A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators

We study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the Hilbert space L^2(\rz^d)\otimes\kz^n into a finite number of almost invariant subspaces. For a certain class of observables, that is preserved by the time evolution, we prove an Egorov theorem. We then associate with each almost invariant subspace of L^2(\rz^d)\otimes\kz^n a classical system on a product phase space \TRd\times\cO, where \cO is a compact symplectic manifold on which the classical counterpart of the matrix degrees of freedom is represented. For the projections of eigenvectors of the quantum Hamiltonian to the almost invariant subspaces we finally prove quantum ergodicity to hold, if the associated classical systems are ergodic

On the Aliphatic versus Aromatic Content of the Carriers of the "Unidentified" Infrared Emission Features

Although it is generally accepted that the so-called "unidentified" infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 micrometer are characteristic of the stretching and bending vibrations of aromatic hydrocarbon materials, the exact nature of their carriers remains unknown: whether they are free-flying, predominantly aromatic gas-phase molecules, or amorphous solids with a mixed aromatic/aliphatic composition are being debated. Recently, the 3.3 and 3.4 micrometer features which are commonly respectively attributed to aromatic and aliphatic C-H stretches have been used to place an upper limit of ~2\% on the aliphatic fraction of the UIE carriers (i.e. the number of C atoms in aliphatic chains to that in aromatic rings). Here we further explore the aliphatic versus aromatic content of the UIE carriers by examining the ratio of the observed intensity of the 6.2 micrometer aromatic C-C feature (I6.2) to that of the 6.85 micrometer aliphatic C-H deformation feature (I6.85). To derive the intrinsic oscillator strengths of the 6.2 micrometer stretch (A6.2) and the 6.85 micrometer deformation (A6.85), we employ density functional theory to compute the vibrational spectra of seven methylated polycyclic aromatic hydrocarbon molecules and their cations. By comparing I6.85/I6.2 with A6.85/A6.2, we derive the fraction of C atoms in methyl(ene) aliphatic form to be at most ~10\%, confirming the earlier finding that the UIE emitters are predominantly aromatic. We have also computed the intrinsic strength of the 7.25 micrometer feature (A7.25), another aliphatic C-H deformation band. We find that A6.85 appreciably exceeds A7.25. This explains why the 6.85 micrometer feature is more frequently detected in space than the 7.25 micrometer feature.Comment: 18 pages, 10 figures, 3 tables; accepted for publication in MNRA

Rotation-Inversion Isomerization of Tertiary Carbamates: Potential Energy Surface Analysis of Multi-Paths Isomerization using Boltzmann Statistics

The front cover artwork is provided by Prof. Rainer Glaser\u27s group at the Missouri University of Science and Technology. The image shows one of four potential energy surfaces generated from our rotation-inversion study of tertiary carbamates and highlights two of the eight possible transition state pathways between two ensembles of E- and Z-minima. In the context of synthetic studies of fluorinated carbamates R1 O-CO-N(R2 )CH2 CF3, we unexpectedly observed two sets of 13C NMR quartets for the CF3 group and we needed to understand their origin. Read the full text of the Research Article at 10.1002/cphc.2022005442

Transition Metal‐Catalyzed and MAO‐Assisted Olefin Polymerization. Cyclic Isomers of Sinn’s Dimer Are Excellent Ligands in Iron Complexes and Great Methylating Reagents

