Magnetically induced current densities and ring-current pathways have been calculated at density functional theory (DFT) and second-order Møller-Plesset perturbation theory (MP2) levels of theory for a set of expanded porphyrins consisting of five or six pyrrolic rings. The studied molecules are sapphyrin, cyclo[6]pyrrole, rubyrin, orangarin, rosarin, and amethyrin. Different functionals have been employed to assess the functional dependence of the ring-current strength susceptibility. Vertical singlet and triplet excitation energies have been calculated at the second-order approximate coupled cluster (CC2), expanded multiconfigurational quasi-degenerate perturbation theory (XMC-DPT2), and time-dependent density functional theory levels. The lowest electronic transition of the antiaromatic molecules was found to be pure magnetic transitions providing an explanation for the large paratropic contribution to the total current density. Rate constants for different nonradiative deactivation channels of the lowest excited states have been calculated yielding lifetimes and quantum yields of the lowest excited singlet and triplet states. The calculations show that the spin-orbit interaction between the lowest singlet ( S) and triplet ( T) states of the antiaromatic molecules is strong, whereas for the aromatic molecule the spin-orbit coupling vanishes. The experimentally detected fluorescence from S to S of amethyrin has been explained. The study shows that there are correlations between the aromatic character and optical properties of the investigated expanded porphyrins.
Here we study the thermo-optical properties of an on-chip silicon nitride Mach-Zehnder interferometer (MZI). The spectral shift of the MZI is associated with a change in the chip temperature. This can be explained by a change in the splitting ratio of the directional couplers, as well as a significant change in phase difference between waveguide arms. We experimentally found a phase shift of 2π when heated by 1.67 °C and changes in resonant wavelength at different temperatures (dλ/dT) equal 12.0 pm/°C, theoretically obtained a formula for an arbitrary splitting ratio of the directional couplers in an MZI, and determined the temperature stability required to the device operation inside a quantum cryptography system.
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