The high-resolution laser-induced fluorescence (LIF) electronic spectrum associated with the 1 1A g→1 1B 1u transition in the perylenetetracarboxylic-dianhydride (PTCDA) molecule is discussed in terms of time-dependent density functional theory at TD-B3LYP/4-31G and TD-B3LYP/cc-pVDZ levels. It is shown that the simple vibronic model based on the displaced harmonic oscillators leads to quite reasonable agreement with the LIF experiment, even if some discrepancies occur. The results of TD-B3LYP/cc-pVDZ computations are compared to those obtained earlier within density-functional tight-binding (DFTB) approximation. We argue that the DFTB approach is inadequate to account correctly for the observed intensity distributions in the absorption spectra associated with the 1 1A g→1 1B 1u transition in the PTCDA molecule.