Electron transfer pathways in mixed-valence paracyclophane-bridged bis-triarylamine radical cations.

A series of paracyclophane (PC) bridged mixed-valence (MV) bis-triarylamine radical cations with different ([2.2], [3.3], [4.4]) linkers, with and without additional ethynyl spacers, have been studied by quantum-chemical calculations (BLYP35-D3/TZVP/COSMO) of ground-state structures, thermal electron-transfer barriers, hyperfine couplings, and lowest-lying excited states. Such PC-bridged MV systems are important intra-molecular model systems for inter-molecular electron transfer (ET) via π-stacked aromatics, since they allow enforcement of a more or less well-defined geometrical arrangement. Closely comparable ET barriers and electronic couplings for all [2.2] and [3.3] bridges are found for these class-II MV systems, irrespective of the use of pseudo-para and pseudo-meta connections. While the latter observation contradicts notions of quantum interference for off-resonant conduction through molecular wires, it agrees with the less intricate nodal structures of the highest occupied molecular orbitals. The ET in such MV systems may be more closely connected with hole conduction in the resonant regime. Computations on model cations, in which the [2.2] linkers have been truncated, confirm predominant through-space π-π electronic coupling. Systems with [4.4] PC bridges exhibit far more structural flexibility and concomitantly weaker electronic interactions between the redox centers.

Validation of the direct-COSMO-RS solvent model for Diels-Alder reactions in aqueous solution.

The modeling of chemical reactions in protic solvents tends to be far more computationally demanding than in most aprotic solvents, where bulk solvent effects are well described by dielectric continuum solvent models. In the presence of hydrogen bonds from a protic solvent to reactants, transition states or intermediates, a faithful modeling of the solvent effects usually requires some kind of molecular dynamics treatment. In contrast, the COSMO-RS (conductor-like screening model for real solvents) approach has been known for about a decade to describe protic solvent effects much better than continuum solvents, in spite of being an implicit solvent model without explicit molecular dynamics. More recently, the self-consistent use of its potential in electronic-structure methods has led to the Direct-COSMO-RS approach. It allows, for example, structure optimization in the presence of a protic solvent, of solvent mixtures, as well as self-consistent property calculations. In view of recent successful tests for electron transfer in organic mixed-valence systems, in this work the wider applicability of D-COSMO-RS for organic reactivity is evaluated by computation of activation and reaction free energies, as well as transition-state structures of two prototypical Diels-Alder reactions, with an emphasis on aqueous solution. D-COSMO-RS indeed provides substantial improvements over the COSMO continuum model and in judicious testing compares well with embedded supermolecular model cluster treatments, without prior knowledge about the average numbers of hydrogen-bonding interactions present.

Relativistic and Solvation Effects on the Stability of Gold(III) Halides in Aqueous Solution.

The redox stability of gold halide complexes in aqueous solution has been examined quantum-chemically by a systematic comparison of scalar- and nonrelativistic pseudopotential calculations, using both COSMO and D-COSMO-RS solvent models for water. After a computational benchmarking of density-functional methods against CCSD(T) results for the gas phase decomposition AuX4(-) → AuX2(-) + X2, B3LYP calculations have been used to establish solvent contributions. While relativity clearly enhances the stability of AuX4(-) (X = F, Cl, Br, I) complexes against X2 elimination, solvation favors the lower oxidation state. Solvation and relativity are nonadditive, due to the relativistic reduction of bond polarity. At scalar relativistic D-COSMO-RS level, the reaction AuX4(-) ⇌ AuX2(-) + X2 is computed to be endergonic, except for X = I, where it is slightly exergonic. Under the chosen conditions, partial hydrolysis of AuCl4(-) to AuCl3OH(-) is exergonic. The latter complex in turn is stable against Cl2 elimination. The disproportionation 3 AuCl2(-) ⇌ AuCl4(-) + 2 Au(s) + 2 Cl(-) is clearly exergonic. All of the computed reaction energies at scalar relativistic D-COSMO-RS level agree well with the observed speciation in dilute pH-neutral solutions at ambient temperatures.

Controlled ligand distortion and its consequences for structure, symmetry, conformation and spin-state preferences of iron(II) complexes.

