Electron transfer in bis(hydrazines), a critical test for application of the Marcus model

Abstract

Electron transfer in the cations of bis(hydrazines), bridged by six different π-systems (compounds 1-6) is studied using ab initio and density functional theory (DFT) methods. Due to ionization from an antibonding combination of the lone-pair orbitals of the nitrogens in one of the hydrazine units, conjugation is introduced in the N-N bond of that unit. This leads to a shortening of the N-N bond distance and an increase of the planarity around the nitrogens. Due to steric hindrance, this causes an increase of the angle, called ϕ, between the lone-pair orbital on the nitrogen attached to the bridge and the p-orbital on the adjacent bridge carbon for the ionized unit in the charge localized, relaxed state of the molecule. This angle controls the magnitude of the electronic coupling. In the fully delocalized symmetric transition state of the ion, however, this angle is low for both units, due to the fact that the conjugation introduced at the ionized hydrazine unit is now shared between both units. An extended π-system is formed including the orbitals of the hydrazine units and the bridge, which leads to a large electronic coupling. The electronic coupling derived by optical methods, corresponding to the structure of the relaxed, asymmetric cation with a large ϕ for the ionized unit, appears to be much smaller. We believe this is due to an approximate cosine dependence on ϕ of the coupling. The calculations carried out support these conclusions.

Tetraalkylalkene vertical ionization potentials revisited

“…The vIP values for 11-13 provide excellent examples of the fact that deforming from an equilibrium geometry can have different effects upon the neutral form and the vertical cation, and that both oxidation states need to be considered in analyzing vertical ionization potentials. The rather poor absolute performance of B3LYP calculations for calculating the vIP values of these alkenes was not expected, and it suggests that despite their good performance for geometries, 15 DFT calculations may not be the best to use for estimating internal reorganization energies (Marcus's l inner ), which is calculated from the energies of n 0 , n and both oxidation states at the relaxed cation geometry. 16 According to AM1 calculations, pyramidalizing to <180°for 12 (s21/21) is calculated to lower vIP because the vertical cation is less destabilized than the neutral form due to overlap with the 1-carbon bridges improving, whereas pyramidalizing to >180°raises vIP because it destabilizes the vertical cation more than the neutral form owing to overlap with the 1-carbon bridges becoming less favorable, combined with the increase in s-hybridization that occurs for both directions of bend.…”

Organische gemischtvalente Verbindungen: ein Spielplatz für Elektronen und Löcher

“…[143][144][145] Andererseits tendieren Dichtefunktionalmethoden dazu, wegen des Selbstwechselwirkungsfehlers sogar in lokalisierten Klasse-II-Systemen Ladungen zu delokalisieren. [117,133,146] Kürzlich umgingen M. Kaupp et al dieses Problem, indem sie den Anteil an exaktem HF-Austausch in Hybrid-Dichtefunktionalmethoden so anpassten, dass das Grenzverhalten an der Klasse II zu Klasse III bei Bis(triarylamin)-Radikalkationen richtig wiedergegeben wird. [147,272] 2.8.…”

Effect of Group Electronegativity on Electron Transfer in Bis(hydrazine) Radical Cations

“…In the adiabatic representation, Koopmans theorem (KT) 37,46 is extensively used to estimate the electronic coupling in oneelectron approximation. In this model, the electronic coupling is related to the energies of the frontier molecular orbitals (MO) at the transition state (TS) geometry, and it is given by 47À51…”