole wave functions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Fourier-like Thermal Relaxation of Nanoscale Explosive Hot Spots

Hot spots are local regions of high temperature that are widely considered to govern explosive initiation. Hot spot dynamics rests on a delicate balance between heat generation due to chemical reactions and heat loss through thermal conduction, making accurate determinations of the conductivity under extreme conditions a key component of predictive explosive models. We develop here an approach to directly determine the thermal transport properties of explosive hot spots with realistic initial structures through a combination of molecular dynamics (MD) and diffusive heat equation (HEq) modeling. Effective thermal conductivity values are determined by fitting HEq models to MD predictions of long timescale hot spot relaxation. The approach is applied to model hot spots in the molecular crystalline explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) for a range of shock strengths and two limiting cases for impact orientation. Isotropic and anisotropic HEq models yield similar results, despite TATB exhibiting some of the largest and most anisotropic thermal conductivity values for explosive near normal conditions. The conductivity is found to be a strong function of density, which parametrically captures dependence on temperature, pressure, and material state. The associated root-mean-square errors of the fitted HEq models are approximately 5% of MD predicted final equilibrium temperatures. Here, the conductivity values determined here for TATB hot spots are considerably larger than those used in a prior hot spot criticality study, which may significantly impact predictions for critical hot spot sizes. The approach provides a convenient foundation for determining the effective thermal conductivity for hot spot problems in other explosives and directly yields information on reasonable approximations that might be taken in higher-level models for those materials.

36 MATERIALS SCIENCE↗

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and electronic gap of rutile titania nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Angstrom (24 atoms) to 10.3 Angstrom (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Angstrom. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS is highly dependent on the shape and size of these particles. Furthermore, the DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigen value distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Extremely Slow Diffusion of Gold Nanoparticles under Confinement in Mesoporous Silica

Here, we report an X-ray photon correlation spectroscopy (XPCS) study of the mobility of colloidal gold nanoparticles with a diameter of approximately 4 nm in glycerol under confinement within the channels of SBA-15 mesoporous silica with pore diameters of approximately 6 and 12 nm. The XPCS correlation functions result from an effective heterodyne signal due to the mixing of the coherent scattering from the nanoparticles and the mesoporous silica. Over the range of wave vectors and hence length scales probed, the nanoparticle dynamics are well described by one-dimensional diffusion. The nanoparticle diffusivity varies with temperature in a manner expected based on the temperature-dependent viscosity of glycerol; however, the magnitudes of the diffusion coefficients are several orders of magnitude smaller than those of the nanoparticles in bulk glycerol. We consider mechanisms that might contribute to this reduction in diffusivity including enhancement in hydrodynamic drag under confinement, effects of nanoparticle adsorption to the pore walls, and slowing structural dynamics in glycerol due to the combination of the nanometer-scale confinement and the presence of the nanoparticles.

36 MATERIALS SCIENCE↗

Pressure-Stabilized MnSb2 with Complex Incommensurate Magnetic Order

Marcasite-type compounds have been proposed as promising hosts of exotic magnetic quantum states, yet experimental realizations in stoichiometric, disorder-free systems remain limited. Here, we report the high-pressure stabilization and magnetic characterization of MnSb2, a marcasite-type compound that is thermodynamically metastable under ambient pressure. Single crystals were synthesized using a cubic multianvil press at 3.3 GPa and 490 °C for 24 h, and powder and single-crystal X-ray diffraction confirm the orthorhombic Pnnm structure. These crystals are stable at ambient pressure for a long time up to between 450 and 500 K. Heat-capacity measurements reveal phase transitions at approximately T0 ∼ 118 K and T1 ∼ 220 K. Neutron diffraction uncovers an unconventional magnetic state below T1 ∼ 220 K. Magnetic powder neutron diffraction refinements reveal possible multiple magnetic configurations that provide comparably acceptable fits to the experimental data. While most solutions are consistent with a spin-density-wave (SDW) description, helical models systematically yield inferior agreement factors. Across a broad range of models, the Mn ordered moment reaches a maximum value of approximately 2 μB and remains predominantly collinear, with minimal canting along the c-axis. At 200 K, the magnetic propagation vector is q = (0, 0.3975, 0.3783); upon cooling, the b component increases toward 0.5, reflecting a temperature-dependent evolution of the modulation. The need for modification of the magnetic model between high and low temperatures further highlights the complex and strongly temperature-dependent nature of the magnetic order in this system. These results establish MnSb2 as a pressure-stabilized marcasite magnet with a tunable, complex magnetic state and a compelling stoichiometric platform for exploring unconventional magnetic behavior, including potential altermagnetism.

