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The one-sided Möbius strip with its characteristic 180° twist in the loop has inspired philosophers, artists and scientists since hundreds of years and continues to do so. On the molecular level, only in the last 15 years have some groups succeeded in synthesizing new expanded porphyrin compounds large enough to adopt Möbius-strip topology and Möbius aromaticity, the first being Lechosław Latos-Grażyński and collaborators in Wroclaw (2007) and Atsuhiro Osuka and collaborators in Kyoto (2008). We report on new studies of expanded porphyrins with either Möbius topology or Hückel topology that were synthesized in these laboratories. In this minireview, we focus on recent continuous-wave and time-resolved EPR, ENDOR and DFT MO studies on open-shell states of di-p-benzi[28]hexaphyrin(1.1.1.1.1.1), specifically, on the ground-state radical cation doublet state (total electron spin S = 1/2) and the first excited triplet state (S = 1). The review is largely based on the results and discussions of two previous publications: Möbius et al. (Appl Magn Reson 47:757–780, 2016) and Ema et al. (J Phys Chem Lett 9:2685–2690, 2018). In the open-shell systems, besides the electron-nuclear hyperfine couplings also the zero-field interaction tensor turned out to be a viable sensor for electronic structure changes between Möbius and Hückel topologies. In the Outlook section, we address the cyclotides, a new class of natural circular mini-proteins, usually less than 100 amino acids long. They are distinguished by exceptional chemical and biological stability. This is due to topological constraints imposed by threefoil knot and Möbius-strip formation. As a result, their physical qualities are “topologically protected”. This makes them highly interesting for medical or agricultural applications, for example as novel active ingredients against autoimmune diseases, viral infections, or as agents against insect damage to crops.

The hydrogen bond plays a key role in weak directional intermolecular interactions. It is operative in determining molecular conformation and aggregation, and controls the function of many chemical systems, ranging from inorganic, organic to biological molecules. Although an enormous amount of spectroscopic information has been collected about hydrogen-bond formation between molecules with closed-shell electronic configuration, the details of such interactions between open-shell radicals and closed-shell molecules are still rare. Here we report on an investigation of hydrogen-bonded complexes between pyrroline-type as well as piperidine-type neutral nitroxide radicals and an alcohol, i.e., 2-propanol. These nitroxide radicals are commonly used as EPR spin labels and probes. To obtain information on the geometry of the complexes and their electronic structure, multi-resonance EPR techniques at various microwave frequencies (X-, Q-, W-band, 244 GHz) have been employed in conjunction with DFT calculations. The planar five-membered ring system of the pyrroline-type nitroxide radical was found to form exclusively well-defined in-plane σ-type hydrogen-bonded complexes with one 2-propanol molecule in the first solvation shell in frozen solution. The measured hyperfine parameters of the hydrogen-bridge proton and the internal magnetic parameters describing the electron Zeeman and the electron-nuclear hyperfine and nuclear quadrupole interactions are in good agreement with values predicted by state-of-the-art DFT calculations. In contrast, multi-resonance EPR on the non-planar six-membered ring system of the piperidine-type nitroxide radical (TEMPOL) reveals a more complex situation, i.e., a mixture of a σ-type with, presumably, an out-of-plane π-type complex, both present in comparable fraction in frozen solution. For TEMPOL, the DFT calculations failed to predict magnetic interaction parameters that are in good agreement with experiment, apparently due to the considerable flexibility of the nitroxide and hydrogen-bonded complex. The detailed information about nitroxide/solvent complexes is of particular importance for Dynamic Nuclear Polarization (DNP) and site-directed spin-labeling EPR studies that employ nitroxides as polarizing agents or spin labels, respectively., Applied magnetic resonance;Vol. 53. 2022, pages 1239–1263

The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite&rsquo, s orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity.

