Excess and excited-state dipole moments of real-life dyes: a comparison between wave-function, BSE/ GW , and TD-DFT values.

In this work, we assess the accuracy of the Bethe-Salpeter equation (BSE) many-body Green's function formalism, adopting the eigenvalue-self-consistent ev GW exchange-correlation kernel, for the calculation of the excited-state ( μ ES ) and excess dipole moments (Δ μ ), the latter ones being the changes of dipole amplitude between the ground and excited states (ES), in organic dyes. We compare the results obtained with wave-function methods [ADC(2), CC2, and CCSD], time-dependent density functional theory (TD-DFT), and BSE/ev GW levels of theory. First, we compute the evolution of the dipole moments of the two lowest singlet excited states of 4-(dimethylamino)benzonitrile (DMABN) upon twisting of the amino group. Next, we use a set of 25 dyes having ES characters ranging from locally excited to charge transfer to determine both μ ES and Δ μ . For DMABN our results show that BSE/ev GW provides Δ μ values closer to the CCSD reference and more consistent trends than TD-DFT. Moreover, a statistical analysis of both Δ μ and μ ES for the set of 25 dyes shows that the BSE/ev GW accuracy is comparable or sometimes slightly better than that of TD-M06-2X and TD-CAM-B3LYP, BSE/ev GW outperforming TD-DFT in challenging cases (zwitterionic and cyanine transitions). Finally, the starting point dependency of BSE/ev GW seems to be larger for Δ μ , ES dipoles, and oscillator strengths than for transition energies.