The wavevector star channel and symmetry group.

The concepts of `wavevector star channel' and `wavevector star channel group' are newly defined, which allow the effective study of phase transitions considering directly the translational symmetry breaking in crystals. A method is suggested by which the wavevector star channels can be found using the image of the representation of the translational group. According to this method, the wavevector star channels are found for the 80 Lifschitz stars in the reciprocal lattice. The wavevector star channel group is defined as the set of symmetry elements of the parent phase which leave the star channel invariant, and the wavevector star channel groups with one, two, three and four arms are calculated. It is shown that the complicated symmetry changes in the pyroelectric crystal Pb1-xCaxTiO3 (PCT) can be described using the new five-component reducible order parameter transformed according to the representation of the wavevector star channel group, rather than the nine-component one based on the theory of the full irreducible representation of the space group.

Reduction of peroxynitrite by some manganoporphyrins of AEOL series: DFT approach with dispersion correction and NBO analysis.

The AEOL series of manganoporphyrins (MnP; AEOL compounds were named by US Aeolus pharmaceuticals) designed as superoxide dismutase mimic are well-known for their powerful catalytic activity to neutralize reactive oxygen and nitrogen species. Reductive oxygen atom cleavage from peroxynitrite (ONOO-) to form NO2 in aqueous solution by some AEOL compounds (AEOL-10113, AEOL-10150, AEOL-11114 and AEOL-11203) was studied by DFT/M06-2X computations with D3 dispersion correction and gCP (geometrical counterpoise correction) for basis set superposition error. DFT computation showed that AEOL-10150 can form the most stable association complex {MnP…OONO} among four AEOL models. AEOL-10150 complex with ONOO- has the lowest deformation energy. In AEOL compounds and their association complexes with ONOO-, Mn atom prefered the high spin state (S = 2) to the intermediate spin state (S = 1). Natural bond orbital analysis showed that electron transfer from the most negative oxygen atom in ONOO- to Mn atom in MnP has the biggest interaction energy among all kinds of donor-acceptor interactions between ONOO- and MnP.