Time-resolved EPR and ODMR studies on the lowest excited triplet states of α-silyl and α-germyl ketones

Sublevel properties of the lowest excited triplet (T¹) nπ* states of α-silyl and α-germyl ketones were examined by means of ODMR, time-resolved EPR and optical spectroscopy. The EPR parameters, D, E and g, population ratios, and triplet lifetimes were obtained. The D value and the triplet lifetime varied among the molecules. In contrast the E value and population ratio remains nearly the same. These properties together with their solvent dependence and emission properties are interpreted in terms of spin-orbit couplings between T₁ (nπ*) and higher S₁ (nπ*), T₂ (ππ*) and S₂ (ππ*) states. An origin of the remarkable red-shifts of ^1,3 (π*) are discussed based on a model of delocalized n, π and π* electrons over the Si and Ge atoms. This model is also consistent with all the triplet properties obtained.     

REPRESENTATIONS OF AFFINE SUPERALGEBRAS AND MOCK THETA FUNCTIONS

We show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra $ {{\widehat{{s\ell}}}_{2|1 }} $ (resp. $ {{\widehat{{ps\ell}}}_{2|2 }} $ ) can be modified, using Zwegers’ real analytic corrections, to form a modular (resp. S-) invariant family of functions. Applying the quantum Hamiltonian reduction, this leads to a new family of positive energy modules over the N?=?2 (resp.N?=?4) superconformal algebras with central charge 3(1???(2?m?+?2)/M), where m ∈ ?_≥0, M ∈ ?_≥2, gcd(2?m?+?2, M)?=?1 if m?>?0 (resp. 6 (m/M???1), where m ∈ ?_≥1, M ∈ ?_≥2, gcd(2?m, M)?=?1 if m?>?1), whose modified characters and supercharacters form a modular invariant family.