Calculations incorporating anharmonic coupling between all of the vibrational states within a wide energy range (plus/minus several hundred wavenumbers minimum) are used to investigate intramolecular vibrational energy redistribution (IVR) in the low vibrational energy region (Evib < 3000 cm-1) of S1 p-difluorobenzene. A simple model is presented for estimating the magnitude of the anharmonic coupling constants required for these calculations. Dispersed fluorescence spectra from the resulting molecular eigenstates are calculated and the trends compared with those from experimental studies. The congestion observed experimentally in dispersed fluorescence spectra is reproduced in the calculated spectra. It is found that the majority of the states contributing to this unstructured emission lie outside the energy spread of typical picosecond sources. Consequently, only a small number of the near-lying states gain sufficient oscillator strength to influence the time dynamics. Our calculations thus suggest that only a subset of the available isoenergetic states plays an effective role in the time dynamical redistribution. The calculations further reveal that the coupling pathways are dominated by the lower order anharmonic terms in this low-energy region. The model developed here to estimate the size of the anharmonic terms is sufficiently general that the results of the p-difluorobenzene calculations are expected to apply to a range of similar molecules.