Intermediate level structure in highly excited electronic states of large molecules

Abstract

In this paper we consider the radiative decay of excited electronic states of a large molecule which correspond to the dense intermediate level spacing situation, encountered for the second excited singlet state of some aromatic hydrocarbons, which is separated from the first excited singlet state by a small (3000 to 4000 cm -1 ) electronic energy gap. Intramolecular interstate coupling and the interaction with the radiation field were handled by a selfconsistent extension of the Wigner-Weisskopf approximation. We were able to derive a general expression for the time and energy resolved decay spectrum of a highly excited state of a large molecule, which yields information concerning the decay pattern, for the fluorescence lifetime(s) and for the corresponding quantum yields, in different spectral regions. Weak and strong coupling limits can be distinguished and defined in terms of the magnitude of the non-adiabatic interstate coupling terms relative to the spacing and the width of the zero states. In the intermediate level spacing in a large molecule, the radiative decay of the excited state should be considered in terms of the decay of a finite set of coupled levels and intramolecular relaxation between these states does not occur in the ‘isolated’ molecule. Resonance fluorescence is amenable to experimental observation from the second excited singlet state of a large molecule which corresponds to this intermediate case. The weak and strong coupling situations can be experimentally distinguished on the basis of energy resolved lifetime measurements. General criteria have been provided for the observation of quantum interference effects in the radiative decay for different coupling schemes. The present theoretical results provide a proper interpretation of some recent experimental data concerning the radiative decay of the second excited state of some aromatic molecules (3,4-benzpyrene and naphthalene).