Luminescence spectroscopy of matrix-isolated z 6P state atomic manganese

The relaxation of electronically excited atomic manganese isolated in solid rare gas matrices is observed from recorded emission spectra, to be strongly site specific. z 6P state excitation of Mn atoms isolated in the red absorption site in Ar and Kr produces narrow a 4D and a 6D state emissions while blue-site excitation produces z 6P state fluorescence and broadened a 4D and a 6D emissions. MnXe exhibits only a single thermally stable site whose emission at 620 nm is similar to the broad a 6D bands produced with blue-site excitation in Ar and Kr. Thus in Ar(Kr), excitation of the red site at 393 (400) nm produces narrow line emissions at 427.5 (427.8) and 590 (585.7) nm. From their spectral positions, linewidths, and long decay times, these emission bands are assigned to the a 4D72 and a 6D92 states, respectively. Excitation of the blue site at 380 (385.5) nm produces broad emission at 413 (416) nm which, because of its nanosecond radiative lifetime, is assigned to resonance z 6P --> a 6S fluorescence. Emission bands at 438 (440) and 625 (626.8) nm, also produced with blue-site excitation, are broader than their red-site equivalents at 427.5 and 590 nm (427.8 and 585.7 nm in Kr) but from their millisecond and microsecond decay times are assigned to the a 4D and a 6D states. The line features observed in high resolution scans of the red-site emission at 427.5 and 427.8 nm in MnAr and MnKr, respectively, have been analyzed with the W(p) optical line shape function and identified as resolved phonon structure originating from very weak (S=0.4) electron-phonon coupling. The presence of considerable hot-phonon emission (even in 12 K spectra) and the existence of crystal field splittings of 35 and 45 cm(-1) on the excited a 4D72 level in Ar and Kr matrices have been identified in W(p) line shape fits. The measured matrix lifetimes for the narrow red-site a 6D state emissions (0.29 and 0.65 ms) in Ar and Kr are much shorter than the calculated (3 s) gas phase value. With the lifetime of the metastable a 6D92 state shortened by four orders of magnitude in the solid rare gases, it is clear that the probability of the "forbidden" a 6D --> a 6S atomic transition is greatly enhanced in the solid state. A novel feature identified in the present work is the large width and shifted 4D and 6D emissions produced for Mn atoms isolated in the blue sites of Ar and Kr. In contrast, these states produce narrow, unshifted (gas-phase-like) 4D and 6D state emissions from the red site.     

Geometric existence theory for the control-affine nonlinear optimal regulator

For infinite horizon nonlinear optimal control problems in which the control term enters linearly in the dynamics and quadratically in the cost, well-known conditions on the linearised problem guarantee existence of a smooth globally optimal feedback solution on a certain region of state space containing the equilibrium point. The method of proof is to demonstrate existence of a stable Lagrangian manifold M and then construct the solution from M in the region where M has a well-defined projection onto state space. We show that the same conditions also guarantee existence of a nonsmooth viscosity solution and globally optimal set-valued feedback on a much larger region. The method of proof is to extend the construction of a solution from M into the region where M no-longer has a well-defined projection onto state space.     

Luminescence of ion-pair states of halogens in liquid perfluorocarbons

The I(2)(D'-A') luminescence in liquid C(7)F(16), C(8)F(18), C(9)F(20), and C(12)F(26) has been observed following irradiation with visible (within the I(2) X → B band region) and UV (λ < 300 nm) lasers. The band is shifted by ~2000 cm(-1) to the red relative to the gas phase and is significantly broader (fwhm ≈ 3000 cm(-1) vs 500 cm(-1) in the gas phase). Two-color excitation of other halogens in C(n)F(2n+2) solvents revealed similarly shifted and strongly broadened D'-A' bands of Br(2), IBr, and BrCl. The stability of the ion-pair states of halogens in room temperature liquids opens new experimental opportunities for condensed phase studies and may be of applied interest considering the increasing industrial applications of perfluorocarbons.     

Chemically induced dynamic electron spin polarization-detected energy transfer. Substrate size effects and solvent dependence

Time-resolved electron paramagnetic resonance spectroscopy is used to probe energy transfer from aromatic photoexcited triplet states to azo compounds in liquid solution. The observation of chemically induced dynamic electron spin polarization in the spectra gives precise information regarding the spin physics and mechanism of the energy transfer process. The substrate size is varied by altering the chain length of alkyl chains covalently attached to the azo compounds via ester or amide linkages. The solvent dependence of the energy transfer process is also investigated. The results are discussed in terms of Dexter and F?rster mechanisms for energy transfer, the properties of the excited states, and the diffusive properties of the molecules in the solvents of interest. Decomposition rate studies and fluorescence measurements are also reported.