H2S‐Mediated Thermal and Photochemical Methane Activation

Sustainable, low‐temperature methods for natural gas activation are critical in addressing current and foreseeable energy and hydrocarbon feedstock needs. Large portions of natural gas resources are still too expensive to process due to their high content of hydrogen sulfide gas (H₂S) mixed with methane, deemed altogether as sub‐quality or “sour” gas. We propose a unique method of activation to form a mixture of sulfur‐containing hydrocarbon intermediates, CH₃SH and CH₃SCH₃, and an energy carrier such as H₂. For this purpose, we investigated the H₂S‐mediated methane activation to form a reactive CH₃SH species by means of direct photolysis of sub‐quality natural gas. Photoexcitation of hydrogen sulfide in the CH₄+H₂S complex resulted in a barrierless relaxation by a conical intersection to form a ground‐state CH₃SH+H₂ complex. The resulting CH₃SH could further be coupled over acidic catalysts to form higher hydrocarbons, and the resulting H₂ used as a fuel. This process is very different from conventional thermal or radical‐based processes and can be driven photolytically at low temperatures, with enhanced control over the conditions currently used in industrial oxidative natural gas activation. Finally, the proposed process is CO₂ neutral, as opposed to the current industrial steam methane reforming (SMR).     

Visualization of the cholesteric texture near a Grandjean line

The twisted structure near a Grandjean line in a cholesterically ordered liquid crystalline network is visualized by scanning electron microscopy. It is shown that the formation of an extra π-rotation in the molecular helix at a Grandjean line occurs at a localized depth in the sample and gives rise to an edge dislocation of strength 1/2, dissociated into a pair of two simple line dislocations.     

Differents in modular invariant theory

Let be a graded polynomial algebra over a field k, such that each variable is homogeneous of positive degree. No restrictions are made with respect to the field. Let the finite group G act on A by graded algebra automorphisms and denote the subalgebra of invariants by B. In this paper the various "different ideals" of the extension are studied that define the ramification locus. We prove, for example, that the subring of invariants is itself a polynomial ring if and only if the ramification locus is pure of height one. Here the ramification locus is defined by either the Kahler different, the Noether different or the Galois different. As a consequence we prove that the invariant ring is itself a polynomial ring if and only if there are invariants whose Jacobian determinant does not vanish and is of degree δ, where δ is the degree of the Dedekind different. Using this criterion we give a quick proof of Serre's result that if the invariant ring is a polynomial algebra, then the group is generated by generalized reflections.     

Broken orbital-symmetry and the description of hole states in the tetrahedral [CrO4]− anion. I. Introductory considerations and calculations on oxygen 1s hole states

The localization of holes in systems containing spatially equivalent sites is discussed in terms of a simple one-particle model in which quantum mechanical delocalization effects compete with essentially classical polarization or dielectric relaxation effects. The predictions of the model for a tetrahedral system like CrO^?₄ compare favourably with the results of symmetry unrestricted SCF calculations on O_1s hole states. The connection with a Cl treatment using symmetry-restricted MOs is discussed. The calculated ionization energies are finally compared with XPS measurements on Na₂CrO₄. To this end the crystal surrounding of the CrO^?₄ anion has been represented by a point charge model and the ensuing Modelung field was included in the SCF calculations. In contrast to the Td restricted result of 551.4 eV, the completely localized C_3v results of 532.6 eV is in satisfactory agreement with the experimental data which are found around 530.0 eV.     

On a proposed alternative to the KdV equation

As an alternative to the KdV equation a second-order non-linear dispersive wave equation has been proposed [1,2]. Upon closer inspection it turns out that this alternative is not a satisfactory one.     

Hidden hamiltonians of first-order equations

There are equations, like the KDV equation, of which the solutions behave like conservative systems although the equation is of first order in time. It is shown how equations of this kind can originate by a direct-product like process of fusion of two canonical conjugate variables. Conversely, for a class of dynamically well-behaved first-order equations a splitting of the independent variable into two conjugate parts and a corresponding hamiltonian functional can be found. It is shown how the action principle and the Noether theorem transform during this fusion or splitting process. A number of examples are discussed. It is shown how a KDV approximation can be derived directly from the hamiltonian of a second-order system without using the second-order wave equations.