Hammett's constants σ quantify the electron donor or electron acceptor power of a chemical group bonded to an aromatic ring. Their experimental values have been successfully used in many applications, but some are inconsistent or not measured. Therefore, developing an accurate and consistent set of Hammett's values is paramount. In this work,we employed different types of machine learning (ML) algorithms combined with quantum chemical calculations of atomic charges to predict theoretically new Hammett's constants σ m , σ p , σ m 0 , σ p 0 , σ p + , σ p − , σ R , and σ I for 90 chemical donor or acceptor groups. New σ values (219), including previously unknown 92, are proposed. The substituent groups were bonded to benzene and meta-and para-substituted benzoic acid derivatives. Among the charge methods (Mulliken, Loẅdin, Hirshfeld, and ChelpG), Hirshfeld showed the best agreement for most kinds of σ values. For each type of Hammett constant, linear expressions depending on carbon charges were obtained. The ML approach overall showed very close predictions to the original experimental values, with meta-and para-substituted benzoic acid derivative values showing the most accurate values. A new consistent set of Hammett's constants is presented, as well as simple equations for predicting new values for groups not included in the original set of 90.

Hammett's constants quantify the electron or electron acceptor power of a chemical group bonded to an aromatic ring. Their experimental values have been successfully used in a large variety of applications, but some of them may have inconsistent values or were not measured. For this reason, developing an accurate and consistent set of Hammett's values is paramount. In this work, we employed the machine learning (ML) regression algorithms Decision Tree Regressor, the neural network Multilayer Perceptron Regressor, and Lasso Lars IC in a cross-validation (CV) approach combined with quantum chemical calculations of atomic charges to estimate theoretically the new Hammett's constants for 90 chemical donor or acceptor groups by employing different types of quantum chemical atomic charges of the groups as input properties. New 219 sigma values, including previously unknown ones, are proposed for 90 chemical donor or acceptor groups by employing different types of quantum chemical atomic charges of the groups as input properties. The different substituent groups were bonded to benzene and meta- and para-substituted benzoic acid derivatives. Among the investigated atomic charge methods (Mulliken, Lwdin, Hirshfeld, and ChelpG), Hirshfeld's method showed the best regressions for most of the different kinds of sigma values. For each type of Hammett constant, linear expressions depending only on the atomic charges of the group were obtained. Correlation coefficients as high as 0.945, mean squared errors (MSE) as low as 0.004, and root mean square errors (RMSE) as low 0.062, were found. The ML approach, in most cases, showed very close predictions to the original experimental values, with the values from meta- and para-substituted benzoic acid derivatives showing the most accurate values. A new consistent set of Hammetts constants is presented, as well as simple equations for predicting new values for groups not included in the original set of 90.

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 ()‐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 , , , , , , , and 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 (), the electron affinity (), the HOMO‐LUMO gaps (), and the maximum absorption wavelengths (), the first excited state transition 1S0→ 1S1 energies () (the optical gap), and exciton binding energies. From the optoelectronic properties and employing typical acceptor systems, the power conversion efficiency (), open‐circuit voltage (), and fill factor () 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 constants were obtained, except for the 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 values can produce higher photovoltaic efficiencies. It was also found that electron‐withdrawing groups (EWGs) reduced and 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.

Diketopyrrolopyrrole (DPP) systems have promising applications in different organic electronic devices. In this work, we investigated the effect of 20 distinct substituent groups on the optoelectronic properties of DPP-based derivatives as the donor (D)-material in an organic photovoltaics (OPV) device. For this purpose, we employed Hammett’s theory, which quantifies the electron-donating or -withdrawing properties of a given substituent group. Machine-Learning (ML)-based σ_m, σ_p, σ_m^0, σ_p^0, σ_p^+, σ_p^-, σ_I, and σ_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), ab initio wave function method, including the adiabatic ionization potential (IP_A), the electro affinity (EA_A), the HOMO-LUMO gaps (E_g), the maximum absorption wavelengths (λ_max), the first excited state transition 1S0 1S1 energies (∆E) (the optical gap), and exciton binding energies. From the optoelectronic properties and employing typical acceptor systems, the power conversion efficiency (PCE), open-circuit voltage (V_OC), and fill factor (FF) were predicted for a DPP-based OPV device. These photovoltaic properties were also correlated with the ML-based Hammett’s constants. Overall, good correlations between all properties and the different types of σ constants were obtained, except for the σ_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 σ values can produce higher photovoltaic efficiencies. It was also found that electron-withdrawing groups 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 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 Hammett’s theory on molecular engineering DPP-based molecules and other conjugated molecules for applications on organic optoelectronic devices.