Theoretical approaches to estimating homolytic bond dissociation energies of organocopper and organosilver compounds

Although organocopper and organosilver compounds are known to decompose by homolytic pathways among others, surprisingly little is known about their bond dissociation energies (BDEs). In order to address this deficiency, the performance of the DFT functionals BLYP, B3LYP, BP86, TPSSTPSS, BHandHLYP, M06L, M06, M06-2X, B97D, and PBEPBE, along with the double hybrids, mPW2-PLYP, B2-PLYP, and the ab initio methods, MP2 and CCSD(T), have been benchmarked against the thermochemistry for the M-C homolytic BDEs (D(0)) of Cu-CH(3) and Ag-CH(3), derived from guided ion beam experiments and CBS limit calculations (D(0)(Cu-CH(3)) = 223 kJ·mol(-1); D(0)(Ag-CH(3)) = 169 kJ·mol(-1)). Of the tested methods, in terms of chemical accuracy, error margin, and computational expense, M06 and BLYP were found to perform best for homolytic dissociation of methylcopper and methylsilver, compared with the CBS limit gold standard. Thus the M06 functional was used to evaluate the M-C homolytic bond dissociation energies of Cu-R and Ag-R, R = Et, Pr, iPr, tBu, allyl, CH(2)Ph, and Ph. It was found that D(0)(Ag-R) was always lower (～50 kJ·mol(-1)) than that of D(0)(Cu-R). The trends in BDE when changing the R ligand reflected the H-R bond energy trends for the alkyl ligands, while for R = allyl, CH(2)Ph, and Ph, some differences in bond energy trends arose. These trends in homolytic bond dissociation energy help rationalize the previously reported (Rijs, N. J.; O'Hair, R. A. J. Organometallics2010, 29, 2282-2291) fragmentation pathways of the organometallate anions, [CH(3)MR](-).     

Ion angular distributions in electron stimulated desorption: Oxygen and CO on W(111)

The ion angular distributions resulting from electron stimulated desorption (ESD) of oxygen and carbon monoxide chemisorbed on a tungsten (111) crystal have been determined. The O⁺ ions released during ESD of adsorbed oxygen exhibit three-fold symmetric angular distributions in orientational registry with the W(111) substrate. The CO⁺ and O⁺ ions released during ESD of a monolayer of CO are desorbed normal to the (111) surface. Models for both oxygen and CO adsorption are discussed. The data for CO are consistent with adsorption of CO in “standing up” carbonyl structures in the virgin and α-CO binding states.     

Elastic stress distributions for hyperbolic and parabolic notches in round shafts under torsion and uniform antiplane shear loadings

Closed-form solutions are developed for the stress fields induced by circumferential hyperbolic and parabolic notches in axisymmetric shafts under torsion and uniform antiplane shear loading. The boundary value problem is formulated by using complex potential functions and two different coordinate systems, providing two classes of solutions. It is also demonstrated that some solutions of linear elastic fracture and notch mechanics reported in the literature can be derived as special cases of the general solutions proposed herein.Finally the analytical frame is used to link the Mode III notch stress intensity factor to the maximum shear stress at the notch tip, as well as to give closed-form expressions for the strain energy averaged over a finite size volume surrounding the notch root.     

Probing Low-Energy Collective Nuclear Modes with Fast Neutrons

The low-energy, low-spin collective modes of nuclei that can be excited through inelastic scattering reactions with fast neutrons are reviewed. Recent studies of quadrupole, octupole, and multiphonon vibrations are described, and more exotic modes, including mixed-symmetry states, scissors mode states, and intruder excitations, are presented. The opportunities afforded through reactions with very energetic neutrons are considered, and a view to the future of nuclear structure studies with energetic neutrons is given.     

General theory of domain decomposition: Indirect methods

According to a general theory of domain decomposition methods (DDM), recently proposed by Herrera, DDM may be classified into two broad categories: direct and indirect (or Trefftz‐Herrera methods). This article is devoted to formulate systematically indirect methods and apply them to differential equations in several dimensions. They have interest since they subsume some of the best‐known formulations of domain decomposition methods, such as those based on the application of Steklov‐Poincaré operators. Trefftz‐Herrera approach is based on a special kind of Green's formulas applicable to discontinuous functions, and one of their essential features is the use of weighting functions which yield information, about the sought solution, at the internal boundary of the domain decomposition exclusively. A special class of Sobolev spaces is introduced in which boundary value problems with prescribed jumps at the internal boundary are formulated. Green's formulas applicable in such Sobolev spaces, which contain discontinuous functions, are established and from them the general framework for indirect methods is derived. Guidelines for the construction of the special kind of test functions are then supplied and, as an illustration, the method is applied to elliptic problems in several dimensions. A nonstandard method of collocation is derived in this manner, which possesses significant advantages over more standard procedures. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 296–322, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10008     

