Complex Frequency-Dependent Polarizability through the π → π* Excitation Energy of Azobenzene Molecules by a Combined Charge-Transfer and Point-Dipole Interaction Model

Abstract

The complex frequency-dependent polarizability and π → π* excitation energy of azobenzene compounds are investigated by a combined charge-transfer and point-dipole interaction (CT/PDI) model. To parametrize the model, we adopted time-dependent density functional theory (TDDFT) calculations of the frequency-dependent polarizability extended with excited-state lifetimes to include also its imaginary part. The results of the CT/PDI model are compared with the TDDFT calculations and experimental data demonstrating that the CT/PDI model is fully capable to reproduce the static polarizability as well as the π → π* excitation energy for these compounds. In particular, azobenzene molecules with different functional groups in the para-position have been included serving as a severe test of the model. The π → π* excitation is to a large extent localized to the azo bond, and substituting with electron-donating or electron-attracting groups on the phenyl rings results in charge-transfer effects and a shift in the excitation energy giving rise to azobenzene compounds with a range of different colors. In the CT/PDI model, the π → π* excitation in azobenzenes is manifested as drastically increasing atomic induced dipole moments in the azo group as well as in the adjacent carbon atoms, whereas the shifts in the excitation energies are due to charge-transfer effects.

Evaluation of Molecular Polarizability and of Intensity Carrying Modes Contributions in Circular Dichroism Spectroscopies

“…Our results, reported in Figure 2, nicely compare with those reported in Figure 3b of Ref. [54]: the maximum value of the imaginary part of Tr(α ee )/3 is about 1000 bohr 3 and the maximum value of the real part of Tr(α ee )/3 is about 600 bohr 3 . We also note that the shapes and linewidths of both the real and imaginary parts of the isotropic electric polarizability in Figure 2 are very close to those reported in Figure 3b of Ref.…”

“…We also note that the shapes and linewidths of both the real and imaginary parts of the isotropic electric polarizability in Figure 2 are very close to those reported in Figure 3b of Ref. [54]. Tr(α ee )) computed by polar from a TDDFT calculation at PBE/cc-pVTZ level: (a) the chemical structure of 4,4'-diaminoazobenzene and the graphical representation of the computed equilibrium structure, which is essentially planar, with the -NH 2 groups slightly pyramidalized; and (b) the results obtained by the polar code for two choices of N, demonstrating good convergence at N = 100 states in this photon energy range.…”

“…As expected, convergence is faster when approaching resonance conditions (e.g., close to 7 eV in Figure 1a), for which single transitions dominate the sum over states expression of the polarizability. In a further independent check, we have validated polar against the reported values of the complex electric dipole polarizability of 4,4'-diaminoazobenzene [54]. A direct numerical comparison is difficult in this case due to the different quantum chemistry code used here (Gaussian09) and in [54] (ADF).…”

“…In a further independent check, we have validated polar against the reported values of the complex electric dipole polarizability of 4,4'-diaminoazobenzene [54]. A direct numerical comparison is difficult in this case due to the different quantum chemistry code used here (Gaussian09) and in [54] (ADF). To approach the computational conditions of Haghdani et al [54], we adopted for 4,4'-diaminoazobenzene the PBE functional and the cc-pVTZ basis set.…”

“…A direct numerical comparison is difficult in this case due to the different quantum chemistry code used here (Gaussian09) and in [54] (ADF). To approach the computational conditions of Haghdani et al [54], we adopted for 4,4'-diaminoazobenzene the PBE functional and the cc-pVTZ basis set. Our results, reported in Figure 2, nicely compare with those reported in Figure 3b of Ref.…”