Theoretical study of the transfer integral and density of states in spiro-linked triphenylamine derivatives

We present a method for calculating the parameters that control hopping transport in disordered molecular solids, i.e., the transfer integrals and the distribution of transport site energies. Average values of these parameters are obtained by performing quantum-chemical calculations on a large ensemble of bimolecular complexes in random relative orientations. The method is applied to triphenylamine (TPA) and three differently substituted spiro-linked phenylamine compounds, 2,2',7,7'-tetrakis-(N,N-di-4-methoxyphenylamino)-9,9'-spirobifluorene (spiro-MeOTAD), 2,2'7,7'-tetrakis-(N,N-diphenylhenylamino)-9,9'-spirobifluorene (spiro-TAD), and 2,2',7,7'-tetrakis-(N,N-di-m-methylphenylamino)-9,9'-spirobifluorene (spiro-m-TTB). In the case of TPA, the dependence of the root-mean-square hole transfer integral J on intermolecular separation r for the ensemble of relative orientations is compared with that obtained by performing the same calculations for a fixed, approximately cofacial, orientation of the two TPA molecules. The calculation for the disordered geometry predicts a larger localization radius r0, where J approximately exp(-r/r0), than the calculation for the fixed orientation and is in better agreement with experiment. In the case of the spiro-linked compounds, results from our method are compared with parameters extracted from time-of-flight mobility measurements analyzed with the Gaussian disorder model (GDM). We find that the highest occupied molecular-orbital (HOMO) energies of the bimolecular complexes are distributed on an asymmetric peak, whose width varies in qualitative agreement with the value of the energetic disorder sigma obtained from experimental data using the GDM. The mean-square hole transfer integral varies in accordance with the experimentally determined value of the mobility prefactor micro0. The differences between the differently substituted compounds are interpreted in terms of differences in the spatial extent of the wave function. Spiro-MeOTAD was found to have a greater localization radius, which leads to both a larger transfer integral and a broader distribution of HOMO energies than either of the other compounds. For these compounds, differences in energetic disorder could not be explained in terms of differences in the permanent dipole moment. Our method is proposed as an approximate means of predicting the effect of chemical structure on the values of transport parameters in disordered molecular films.