Xu, Mingyu [Michigan State University , , , ,; Iow↗

How Well Does Kohn–Sham Regularizer Work for Weakly Correlated Systems?

Kohn–Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn–Sham density functional theory that works for strongly correlated systems. Here we test KSR for a weak correlation. We propose spin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations found by minimizing density and total energy loss. We assess the atoms-to-molecules generalizability by training on one-dimensional (1D) H, He, Li, Be, and Be 2+ and testing on 1D hydrogen chains, LiH, BeH 2 , and helium hydride complexes. The generalization error from our semilocal approximation is comparable to other differentiable approaches, but our nonlocal functional outperforms any existing machine learning functionals, predicting ground-state energies of test systems with a mean absolute error of 2.7 mH.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inelastic Triatom-Atom Quantum Close-Coupling Dynamics in Full Dimensionality: All Rovibrational Mode Quenching of Water Due to the H Impact on a Six-Dimensional Potential Energy Surface

The rovibrational level populations, and subsequent emission in various astrophysical environments, are driven by inelastic collision processes. The available rovibrational rate coefficients for water have been calculated using a number of approximations. We present a numerically exact calculation for the rovibrational quenching for all water vibrational modes due to collisions with atomic hydrogen. The scattering theory implements a quantum close-coupling (CC) method on a high level ab initio six-dimensional (6D) potential energy surface (PES). Total rovibrational quenching cross sections for excited bending levels were compared with earlier results on a 4D PES with the rigid-bender closecoupling (RBCC) approximation. General agreement between 6D-CC and 4DRBCC calculations are found, but differences are evident including the energy and amplitude of low-energy orbiting resonances. Quenching cross sections from the symmetric and asymmetric stretch modes are provided for the first time. The current 6D-CC calculation provides accurate inelastic data needed for astrophysical modeling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermal Properties of Polymer Hole-Transport Layers Influence the Efficiency Roll-off and Stability of Perovskite Light-Emitting Diodes

While the performance of metal halide perovskite light-emitting diodes (PeLEDs) has rapidly improved in recent years, their stability remains a bottleneck to commercial realization. Here, we show that the thermal stability of polymer hole-transport layers (HTLs) used in PeLEDs represents an important factor influencing the external quantum efficiency (EQE) roll-off and device lifetime. We demonstrate a reduced EQE roll-off, a higher breakdown current density of approximately 6 A cm -2 , a maximum radiance of 760 W sr -1 m -2 , and a longer device lifetime for PeLEDs using polymer HTLs with high glass-transition temperatures. Furthermore, for devices driven by nanosecond electrical pulses, a record high radiance of 1.23 MW sr -1 m -2 and an EQE of approximately 1.92% at 14.6 kA cm -2 are achieved. Thermally stable polymer HTLs enable stable operation of PeLEDs that can sustain more than 11.7 million electrical pulses at 1 kA cm -2 before device failure.

14 SOLAR ENERGY↗

Rhodium-Catalyzed Oxidative Alkenylation of Anisole: Control of Regioselectivity

We report the conversion of anisole and olefins to alkenyl anisoles via a transition metal-catalyzed arene C–H activation and olefin insertion mechanism. The catalyst precursor, [(η 2 -C 2 H 4 ) 2 Rh(μ-OAc)] 2 , and the in situ oxidant Cu(OPiv) 2 (OPiv = pivalate) convert anisole and olefins (ethylene or propylene) to alkenyl anisoles. When ethylene is used as the olefin, the o/m/p ratio varies between approximately 1:3:1 (selective for 3-methoxystyrene) to 1:5:10 (selective for 4-methoxystyrene). When propylene is the olefin, the o/m/p regioselectivity varies between approximately 1:8:20 to 1:8.5:1. The o/m/p ratios depend on concentration of pivalic acid and olefin. For example, when using ethylene, at relatively high pivalic acid concentrations and low ethylene concentrations, the o/m/p regioselectivity is 1:3:1. Conversely, again for use of ethylene, at relatively low pivalic acid concentrations and high ethylene concentrations, the o/m/p regioselectivity is 1:5:10. Mechanistic studies of the conversion of anisole and olefins to alkenyl anisoles provides evidence that the regioselectivity is likely under Curtin-Hammett conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