The one-sided Mobius band topology with its characteristic 180° twist has fascinated and inspired philosophers, artists and scientists since a long time. On the molecular level, only in the last 13 years a few chemistry groups succeeded to artificially create novel compounds with Mobius symmetry by theory-based molecular design and elaborate chemical synthesis. The interest in molecules with Mobius band symmetry was greatly stimulated in 1964 by a theoretical paper by Edgar Heilbronner from the ETH Zurich. He predicted that sufficiently large [n]annulenes with a closed-shell electron configuration of 4n π-electrons should allow for sufficient π-overlap stabilization to be synthesizable by twisting them into the Mobius topology of their hydrocarbon skeleton. In 2003, the first synthesis of an aromatic Mobius annulene was accomplished by Rainer Herges and co-workers in Kiel. In 2007, Lechoslaw Latos-Grazynski and co-workers in Wroclaw succeeded in synthesizing free-base di-p-benzi (Yoneda et al., Angew Chem Int Ed 53: 13169–13173, 2014) hexaphyrin (1.1.1.1.1.1), compound 1, an expanded porphyrin which can dynamically switch between Huckel and Mobius conjugation upon changes of solvent and temperature. Shortly thereafter, in 2008, Atsuhiro Osuka and his co-workers from Kyoto, Seoul and Hyogo published the synthesis of an expanded porphyrin in which metalation triggered the production of molecular twisting and Mobius aromaticity. In this minireview, among other studies also our recent EPR, ENDOR and DFT studies on open-shell states of 1, i.e., on the ground-state radical cation doublet state (total electron spin S = 1/2) and the first excited triplet state (S = 1) are summarized. The review is largely based on a previous joint publication of the current authors with the Latos-Grazynski group on radical cations of 1 (Mobius et al., Phys Chem Chem Phys 17:6644–6652, 2015). The radical cation study was the first one of an open-shell π-system with Mobius topology. In the doublet state, the hyperfine interactions of the unpaired electron spin with specific magnetic nuclei in the molecule was used as a sensitive probe for the electronic structure of the molecule and its symmetry properties. This work has now been extended to state-of-the-art DFT theory studies on photo-excited triplet states of 1. In the open-shell triplet state, besides hyperfine couplings, a change of the zero-field splitting interaction between the two unpaired electron spins is predicted to be a viable sensor for electronic structure changes upon Mobius-to-Huckel topology switching.

The primary electron donor (P) in the photosynthetic bacterial reaction center of Rhodobacter sphaeroides and Blastochloris viridis consists of a dimer of bacteriochlorophyll a and b cofactors, respectively. Its photoexcited triplet state in frozen solution has been investigated by time resolved ENDOR spectroscopy at 34 GHz. The observed ENDOR spectra for 3P865 and 3P960 are essentially the same, indicating very similar spin density distributions. Exceptions are the ethylidene groups unique to the bacteriochlorophyll b dimer in 3P960. Strikingly, the observed hyperfine coupling constants of the ethylidene groups are larger than in the monomer, which speaks for an asymmetrically delocalized wave function over both monomer halves in the dimer. The latter observation corroborates previous findings of the spin density in the radical cation states P 865 •+ (Lendzian et al. in Biochim Biophys Acta 1183:139–160, 1993) and P 960 •+ (Lendzian et al. in Chem Phys Lett 148:377–385, 1988). As compared to the bacteriochlorophyll monomer, the hyperfine coupling constants of the methyl groups 21 and 121 are reduced by at least a factor of two, and quantitative analysis of these couplings gives rise to a ratio of approximately 3:1 for the spin density on the halves PL:PM. Our findings are discussed in light of the large difference in photosynthetic activity of the two branches of cofactors present in the bacterial reaction center proteins.

We report on recent 95 and 360 GHz high-field electron paramagnetic resonance (EPR), electron-nuclear double resonance (ENDOR) and pulsed electron-electron double resonance (PELDOR) studies of wild-type and mutant reaction centers (RCs) from the photosynthetic bacteriumRhodobacter sphaeroides. Taking advantage of the excellent spectral and temporal resolution of EPR at 95 and 360 GHz, the electron-transfer (ET) cofactors radical ions and spin-correlated radical pairs were characterized by theirg- and hyperfine-tensor components, their anisotropicT2 relaxation as well as by the dipolar interaction between P865•+QA•− radical pairs. The goal of these studies is to better understand the dominant factors determining the specificity and directionality of transmembrane ET processes in photosynthetic RC proteins. In particular, our multifrequency experiments elucidate the subtle cofactor-protein interactions, which are essential for fine-tuning the ET characteristics, e.g., the unidirectionality of the light-induced ET pathways along the A branch of the RC protein. By our high-field techniques, frozen-solution RCs of novel site-specific single and double mutants ofR. sphaeroides were studied to modulate the ET characteristics, e.g., even to the extent that dominant B branch ET prevails. The presented multifrequency EPR work culminates in first 360 GHz ENDOR results from organic nitroxide radicals as well as in first 95 GHz high-field PELDOR results from orientationally selected spin-polarized radical pairs P865•+QA•−, which allow to determine the full geometrical structure of the pairs even in frozen-solution RCs.

