A theoretical study on one-electron redox potentials of organotrifluoroborate anions

Abstract

In the dual catalytic Suzuki–Miyaura reactions, the cross-coupling of C_sp³-hybridized center organotrifluoroborate salts has been implemented successfully by single-electron transfer (SET), where the redox potentials are important for understanding the reactivities of organotrifluoroborate salts. To this end, the ΔG_gas values of 27 organotrifluoroborate anions were calculated by using different composite high-level ab initio and DFT methods. Among different DFT methods, the M05-2X method gave the highest precision with a smallest RMSE of 1.58 kcal mol⁻¹. Then, the 24 E° values of organotrifluoroborate anions were calculated by using the M05-2X method with two types of solvation models including PCM and SMD. It was found that the M05-2X method with a PCM–UAHF model can provide the most accurate results with the lowest RMSE value of 0.16 V. Therefore, the E° values of C_sp³-hybridized center organotrifluoroborate anions (R–CH₂–BF₃⁻) including R = alkenyl, alkynyl, aryl and heterocyclyl and the C_sp²-hybridized center vinyltrifluoroborate anions were systematically investigated with this theoretical protocol. The results indicated that for the C_sp³-hybridized center organotrifluoroborate anions, the E° values range from 0.36 V to 1.57 V, and the electron-donating groups (EDG) of –N(CH₃)₂, –NHCH₃etc. can significantly lower the E° values of organotrifluoroborate anions, which are favorable for reactions, whereas the electron-withdrawing groups (EWG) of –NO₂, –CN etc. make the organotrifluoroborate anions unfavorable for reactions. For the C_sp²-hybridized center organotrifluoroborate anions, the E° values range from 1.38 V to 2.43 V. In addition, the analysis of the natural bond orbital (NBO), the ground-state effect (GE), the radical-state effect (RE) and the energies of frontier orbitals was performed in order to further disclose the essence of the E° value change patterns. The linear relationships between the E° values with substituent constants σ⁺_p and the natural charges of the corresponding C atoms of radicals, etc. were found in different types of organotrifluoroborate anions.