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Mixed-valent compounds

general structure of mixed-valence (MV) systems
Bottom left: General structure of mixed-valence (MV) systems, containing two redox centers which are coupled via a ?-conjugated bridge. Unten Mitte: Model of the Oxygen-Evolving Complex including the four Manganese atoms (aquamarine). Middle: Spin density
Lupe

In many areas of chemistry, for example in bioinorganic chemistry or molecular electronic devices, but also in other fields like physics, nano technology, homogenous or heterogenous catalysis, electron transfer (ET) reactions play a decisive role. These processes depend on a variety of factors, like the distance between the redox centers, the molecular conformation etc., and as a consequence have proven to be hard to study by direct measurement. Artificially designed mixed-valence (MV) compounds offer a way to examine and understand the key processes of ET under known conditions and are hence used as model systems. Moreover, MV compounds have been suggested to actually be applicable in molecular-based electronics technology, for example as molecular wires and switches. A recently developed field of research are "quantum-dot cellular automata" (QCA) based on MV systems, which among other things are hoped to offer a new way for coding information in quantum computers.

A MV system contains usually two or more redox centers in different oxidation states. Typical MV model systems are made from two redox centers linked by a bridge, which enables control of the charge transfer. The redox centers are either inorganic coordination complexes or organic compounds e.g. triarylamines.

An accurate quantum-chemical characterization of  mixed-valence systems proved difficult, as pure Hartree-Fock (HF) calculations strongly tend to give a localization of charge density at one redox center. On the other hand density functional theory (DFT) with standard functionals overestimates delocalization due to unphysical self-interaction of the unpaired electron. An accurate description can be achieved by using modern ab initio post-Hartree-Fock methods, but the size of MV systems of interest makes such calculations rather involved and expensive. Semiempirical CI approaches lead to a more realistic charge distribution, but their predictive power is limited.

By a judicious construction of non-standard hybrid functionals combined with a treatment of solvent effects, we have been able to set up a computational protocol that describes organic MV systems near the localized/delocalized borderline much better than hitherto possible. With about 35% HF exchange, the character of the ground-state structures, ET barriers or dipole moments may be bracketed accurately, and intervalence charge-transfer (IVCT) bands are also reproduced in good agreement with experimental data [1]. While initial validation studies concentrated on four bis-triaryl amine radical cations, the protocl has meanwhile been extended to a much larger number of systems [2]. Current studies indicate also good applicability to, e.g., radical anions. Extension to mixed-valent transition metal complexes is one of the goals of our present work.

The class of mixed-valent compounds includes also also bioinorganic systems like the oxygen-evolving complex of Photosystem II. Quantum chemical investigations, especially the calculation of EPR parameters, can provide important contributions to structure elucidation.[3-5]

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References:

[1] A  reliable quantum-chemical protocol for the characterization of organic mixed-valence compounds M. Renz, K. Theilacker, C. Lambert, M. Kaupp, J. Am. Chem. Soc. 2009, 131,16292.

[2] Computational and Spectroscopic Studies of Organic Mixed-Valence Compounds: Where is the Charge?M. Kaupp, M. Renz, M. Parthey, C. Lambert, M. Stolte, F. Würthner Phys. Chem. Chem. Phys. 2011, 13, 16973-16986.

[3] Validation of Broken-Symmetry Density Functional Methods for the Calculation of Electron Paramagnetic Resonance Parameters of Dinuclear Mixed-Valence MnIVMnIII Complexes S. Schinzel, M. Kaupp Can. J. Chem. 2009, 87, 1521-1539.

[4] Density Functional Calculations of  55Mn, 14N and 13C Electron Paramagnetic Resonance Parameters Support an Energetically Feasible Model System for the S2 State of the Oxygen-Evolving Complex of Photosystem II S. Schinzel, J. Schraut, A. V. Arbuznikov, P. E. M. Siegbahn, M. Kaupp Chem. Eur. J., 2010, 16, 10424.

[5] Computation of Hyperfine Tensors for Dinuclear MnIIIMnIV Complexes by Broken-Symmetry Approaches: Anisotropy Transfer Induced by Local Zero-Field Splitting J. Schraut, A. V. Arbuznikov, S. Schinzel, M. Kaupp ChemPhysChem 2011, 12, 3170-3179.

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Prof. Dr. M. Kaupp
Theoretical Chemistry
Quantum Chemistry
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