We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol. 相似文献
Tensor products of Calgebras over an abelian Walgebra are studied. The minimal Cnorm on is shown to be just the quotient of the minimal Cnorm on if or is exact.
Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing
which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.
A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.
A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.
The application of coherent anti-Stokes Raman spectroscopy (CARS) to an electric are test reactor is described in which acetylene synthesis in analogy to the large-scale industrial process is .studied. We report on spatially resolved measurements of H2-CARS spectra, the comparison with calculated spectra, and the determination of temperatures in the reaction zone.Dedicated to Prof. Rudolf Wienecke on the occasion of his 65 birthday. 相似文献
In this work it is reported that the kinetic modelling of the separation of cadmium from phosphoric acid by non-dispersive solvent extraction. Using Cyanex 302 as selective extractant, the extraction step was carried out in a hollow fibre module containing polypropylene fibres, whereas the concentration step required a ceramic module with tubular channels due to the high acidity of the backextraction agent. Application of the methodology previously reported by the authors led to the development of a kinetic model with three design parameters, i.e., equilibrium constant of the extraction reaction (K'e = 6 × 103 mol−2/l−2), membrane mass transport coefficient of the extraction module Kme=8.33×10−8 m/s) and of the backextraction module (Kms=3.33×10−8 m/s), that described satisfactorily the behaviour of the separation-concentration system. Thus, in this work a new application of the non-dispersive solvent extraction technology is presented, characterising at the same time the behaviour and parameters of a new type of contactor, i.e., a tubular ceramic module. 相似文献
Interatomic distances in the reaction centers of the addition reactions of (i) H· to the C=C, C=O, N≡C, and C≡C bonds, (ii) ·CH3 radical to the C=C, C=O, and C≡C bonds, and (iii) alkyl, aminyl, and alkoxyl radicals to olefin C=C bonds were determined
using a new semiempirical method for calculating transition-state geometries of radical reactions. For all reactions of the
type X· + Y=Z → X— Y—Z· the r#X...Y distance in the transition state is a linear function of the enthalpy of reaction. Parameters of this dependence were determined
for seventeen classes of radical addition reactions. The bond elongation, Δr#X...Y, in the transition state decreases as the triplet repulsion, electronegativity difference between the atoms X and Y in the
reaction center, and the force constant of the attacked multiple bond increase.
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Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 894–902, April, 2005. 相似文献
The title compound (4,4'-H2bipy)[CdBr4]·H2O 1 has been synthesized via hydrothermal reaction and characterized by X-ray diffraction. The crystal belongs to monoelinic,space group P21/c with a=8.260(3), b=23.926(7), c=9.774(2) (A), β=106.777(9)°,C10H12Br4CdN2O, Mr=608.26, V=1849.4(9)(A)3, Z=4, Dc=2.185 g/cm3, S=1.005, μ(MoKα)=9.814 mm-1, F(000)=1128, R=0.0646 and wR=0.0989. The crystal structure analysis of 1reveals that the title compound features an isolated structure, based on discrete 4,4'-H2bipy moieties and lattice water molecules which are linked by hydrogen bonds together with tetrahedral cadmium atoms terminally coordinated by four bromine atoms. 相似文献