Methylaluminoxane (MAO) is the most commonly used co‐catalyst for transition metalcatalyzed olefin polymerization, but the structures of MAO species and their catalytic functions remain topics of intensive study. We are interested in MAO‐assisted polymerization with catalysts L(R2)FeCl2 (L = tridentate pyridine‐2,6‐diyldimethanimine; imine‐R = Me, Ph). It is our hypothesis that the MAO species is not merely enabling Fe−Me bond formation but functions as an integral part of the active catalyst, a MAO adduct of the Fe‐precatalyst [L(R2)FeCl]+. In this paper, we explored the possible structures of acyclic and cyclic MAO species and their complexation with pre‐catalysts [L(R2)FeCl]+ using quantum chemical approaches (MP2 and DFT). We report absolute and relative oxophilicities associated with the Fe←O(MAO) adduct formation and provide compelling evidence that oxygen of an acyclic MAO species (i.e., O(AlMe2)2, 4) cannot compete with the O‐donor in cyclic MAO species (i.e., (MeAlO)2, 7; MeAl(OAlMe2)2, cyclic 5). Significantly, our work demonstrates that intramolecular O→Al dative bonding results in cyclic isomers of MAO species (i.e., cyclic 5) with high oxophilicities. The stabilities of the [L(R2)FeClax(MAO)eq]+ species demonstrate that 5 provides for the ligating benefits of the cyclic MAO species 4 without the thermodynamically costly elimination of TMA. Mechanistic implications are discussed for the involvement of such Fe−O−Al bridged catalyst in olefin polymerization

Theoretical Study of Structure and Reactions of Metalated Oximes and Oxime Ethers

The potential energy surfaces of acetaldoxime carbanion and its ion pairs formed with lithium and sodium cations ions have been explored with ab initio methods to model and study the regiochemistry of metalated oxime ethers. Planar structures of the carbanions produced by deprotonating acetaldoxime are minima on the potential energy surface. The syn-isomer is 2.6 Kcal/mole more stable than the anti. This difference is not a manifestation of cyclic conjugation but more likely is a result of electrostatic effects. Two chiral and almost isoenergetic minima have been located for the ion pairs formed by either of the isomeric carbanions with Li+ or Na+. The gegenion engages either in face coordination or bridges the NO-bond in a n2-fashion. In oxime ethers face coordination is expected to become dominant for steric reasons. LiC-contacts are surprisingly long in all of the ion pairs. Bonding to the metals in the ion pairs is predominantly ionic. Ion pair formation increases the syn preference energy compared to the free anions, and the syn preference energy is greater for Na+ than for Li+. Reactions with electrophiles via the syn-coordinated metal permits prior coordination and ion pair formation in the product

Origin of the Second-Order Proton Catalysis of Ferriin Reduction in Belousov-Zhabotinsky Reactions: Density Functional Studies of Ferroin and Ferriin Aggregates with Outer Sphere Ligands Sulfate, Bisulfate, and Sulfuric Acid

The detailed mechanisms of Belousov-Zhabotinsky oscillating reactions continue to present grand challenges, even after half a century of study. The origin of the pH dependence of the oscillation pattern had never been rigorously identified. In our recent kinetic study of one of the key Belousov-Zhabotinsky reactions, the iron-catalyzed bromate oxidation of malonic acid, compelling agreement between experiments and kinetic simulations was achieved only with the inclusion of second-order proton catalysis of the reduction of the [Fe(phen)3]3+ species. After exhausting all other avenues in search of an explanation of this proton catalysis, we considered the possibility that the parent iron-phenanthroline complexes could aggregate with neutral and anionic outer sphere ligands (OSLs) in the highly concentrated sulfuric acid solution, and we hypothesized that OSL protonation would increase the capacity of the aggregated complex to oxidize the organic fuel. We performed potential energy surface analyses at the SMD(APFD/6-311G*) level of complexes of the types [Fe(phen)3(SO42-)m(HSO4-)n(H2SO4)o](c-2m-n)+ for ferriin (c = 3) and ferroin (c = 2) aggregated with m sulfate, n bisulfate, and o sulfuric acid OSLs. We present structures of the OSL aggregates, develop a nomenclature for their description, and characterize their electronic structure. The structural chemistry provides the foundation to discuss the ferroin/ferriin redox couple with emphasis on the relationship between the vertical electron affinities of ferriin aggregates and their OSL protonation states. For proton catalysis to manifest itself, double-protonation paths that are slightly endergonic should be present, and proton affinities of aggregated OSLs allow the identification of such double-protonation chains. As a first test of our mechanistic proposal for the second-order proton catalysis of the Belousov-Zhabotinsky reaction, the results presented here provide compelling evidence in support of the importance of outer sphere ligation of the iron catalyst

