Influence of the Chemical Structure on the Luminescence Properties of Organic Dye Molecules
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II
III
C12 H25
C 12H25
C12 H25
C 12H25
IV
Figure 1: Chemical structure of the investigated dye molecules electric dipole transition moment µ is given by
A=
2 1 E 3B = E3ì h c 3ε0 h 4 c3 2 3
2
(1),
with B being the Einstein B coefficient (describing absorption and stimulated emission) and E equal to the energy of the transition. Equation (1) can be derived from the standard quantum-mechanical results for B either by statistical or quantum electrodynamic considerations.6 The radiative lifetime τrad is then given by the reciprocal value of A. An important feature of equation (1) is that the radiative recombination rate is proportional to the third power of the energy of the corresponding transition. This makes an accurate determination of the transition energy crucial, when deriving lifetimes and transition rates from the quantum-mechanically calculated dipole transition moments. The luminescence lifetimes experimentally determined by the used modulation spectroscopy technique correspond to the total lifetimes τtot of the excited species. They depend on both radiative τrad and non-radiative τn-rad lifetimes and are linked to the quantum efficiencies (QEs) of the investigated materials as given in the following equations:
1 1 1 = + τtot τrad τn − rad τ QE = tot 100 % τrad
(2) (3)
From equations (2) and (3) it can be concluded that the measured total lifetimes can be regarded as a lower limit for the radiative lifetimes of the investigated materials. For quantum efficiencies close to 100% (as can be expected for dilute solutions of molecules like those inves tigated in this paper) τtotal becomes equal to τrad.
THEORETICAL AND EXPERIMENTAL METHODOLOGY The geometries of the molecules are optimized with the semiempirical HartreeFock Austin Model 1 (AM1) method.7 To calculate relaxed excited state geometries the AM1 Hamiltonian is coupled to a multi electron configuration interaction (MECI) technique.8 The details of the calculations are described e.g. in Ref. [9]. Transition energies and optical dipole transition moments are calculated on the basis of the semiempirical Hartree-Fock Intermediate Neglect of Differential Overlap (INDO) method,10,11 with the Coulomb repulsion terms expressed via the MatagaNishimoto potential. 12 Here electron correlation effects are included by a Single Configuration-Interaction technique (SCI) with the number of CI active occupied and unoccupied orbitals equal to the number of π electrons of each molecule. According to the Franck-Condon principle the transition energies calculated either for the fixed ground (absorption) or excited (e mission) state geometries correspond to the center of the experimentally observed vibronic progressions. The optical absorption spectra have been measured for dilute dichloromethane solutions with a Perkin Elmer λ-9 spectrometer. A Schimadzu RF-5301PC spectrofluorimeter has been used to record emission spectra. Lifetimes are measured using a phase-modulation-fluorimeter,13 in which the sample is excited using sinusoidally modulated light (modulat
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