Theoretical Studies for the Structural Properties and Electron Transfer Reactivity of C₄H₅N/C₄H₅N⁺ Coupling System

Abstract

The geometries and vibrational frequencies of pyrrole, pyrrole cation, and their corresponding encounter complexes have been determined using density functional theory (DFT) and/or ab initio methods with 6-31G* and/or 6-311+G* basis sets. Optimizations indicate that there are three stable complex modes. One mode has the ring−ring parallel contact (face−face) and each N atom in two rings is vertically over the center of another ring (complex 1). In the second mode (complex 2), two rings are also parallel, but they are directly contacted by only one N−C bond in each ring (side-side). The third mode (complex 3) is H−bond mode, in which the N−H of one pyrrole ring is nearly collinearly directed to the N center of another pyrrole ring and two rings are perpendicular to each other. For three-encounter complexes, their main bond lengths are between those of the pyrrole and those of the pyrrole cation. The character contact distances are 2.754 Å (C3···C13), 2.727 Å (C3···C12), and 2.632 Å (N1···H16) at the B3P86/6-31G* level, respectively. The stabilization energies of the three encounter complexes are calculated to be 21.4 (complex 1), 20.2 (complex 2), and 15.9 (complex 3) kcal/mol at the B3LYP-DFT/6-311+G* level with the correction for BSSE. The inapplicability of DFT methods has been discussed in predicting the energy curves, especially with long contact distance in which the DFT methods give the abnormal behavior for the dissociation of the complexes due to the “inverse symmetry breaking” problem. On the basis of three stable encounter complexes, three coupling modes have been designed by keeping the relative orientation and changing the contact distance for further investigating electron-transfer reactivity. The contact distance dependences of the activation energy, the coupling matrix element, and the electron-transfer rate have also been determined at the MP2/6-31G* level. Electron transfer can occur over a range of encounter distance. For the C4H5N/C4H5N+ coupling system, electron transfer occurs chiefly over a range of contact distances where 2.0Ra-b <6.0 Å. The most favorable coupling mode to electron transfer is the coupling mode 3, which is related to complex 3. It should be noted that it is not always true that the electron transfer must take place via the most stable encounter complex mechanism. For the C4H5N/C4H5N+ systems, the most stable encounter complex is complex 1, but the most favorable coupling mode for the electron transfer is coupling mode 3, depending on the different contact distance ranges