Theoretical investigation into the mechanism of reductive elimination from bimetallic palladium complexes

Reductive elimination of C-Cl and C-C bonds from binuclear organopalladium complexes containing Pd-Pd bonds with overall formal oxidation state +III are explored by density functional theory for dichloromethane and acetonitrile solvent environments. An X-ray crystallographically authenticated neutral complex, [(L-C,N)ClPd(μ-O(2)CMe)](2) (L = benzo[h]quinolinyl) (I), is examined for C-Cl coupling, and the proposed cation, [(L-C,N)PhPd(1)(μ-O(2)CMe)(2)Pd(2)(L-C,N)](+) (II), examined for C-C coupling together with (L-C,N)PhPd(1)(μ-O(2)CMe)(2)Pd(2)Cl(L-C,N) (III) as a neutral analogue of II. In both polar and nonpolar solvents, reaction from III via chloride dissociation from Pd(2) to form II is predicted to be favored. Cation II undergoes Ph-C coupling at Pd(1) with concomitant Pd(1)-Pd(2) lengthening and shortening of the Pd(1)-O bond trans to the carbon atom of L; natural bond orbital analysis indicates that reductive coupling from II involves depopulation of the d(x(2)-y(2)) orbital of Pd(1) and population of the d(z(2)) orbitals of Pd(1) and Pd(2) as the Pd-Pd bond lengthens. Calculations for the symmetrical dichloro complex I indicate that a similar dissociative pathway for C-Cl coupling is competitive with a direct (nondissociative) pathway in acetonitrile, but the direct pathway is favored in dichloromethane. In contrast to the dissociative mechanism, direct coupling for I involves population of the d(x(2)-y(2)) orbital of Pd(1) with Pd(1)-O(1) lengthening, significantly less population occurs for the d(z(2)) orbital of Pd(1) than for the dissociative pathway, and d(z(2)) at Pd(2) is only marginally populated resulting in an intermediate that is formally a Pd(1)(I)-Pd(2)(III) species, (L-Cl-N,Cl)Pd(1)(μ-O(2)CMe)Pd(2)Cl(O(2)CMe)(L-C,N) that releases chloride from Pd(2) with loss of Pd(I)-Pd(III) bonding to form a Pd(II) species. A similar process is formulated for the less competitive direct pathway for C-C coupling from III, in this case involving decreased population of the d(z(2)) orbital of Pd(2) and strengthening of the Pd(I)-Pd(III) interaction in the analogous intermediate with η(2)-coordination at Pd(1) by L-Ph-N, C(1)-C(2).     

Development of a GC/Q-ToF-MS Method Coupled with Headspace Solid-Phase Microextraction to Evaluate the In Vitro Metabolism of β-Caryophyllene

Sample preparation remains both a challenging and time-consuming process in the field of bioanalytical chemistry. Many traditional techniques often require multi-step processes, which can introduce additional errors to the analytical method. Given the complexity of many biological matrices, thorough analyte extraction presents a major challenge to researchers. In the present study, a headspace solid-phase microextraction (HS-SPME) coupled with a GC/Q-ToF-MS method, was developed to quantify in vitro metabolism of β-caryophyllene by both human liver microsome (HLM) and S9 liver fractions. Validation of the method was demonstrated both in terms of linearity (R² = 0.9948) and sensitivity with a limit of detection of 3 ng/mL and a limit of quantitation of 10 ng/mL. In addition, the method also demonstrated both inter- and intra-day precision with the relative standard deviation (RSD) being less than 10% with four concentrations ranging from 50–500 ng/mL. Since this method requires no solvents and minimal sample preparation, it provides a rapid and economical alternative to traditional extraction techniques. The method also eliminates the need to remove salts or buffers, which are commonly present in biological matrices. Although this method was developed to quantify in vitro metabolism of one analyte, it could easily be adapted to detect or quantify numerous volatiles and/or semi-volatiles found in biological matrices.     

Quasar red shifts

The results of techniques developed in earlier papers are used in a discussion of the quasar red shifts. An expression with the form of a kinetic energy arises in relation to the probability distribution of red shifts. Agreement with the Hoyle & Burbridge (1966) red shift data at the time of writing is statistically significant, the correlation coefficient being 0·82.