The ligand-field strength in metal complexes of polydentate ligands depends critically on how the ligand backbone places the donor atoms in three-dimensional space. Distortions from regular coordination geometries are often observed. In this work, we study the isolated effect of ligand-sphere distortion by means of two structurally related pentadentate ligands of identical donor set, in the solid state (X-ray diffraction, (57)Fe-Mössbauer spectroscopy), in solution (NMR spectroscopy, UV/Vis spectroscopy, conductometry), and with quantum-chemical methods. Crystal structures of hexacoordinate iron(II) and nickel(II) complexes derived from the cyclic ligand L(1) (6-methyl-6-(pyridin-2-yl)-1,4-bis(pyridin-2-ylmethyl)-1,4-diazepane) and its open-chain congener L(2) (N(1),N(3),2-trimethyl-2-(pyridine-2-yl)-N(1),N(3)-bis(pyridine-2-ylmethyl) propane-1,3-diamine) reveal distinctly different donor set distortions reflecting the differences in ligand topology. Distortion from regular octahedral geometry is minor for complexes of ligand L(2), but becomes significant in the complexes of the cyclic ligand L(1), where trans elongation of Fe-N bonds cannot be compensated by the rigid ligand backbone. This provokes trigonal twisting of the ligand field. This distortion causes the metal ion in complexes of L(1) to experience a significantly weaker ligand field than in the complexes of L(2), which are more regular. The reduced ligand-field strength in complexes of L(1) translates into a marked preference for the electronic high-spin state, the emergence of conformational isomers, and massively enhanced lability with respect to ligand exchange and oxidation of the central ion. Accordingly, oxoiron(IV) species derived from L(1) and L(2) differ in their spectroscopic properties and their chemical reactivity.

Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data.

Due to their position-dependent exact exchange admixture, local hybrid functionals offer a higher flexibility and thus the potential for more universal and accurate exchange correlation functionals compared to global hybrids with a constant admixture, as has been demonstrated in previous work. Yet, the local hybrid constructions used so far do not account for the inclusion of dispersion-type interactions. As a first exploratory step toward a more general approach that includes van der Waals-type interactions with local hybrids, the present work has added DFT-D3-type corrections to a number of simple local hybrid functionals. Optimization of only the s(8) and s(r,6) parameters for the S22 set provides good results for weak interaction energies but deteriorates the excellent performance of the local hybrids for G3 atomization energies and for classical reaction barriers. A combined optimization of the two DFT-D3 parameters with one of the two parameters of the spin-polarized local mixing function (LMF) of a local hybrid for a more general optimization set provides simultaneously accurate dispersion energies, improved atomization energies, and accurate reaction barriers, as well as excellent alkane protobranching ratios. For other LMFs, the improvements of such a combined optimization for the S22 energies have been less satisfactory. The most notable advantage of the dispersion-corrected local hybrids over, for example, a B3LYP-D3 approach, is in the much more accurate reaction barriers.

A reliable quantum-chemical protocol for the characterization of organic mixed-valence compounds.

Structures, dipole moments, electron-transfer barriers, and spin density distributions of a series of mixed-valent bistriarylamin radical cations have been studied systematically by hybrid density functional methods with variable exact-exchange admixture combined with a continuum solvent model. The chosen systems differ in their bridging units and are all relatively close, from both sides, to the class II/III borderline of the Robin-Day classification of mixed-valence systems. Solvent effects are found to have a dramatic influence on the localized vs delocalized character of these cations. While gas-phase calculations or computations in a nonpolar solvent place all systems on the delocalized class III side, a more polar solvent like acetonitrile enables observation of symmetry breaking and charge localization with moderate exact-exchange admixtures in a hybrid functional for the systems on the class II side (with diphenylbutadiyne and diphenylethyne bridges). In contrast, the cations with the shortest bridges (phenylene, biphenylene) are characterized as class III. The comparison of computed intervalence charge-transfer excitation frequencies with experiment confirms the system with the diphenylbutadiyne bridge, and probably the system with the diphenylethyne bridge, to be class II, whereas in the dichloromethane solvent employed for spectroscopic measurements, the two other systems are on the class III side. Nonstandard hybrid density functional calculations with 35% Hartree-Fock-like exchange combined with continuum solvent models are suggested as a practical protocol for the quantum-chemical characterization of organic mixed-valence systems. This approach should allow closer examinations and provides a basis for the evaluation of other computational methods.