Ab initio and semi-empirical studies of electron transfer and spectra of binuclear complexes with organic bridges

[Al2O4](-), a Benchmark Gas-Phase Class II Mixed-Valence Radical Anion for the Evaluation of Quantum-Chemical Methods

The radical anion [Al2O4](-) has been identified as a rare example of a small gas-phase mixed-valence system with partially localized, weakly coupled class II character in the Robin/Day classification. It exhibits a low-lying C2v minimum with one terminal oxyl radical ligand and a high-lying D2h minimum at about 70 kJ/mol relative energy with predominantly bridge-localized-hole character. Two identical C2v minima and the D2h minimum are connected by two C2v-symmetrical transition states, which are only ca. 6-10 kJ/mol above the D2h local minimum. The small size of the system and the absence of environmental effects has for the first time enabled the computation of accurate ab initio benchmark energies, at the CCSDT(Q)/CBS level using W3-F12 theory, for a class-II mixed-valence system. These energies have been used to evaluate wave function-based methods [CCSD(T), CCSD, SCS-MP2, MP2, UHF] and density functionals ranging from semilocal (e.g., BLYP, PBE, M06L, M11L, N12) via global hybrids (B3LYP, PBE0, BLYP35, BMK, M06, M062X, M06HF, PW6B95) and range-separated hybrids (CAM-B3LYP, ωB97, ωB97X-D, LC-BLYP, LC-ωPBE, M11, N12SX), the B2PLYP double hybrid, and some local hybrid functionals. Global hybrids with about 35-43% exact-exchange (EXX) admixture (e.g., BLYP35, BMK), several range hybrids (CAM-B3LYP, ωB97X-D, ω-B97), and a local hybrid provide good to excellent agreement with benchmark energetics. In contrast, too low EXX admixture leads to an incorrect delocalized class III picture, while too large EXX overlocalizes and gives too large energy differences. These results provide support for previous method choices for mixed-valence systems in solution and for the treatment of oxyl defect sites in alumosilicates and SiO2. Vibrational gas-phase spectra at various computational levels have been compared directly to experiment and to CCSD(T)/aug-cc-pV(T+d)Z data.

Quantum-chemical insights into mixed-valence systems: within and beyond the Robin–Day scheme

The application of quantum-chemical methods to both organic and transition-metal mixed-valence systems is reviewed, with particular emphasis on how to describe correctly delocalisation vs. localisation near the borderline between Robin–Day classes II and III.

Excited State Intervalence Transfer in a Rigid Polymeric Film

The ligand-bridged complex cis,cis-[(bpy)2ClRu(pz)RuCl(bpy)2]2+ as the PF6- salt, (1)(PF6)2, is stabilized toward photochemical ligand loss in poly(methyl methacrylate) (PMMA). Stabilization allows measurement of metal-to-ligand charge transfer (MLCT) photophysical properties--emission and transient absorption. This includes appearance of an intervalence transfer absorption band in the near IR spectrum of the photochemically prepared, mixed valence form, [(bpy)2ClRuIII(pz(-*))RuIICl(bpy)2](PF6)2* (1*(PF6)2). Comparison of its IT band properties with those of ground state cis,cis-(bpy)2ClRuIII(pz)RuIICl(bpy)2]3+ in CD3CN allows a comparison to be made between pz and pz(-*) as bridging ligands. A model based on differences between rigid and fluid media provides an explanation for decreased IT band energies and widths in PMMA and provides important insight into electron transfer in rigid media.

Localization or Delocalization in the Electronic Structure of Creutz−Taube-Type Complexes in Aqueous Solution

Creutz-Taube complex, [(NH3)5Ru-pyrazine-Ru(NH3)5]5+ (1), and its analogues, [(NH3)5Os-pyrazine-Os(NH3)5]5+ (2), [(NH3)5Ru(4,4'-bipyridine)Ru(NH3)5]5+ (3), and [(NH3)5Os(4,4'-bipyridine)Os(NH3)5]5+ (4), were theoretically investigated by the combination of a two-state model and the dielectric continuum model. Their electronic structures are very sensitive to the metal, ligand, and solvent. In the gas phase, the electronic structures of 1-4 would be completely delocalized. In aqueous solution, that of 3 becomes localized because the polar solvent stabilizes the localized electronic structure with the large dipole moment. However, 1 and 2 are still delocalized in aqueous solution. In 4, the electronic structure would be localized when the dihedral angle between two pyridyl rings is 80 degrees , while it would become delocalized when the angle is small. The origins of the difference are the smaller overlap integral and larger energy difference between two diabatic states, of which electronic structure is almost localized on each metal center.

Optimized Spin Crossings and Transition States for Short-range Electron Transfer in Transition Metal Dimers

Electron-transfer reactions in eight mixed-valence manganese dimers are studied using B3LYP. One of the dimers is a model of the active site of manganese catalase, while another represents a basic building block of the oxygen-evolving complex in photosystem II. The adiabatic reactions are characterized by fully optimized transition states where the single imaginary frequency represents the electron-transfer coordinate. When there is antiferromagnetic coupling between different high-spin centers, electron transfer must be accompanied by a spin transition. Spin transitions are characterized by minimum-energy crossing points between spin surfaces. Three reaction mechanisms have been investigated. First, a single-step reaction where spin flip is concerted with electron transfer. Second, an initial transition to a center with intermediate spin that can be followed by electron transfer. Third, an initial transition to a ferromagnetic state from which the electron can be transferred adiabatically. The complexes prefer the third route with rate-determining barriers ranging from 5.7 kcal/mol to 17.2 kcal/mol for different complexes. The origins of these differences are discussed in terms of oxidation states and ligand environments. Many DFT functionals overestimate charge-transfer interactions, but for the present complexes, the error should be limited because of short Mn-Mn distances.

