Optical Behaviors and Electronic Properties of Mo₂–Mo₂ Mixed-Valence Complexes within or beyond the Class III Regime: Testing the Limits of the Two-State Model

Abstract

Three symmetric Mo 2 dimers [Mo 2 (DAniF) 3 ](µ-E 2 CCE 2)[Mo 2 (DAniF) 3 ] (DAniF = N, Nʹ-di(p-anisyl)formamidinate) with oxalate (E = O) or the thiolated derivatives (E = O or S) as bridging ligands have been synthesized, and the optical properties of the mixed-valence (MV) derivatives obtained by one-electron oxidation studied within the framework of the vibronic two-state model. These Mo 2 −Mo 2 systems are effective models for testing electron transfer theories, with the δ electrons of the Mo 2 fragments that are responsible for the redox and optical properties of the MV complex being well isolated from other metal d and ligand π-type orbitals. This in turn gives rise to unique, well-resolved metal to ligand (MLCT) and intervalence charge transfer (IVCT) absorption bands that permit accurate analyses based on band-shape. In the series [Mo 2 (DAniF) 3 ](µ-E 2 CCE 2)[Mo 2 (DAniF) 3 ], the extent of electron delocalization between the Mo 2 cores increases with increasing number of sulfur atoms, E, in the bridge. Higher energy IVCT absorption bands are observed for the more strongly coupled complex, but in contrast to the predictions from the two-state model, the IVCT band becomes more symmetric in shape as the electronic coupling constant increases beyond the Class III border and 2H ab /λ >> 1. Thus, the oxalate-bridged complex (E 2 = O 2) is situated on the Class II-III borderline, while the two thiolated 2 species are well placed deep into Class III, where novel optical behavior can be observed. The electronic coupling matrix elements (H DA) estimated from the transition energy E IT (H DA = E IT /2, 2000-2500 cm − 1) are in excellent agreement with data (H ab , 2400-3000 cm − 1) calculated from the modified Mulliken-Hush expression for Class III systems. DFT calculations show that linear combinations of the δ orbitals of the Mo 2 centers generate the HOMO (out-of-phase, δ−δ) and HOMO-1 (in-phase, δ+δ), with the energy difference corresponding to the E IT. This study illustrates a systematic transition from strongly coupled MV complex near the Class II-III border, to Class III and to systems in which the underlying ground state is better described in terms of simple delocalized electronic states rather evolving from strongly coupled diabatic states which define Class III.

Mediation of Electron Transfer by Quadrupolar Interactions: The Constitutional, Electronic, and Energetic Complementarities in Supramolecular Chemistry

“…The molecular structures were determined by single-crystal X-ray diffraction, as shown in Figures 3A–3C; the crystallographic data and selected bond parameters are presented in Tables S1 and S2, respectively. The Mo−Mo bond distances of ∼2.10 Å are in agreement with those of the quadruply bonded Mo 2 cores in similar ligand environments (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017). The Mo−N, Mo−O, and Mo−S bond lengths in these complexes are comparable with those in the thiooxamidate (Cotton et al., 2007) and thiooxalate (Tan et al., 2017) bridged analogues.…”

“…The Mo−Mo bond distances of ∼2.10 Å are in agreement with those of the quadruply bonded Mo 2 cores in similar ligand environments (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017). The Mo−N, Mo−O, and Mo−S bond lengths in these complexes are comparable with those in the thiooxamidate (Cotton et al., 2007) and thiooxalate (Tan et al., 2017) bridged analogues. In [ thi- ( NS) 2 ] and [ thi- ( OS) 2 ], the chelating atoms N(O) and S on the bridging ligands are positioned in cis arrangement with respect to the thienylene bridge (Figures 3A–3C), unlike the phenylene bridged analogues, which have the different chelating atoms of the bridging ligands in trans positions (Xiao et al., 2013, Shu et al., 2014).…”

“…Apparently, the non-co-planarity of this molecule is caused by the steric hindrance of the amidate hydrogen (N- H ). These compounds and the other reported Mo 2 dimers having DAniF auxiliary ligands (Xiao et al., 2013, Shu et al., 2014, Tan et al., 2017) share the same molecular scaffold, which may be described topologically by an architecture with two inverse U-shaped clefts on the top and bottom in the middle of the molecule (Figure 2). The U-shaped clefts are shaped with a width of ∼10 Å and a depth of ∼8 Å, about 1 Å narrower than those for the phenylene analogues (Shu et al., 2014), because of the reduced size of the bridge.…”

Crossover between the Adiabatic and Nonadiabatic Limits of Thermal Electron Transfer: Verifying the Landau-Zener Formula

“…18,22,25 Given the characteristic IVCT bands, mixed-valence D-B-A molecular systems with a quadruply-bonded Mo2 unit 26 as the donor and a Mo2 unit having a bond order 3.5 as the acceptor are desirable experimental models for study of thermal and optical ET, in which single electron migration is ensured and the transferring electron is specified to be one of the d electrons. 27,28,29 Hereby, nine MV complexes of three series with a general formula [Mo2(DAniF)3]2(µ-4,4'- N′-di(p-anisyl)formamidinate, E, E¢ = O or S and n = 1-3), denoted as [EE¢-(ph)n-EE¢] + ( Fig. 1), were investigated as a testbed of the LZ theory.…”

“…where h is an effective one-electron Hamiltonian. 13,29 The energies of the adiabatic states, obtained by solving the two-state secular determinant, are given by eq 5, 24,35 (5a)…”