Nuclear Magnetic Resonance Study Of CO2 Capture By Fluoroalkylamines: Ammonium Ion PKa Depression Via Fluorine Modification And Thermochemistry Of Carbamylation

We are developing energy-efficient and reversible carbon capture and release (CCR) systems that mimic the Lys201 carbamylation reaction in the active site of ribulose-1,5-bisphosphate carboxylase-oxygenase (RuBisCO). The multiequilibria scenario ammonium ion Xa ⇌ amine Xb ⇌ carbamic acid Xc ⇌ carbamate Xd requires the presence of both free amine and CO2 for carbamylation and is affected by the pKa(Xa). Two fluorination strategies aimed at ammonium ion pKa depression and low pH carbamylation were analyzed with (2,2,2-trifluoroethyl) butylamine 2b and 2,2-difluoropropylamine 3b and compared to butylamine 1b. The determination of K1 and ΔG1 of the carbamylation reactions requires the solution of multiequilibria systems of equations based on initial conditions, 1H NMR measurements of carbamylation yields over a wide pH range, and knowledge of K2-K5 values. K2 and K3 describe carbonic acid acidity, and ammonium ion acidities K4 were measured experimentally. We calibrated carbamic acid acidities K5 based on the measured value K6 of aminocarbamic acid using isodesmic reactions. The proton exchange reactions were evaluated with ab initio computations at the APFD/6-311+G* level in combination with continuum solvation models and explicit solvation. The utilities of 1-3 will be discussed as they pertain to the development of fluorine-modified RuBisCO-mimetic reversible CCR systems

Polycyclic Aromatic Hydrocarbons with Aliphatic Sidegroups: Intensity Scaling for the C-H Stretching Modes and Astrophysical Implications

The so-called unidentified infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 μm ubiquitously seen in a wide variety of astrophysical regions are generally attributed to polycyclic aromatic hydrocarbon (PAH) molecules. Astronomical PAHs may have an aliphatic component, as revealed by the detection in many UIE sources of the aliphatic C-H stretching feature at 3.4 mm. The ratio of the observed intensity of the 3.4 mm feature to that of the 3.3 μm aromatic C-H feature allows one to estimate the aliphatic fraction of the UIE carriers. This requires knowledge of the intrinsic oscillator strengths of the 3.3 mm aromatic C-H stretch (A3.3) and the 3.4 μm aliphatic C-H stretch (A3.4). Lacking experimental data on A3.3 and A3.4 for the UIE candidate materials, one often has to rely on quantum-chemical computations. Although the second-order Møller-Plesset (MP2) perturbation theory with a large basis set is more accurate than the B3LYP density functional theory, MP2 is computationally very demanding and impractical for large molecules. Based on methylated PAHs, we show here that, by scaling the band strengths computed at an inexpensive level (e.g., B3LYP/6-31G), we are able to obtain band strengths as accurate as those computed at far more expensive levels (e.g., MP2/6-311+G(3df,3pd)). We calculate the model spectra of methylated PAHs and their cations excited by starlight of different spectral shapes and intensities. We find that (I3.4/I3.3)mod, the ratio of the model intensity of the 3.4 μm feature to that of the 3.3 μm feature, is insensitive to the spectral shape and intensity of the exciting starlight. We derive a straightforward relation for determining the aliphatic fraction of the UIE carriers (i.e., the ratio of the number of C atoms in aliphatic units NC,ali to that in aromatic rings NC,aro) from the observed band ratios (I3.4/I3.3)obs: NC,ali/NC,aro ≈ 0.57 x (I3.4/I3.3)obs for neutrals and NC,ali NC,aro ≈ 0.26 x (I3.4/I3.3)obs for cations