Ab Initio Based Calculations of Electron-Transfer Rates in Metalloproteins

A long-standing challenge in electron-transfer theory is to compute accurate rates of long-distance reactions in proteins. We describe an ab initio Hartree-Fock approach to compute electronic-coupling interactions and electron-transfer rates in proteins that allows the favorable comparison with experiment. The method includes the following key features; each is essential for reliable rate computations: (1) summing contributions over multiple tunneling pathways, (2) averaging couplings over thermally accessible protein conformations, (3) describing donor and acceptor electronic structure explicitly, including solvation effects, and averaging coupling over multiple energy-level crossings of the nearly degenerate donor-acceptor ligand-field states, and (4) eliminating basis set artifacts associated with diffuse basis functions. The strong dependence of coupling on donor-acceptor distance and on pathway interferences causes large variations of the computed electron-coupling values with protein geometry, and the strongest coupled conformers dominate the electron-transfer rate. As such, averaging over thermally accessible conformers of the protein and of the redox cofactors is essential. This approach was tested on six ruthenium-modified azurin derivatives using the high temperature nonadiabatic rate expression and compared with simpler pathways, average barrier, and semiempirical INDO models. Results of ab initio Hartree-Fock calculations with a split-valence basis set are in good agreement with the experimental rates. Predicted rates in the longer-distance derivatives are underestimated by 3-8-fold. This analysis indicates that the key ingredients needed for quantitatively reliable protein electron-transfer rate calculations are accessible.

Photophysical Properties of Ruthenium(II) Polyazaaromatic Compounds: A Theoretical Insight

Quantum-chemical methods are applied to study the nature of the excited states relevant in the photophysical processes (absorption and emission) of a series of polyazaaromatic-ligand-based ruthenium(II) complexes. The electronic and optical properties of the free polyazaaromatic ligands and their corresponding ruthenium(II) complexes are determined on the basis of correlated Hartree-Fock semiempirical approaches. While the emission of complexes containing small-size ligands, such as 1,10-phenanthroline or 2,2'-bipyridine, arises from a manifold of metal-to-ligand charge-transfer triplet states ((3)MLCTs), an additional ligand-centered triplet state ((3)L) is identified in the triplet manifold of complexes containing a pi-extended ligand such as dipyrido[3,2-a:2',3'-c]phenazine, tetrapyrido[3,2-a:2',3'-c:3'',2''-h:2''',3'''-j]phenazine, and 1,10-phenanthrolino[5,6-b]-1,4,5,8,9,12-hexaazatriphenylene. Recent experimental data are interpreted in light of these theoretical results; namely, the origin for the abnormal solvent- and temperature-dependent emission measured in pi-extended Ru complexes is revisited.

Intervalence Transfer at the Localized-to-Delocalized, Mixed-Valence Transition in Osmium Polypyridyl Complexes

The mixed-valence complexes [(bpy)(2)(Cl)Os(III)(BL)Os(II)(Cl)(bpy)(2)](3+) and [(tpy)(bpy)Os(III)(BL)Os(II)(bpy)(tpy)](5+) (bpy is bipyridine; tpy is 2,2':6',2' '-terpyridine; BL is a bridging ligand, either 4,4'-bipyridine (4,4'-bpy) or pyrazine (pz)) have been prepared and studied by infrared and near-infrared measurements in different solvents. For BL = 4,4'-bpy, there is clear evidence for localized Os(II) and Os(III) oxidation states in the appearance of the expected two interconfigurational dpi --> dpi bands at Os(III) and additional, broad absorption features in the near-infrared arising from intervalence transfer (IT) transitions. For [(bpy)(2)(Cl)Os(pz)Os(Cl)(bpy)(2)](3+) and [(tpy)(bpy)Os(pz)Os(bpy)(tpy)](5+), unusually intense nu(pz) bands appear in the infrared at 1599 cm(-)(1) (epsilon = 2600 M(-)(1) cm(-)(1)) for the former and at 1594 cm(-)(1) (epsilon = 2020 M(-)(1) cm(-)(1)) for the latter. They provide an oxidation state marker and evidence for localized oxidation states. A series of bands appear in the near-infrared from 2500 to 8500 cm(-)(1) that can be assigned to a combination of interconfigurational dpi --> dpi and IT transitions. In CD(3)CN, in the mid-infrared, bands arising from nu(bpy) ring stretching modes from 1400 to 1500 cm(-)(1) are averaged for [(bpy)(2)(Cl)Os(pz)Os(Cl)(bpy)(2)](3+) or significantly perturbed for [(tpy)(bpy)Os(pz)Os(bpy)(tpy)](5+) compared to electronically isolated Os(II) and Os(III) complexes. The pyrazine-bridged complexes have properties that place them in a new class of mixed-valence molecules, Class II-III having properties associated with both Class II and Class III in the Robin and Day classification scheme. The characteristic features of this class are that oxidation states are localized because of vibrational coupling but that solvent orientational motions are uncoupled because of rapid intramolecular electron transfer.