Computational study on the mechanism and selectivity of C-H bond activation and dehydrogenative functionalization in the synthesis of rhazinilam

The key platinum mediated C-H bond activation and functionalization steps in the synthesis of (-)-rhazinilam (Johnson, J. A.; Li, N.; Sames, D. J. Am. Chem. Soc. 2002, 124, 6900) were investigated using the M06 and B3LYP density functional approximation methods. This computational study reveals that ethyl group dehydrogenation begins with activation of a primary C-H bond in preference to a secondary C-H bond in an insertion/methane elimination pathway. The C-H activation step is found to be reversible while the methane elimination (reductive elimination) transition state controls rate and diastereoselectivity. The chiral oxazolinyl ligand induces ethyl group selectivity through stabilizing weak interactions between its phenyl group (or cyclohexyl group) and the carboxylate group. After C-H activation and methane elimination steps, Pt-C bond functionalization occurs through β-hydride elimination to give the alkene platinum hydride complex.     

Quantum Fields Obtained from Convoluted Generalized White Noise Never Have Positive Metric

It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (Lévy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from a criterion by Baumann, based on the Dell’Antonio–Robinson–Greenberg theorem, for a relativistic quantum field in positive metric to be a free field.     

Generalizations of Heilbronn’s triangle problem

For given integers d,j≥2 and any positive integers n, distributions of n points in the d-dimensional unit cube [0,1]^d are investigated, where the minimum volume of the convex hull determined by j of these n points is large. In particular, for fixed integers d,k≥2 the existence of a configuration of n points in [0,1]^d is shown, such that, simultaneously for j=2,…,k, the volume of the convex hull of any j points among these n points is Ω(1/n^{(j−1)/(1+|d−j+1|)}). Moreover, a deterministic algorithm is given achieving this lower bound, provided that d+1≤j≤k.     

Activation Energies and Reaction Energetics for 1,3‐Dipolar Cycloadditions of Hydrazoic Acid with C?C and C?N Multiple Bonds from High‐Accuracy and Density Functional Quantum Mechanical Calculations

The reactions of hydrazoic acid (HN₃) with ethene, acetylene, formaldimine (H₂CNH), and HCN were explored with the high‐accuracy CBS‐QB3 method, as well as with the B3LYP and mPW1K density functionals. CBS‐QB3 predicts that the activation energies for the reactions of hydrazoic acid with ethylene, acetylene, formaldimine, and HCN have remarkably similar activation enthalpies of 19.0, 19.0, 21.6, and 25.2 kcal/mol, respectively. The reactions are calculated to have reaction enthalpies of −21.5 for triazoline formation from ethene, and −63.7 kcal/mol for formation of the aromatic triazole from acetylene. The reaction to form tetrazoline from formaldimine has a reaction enthalpy of −8 kcal/mol (ΔG_rxn=+5.6 kcal/mol), and the formation of tetrazole from HCN has a reaction enthalpy of −23.0 kcal/mol. The trends in the energetics of these processes are rationalized by differences in σ‐bond energies in the transition states and adducts, and the energy required to distort hydrazoic acid to its transition‐state geometry. The density functionals predict activation enthalpies that are in relatively good agreement with CBS‐QB3, the results differing from CBS‐QB3 results by ca. 1–2 kcal/mol. Significant errors are revealed for mPW1K in predicting the reaction enthalpies for all reactions.     

Combined approach of isotope mass balance and hydrological water balance methods to constrain the sources of lake water as exemplified on the small dimictic lake Silbersee,northern Germany

Stable isotopes of hydrogen and oxygen are often used for water balance calculations of lakes. We present an approach combining the lake water balance with an isotope mass balance to constrain the sources and sinks of the water of a small dimictic lake subjected to eutrophication. Meteorological and hydraulic data in combination with measured isotope signatures of the different water compartments enabled to assess the degree of surface water/groundwater interaction and the amount of overland flow into the lake. Groundwater could be excluded as a lake water source, as its water level was always below the lake water level. In the absence of a channelled inflow, precipitation and overland flow were the remaining options, whereby the latter was only active during periods of exceptionally high rainfall. While the groundwater signatures adjacent to the lake showed an influence of lake water, the lake water balance itself indicated that the associated volumetric water loss to groundwater is rather negligible. In the present case, only a combined assessment of hydrological and isotopic data allowed for an accurate characterization of the studied lake and a quantification of its water sources and sinks, highlighting the importance of using more than one methodological approach for such a purpose.     

An Indefinite Metric Model for Interacting Quantum Fields on Globally Hyperbolic Space-Times

We consider a relativistic ansatz for the vacuum expectation values (VEVs) of a quantum field on a globally hyperbolic space-time which is motivated by certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t. an in-field in a quasi-free representation of the canonic commutation relations (CCR) leads to a solution of this ansatz for the VEVs. A GNS-like construction on a non-degenerate inner product space then gives local, covariant quantum fields with indefinite metric on a globally hyperbolic space-time. The non-trivial scattering behavior of quantum fields is analyzed by construction of the out-fields and calculation of the scattering matrix. A new combined effect of non-trivial quantum scattering and non-stationary gravitational forces is described for this model, as quasi-free in- fields are scattered to out-fields which form a non-quasi-free representations of the CCR. The asymptotic condition, on which the construction is based, is verified for the concrete example of de Sitter space-time. Communicated by Klaus Fredenhagen submitted 03/05/02, accepted: 18/07/03