Sufficient Conditions for the Existence of Bound States in a Potential without Spherical Symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.

Photophysics of Re(I) and Ru(II) diimine complexes covalently linked to pyrene: Contributions from intra-ligand charge transfer states

The photophysical properties of Ru(II) and Re(I) polypyridyl complexes including a bis-bipyridyl pyrene ligand are presented. The complexes ([(bpy)(2)Ru](2)bpb)(4+) and [(CO)(3)ReCl(bpb)] (bpy = 2,2'-bipyridine, bpb = 1,6-bis-(4-(2,2'-bipyrid-yl)-pyrene) were designed with the intent of examining intramolecular energy migration between MLCT states localized on the metal complexes and pyrene-localized (3)(pi-pi) states. Absorption spectroscopy of both complexes containing the bpb ligand reveals that in addition to the MLCT and the pyrene-centered (1)(pi-pi) transitions, a new absorption band is observed near 400 nm for both complexes. Absorption spectral data for the Re(I) complex strongly suggest the presence of a pyrene(pi) to bpy(pi) intraligand charge transfer (ILCT) transition. Emission spectra at room temperature and at 77 K are almost identical for the Ru(II) and Re(I) complexes containing the bpb ligand. The (3)MLCT emission of related bipyridyl compounds lacking the pyrene is observed at higher energy than for the pyrene-containing complexes, ([(bpy)(2)Ru](2)bpb)(4+) and [(CO(3)ReCl(bpb)]. The Ru(II) complex emits at room temperature with a remarkably long lifetime (130 micros in degassed DMSO). This emission is also strongly sensitive to oxygen and is almost entirely quenched in an aerated solution. In addition, excited-state absorption spectra exhibit features not consistent with (3)MLCT or (3)(pi-pi) states of the parent chromophores. The combined characteristics suggest the emission arises from either (3)(pi-pi) or (3)ILCT states or a state with mixed parentage.