A Hammett's analysis of the substituent effect in functionalized diketopyrrolopyrrole (DPP) systems: Optoelectronic properties and intramolecular charge transfer effects

Abstract

Diketopyrrolopyrrole (DPP) systems have promising applications in different organic electronic devices. In this work, we investigated the effect of 20 different substituent groups on the optoelectronic properties of DPP-based derivatives as the donor ( $D$ )-material in an organic photovoltaic (OPV) device. For this purpose, we employed Hammett's theory (HT), which quantifies the electron-donating or -withdrawing properties of a given substituent group. Machine learning (ML)-based ${\sigma }_m$ , ${\sigma }_p$ , ${\sigma }_m^0$ , ${\sigma }_p^0$ , ${\sigma }_p^{+}$ , ${\sigma }_p^{-}$ , ${\sigma }_I$ , and ${\sigma }_R$ Hammett's constants previously determined were used. Mono- (DPP-X₁ ) and di-functionalized (DPP-X₂ ) DPPs, where X is a substituent group, were investigated using density functional theory (DFT), time-dependent DFT (TDDFT), and ab initio methods. Several properties were computed using CAM-B3LYP and the second-order algebraic diagrammatic construction, ADC(2), an ab initio wave function method, including the adiabatic ionization potential ( $I{P}_A$ ), the electron affinity ( $E{A}_A$ ), the HOMO-LUMO gaps ( $E_g$ ), and the maximum absorption wavelengths ( ${\lambda }_{\max }$ ), the first excited state transition ¹ S₀ → ¹ S₁ energies ( $∆E$ ) (the optical gap), and exciton binding energies. From the optoelectronic properties and employing typical acceptor systems, the power conversion efficiency ( $\mathrm{PCE}$ ), open-circuit voltage ( $V_{\mathrm{OC}}$ ), and fill factor ( $\mathrm{FF}$ ) were predicted for a DPP-based OPV device. These photovoltaic properties were also correlated with the machine learning (ML)-based Hammett's constants. Overall, good correlations between all properties and the different types of $\sigma$ constants were obtained, except for the ${\sigma }_I$ constants, which are related to inductive effects. This scenario suggests that resonance is the main factor controlling electron donation and withdrawal effects. We found that substituent groups with large $\sigma$ values can produce higher photovoltaic efficiencies. It was also found that electron-withdrawing groups (EWGs) reduced $E_g$ and $∆E$ considerably compared to the unsubstituted DPP-H. Moreover, for every decrease (increase) in the values of a given optoelectronic property of DPP-X₁ systems, a more significant decrease (increase) in the same values was observed for the DPP-X₂ , thus showing that the addition of the second substituent results in a more extensive influence on all electronic properties. For the exciton binding energies, an unsupervised machine learning algorithm identified groups of substituents characterized by average values (centroids) of Hammett's constants that can drive the search for new DDP-derived materials. Our work presents a promising approach by applying HT on molecular engineering DPP-based molecules and other conjugated molecules for applications on organic optoelectronic devices.

Keywords: Diketopyrrolopyrrole; Hammett theory; donor properties; optoelectronic properties; organic electronics; substituent effects.