The X-ray structure analysis of photosystem (PS) I single crystals showed that the primary electron donor P700 is a heterodimer formed by one chlorophyll (Chl) a and one Chl a′ [Nature 411 (2001) 909]. The electronic structure of the cation radical P700+ of the primary donor, which is created in the charge separation process, has been probed by semiempirical molecular orbital calculations including spin polarization effects (RHF-INDO/SP). The calculations, which were based on the X-ray structure, clearly show that P700 is a supermolecule formed by two chlorophyll species. They furthermore predict an asymmetrical charge and spin density distribution in favor of the monomeric Chl a half of this dimer in accordance with results from earlier EPR and ENDOR studies [J. Phys. Chem. B 105 (2000) 1225]. The stepwise inclusion of various electrostatic interactions of the dimer with its nearest surrounding (one threonine forming a hydrogen bond to the keto group of Chl a′ and two histidines liganding the Mg atoms of the two chlorophylls) leads to a systematic enhancement of this electronic asymmetry yielding a spin density ratio of almost 5:1 as also found experimentally. A large part of this value is caused by spin polarization effects. This result is only weakly affected by the electrostatic field of more remote amino acid residues and other pigment molecules (‘accessory’ Chl a molecules) present in PS I. A separate group of calculations involving local geometry optimizations by energy minimization techniques yields a further enhancement of the spin density asymmetry. A particularly strong effect is obtained by allowing for variations of the geometry of the vinyl groups on both chlorophylls of the P700 dimer. Theoretical results for individual isotropic proton and nitrogen hyperfine coupling constants, showing a satisfactory agreement with experimental findings, are also presented.

The frozen solution electron paramagnetic resonance spectrum of the primary donor cation P + in reaction centers of site-directed mutants of Rhodobacter ( Rb. ) sphaeroides has been obtained at a microwave frequency ν =360 GHz and a magnetic field B 0 =12.8 T. Due to the high Zeeman resolution of the powder pattern, all three principal components of the rhombic g -tensors at T =160 K could be determined with high accuracy. We compare spectra of the site-directed mutants, in which the axial ligand histidine M202 of the primary donor is replaced by glutamic acid (HE(M202)) or leucine (HL(M202)), with those of the strain R26, whose primary donor is similar to that of the wild type and only lacks the carotenoid. For HE(M202), this is the first determination of its g -tensor with the principal components g xx =2.00335(3), g yy =2.00236(2) and g zz =2.00191(2). While in R26 the primary donor is a bacteriochlorophyll a dimer, the HL(M202) and HE(M202) mutants have previously been shown to be bacteriochlorophyll:bacteriopheophytin heterodimers. Their g -tensor anisotropy Δ g = g xx − g zz shows significant variations in opposite directions when compared with R26, with an increased anisotropy for HE(M202) and a decreased one for HL(M202). Calculations employing Density Functional Theory suggest that the observed shifts originate in different torsional angles of the acetyl group attached to the spin-carrying bacteriochlorophyll half L of the dimer.

The symmetry of the arrangement of objects has fascinated philosophers, artists and scientists for a long time, and still does. Symmetries often exist in nature, but are also created artificially, for instance by chemical synthesis of novel molecules and materials. The one-sided, non-orientable Möbius band topology is a paradigm of such a symmetry-based fascination. In the early 1960s, in synthetic organic chemistry the interest in molecules with Möbius symmetry was greatly stimulated by a short paper by Edgar Heilbronner. He predicted that sufficiently large [n]annulenes with a closed-shell electron configuration of 4n π-electrons should allow for sufficient π-overlap stabilization to be synthesizable by twisting them with a 180° phase change into the Möbius symmetry of their hydrocarbon skeleton. In 2007, the group of Lechosław Latos-Grażyński succeeded in synthesizing the compound di-p-benzi[28 ]hexa-phyrin(1.1.1.1.1.1), compound 1, which can dynamically switch between Hückel and Möbius conjugation depending, in a complex manner, on the polarity and temperature of the surrounding solvent. This discovery of “topology switching” between the two-sided (Hückel) and one-sided (Möbius) molecular state with closed-shell electronic configuration was based primarily on the results of NMR spectroscopy and DFT calculations. The present EPR and ENDOR work on the radical cation state of compound 1 is the first study of a ground- state open-shell system which exhibits a Hückel–Möbius topology switch that is controlled by temperature, like in the case of the closed-shell precursor. The unpaired electron interacting with magnetic nuclei in the molecule is used as a sensitive probe for the electronic structure and its symmetry properties. For a Hückel conformer with its higher symmetry, we expect – and observe – fewer ENDOR lines than for a Möbius conformer. The ENDOR results are supplemented by and in accordance with theoretical calculations based on density functional theory at the ORCA level.

Semiempirical molecular orbital methods (PM3, INDO, ZINDO/S) have been used to calculate the effects of local electric fields and of hydrogen bonding on the g and hyperfine tensors of a nitroxide spin label model system. The results yield a linear correlation between the two principal tensor components g xx and A N zz at label sites of varying polarity. Hydrogen bonding with a single water molecule produces a constant shift of Δg xx ≅ −4 × 10−4. These theoretical results are used to interpret recent high field (3.4 T, 95 GHz) electron paramagnetic resonance investigations on site-directed spin labelled bacteriorhodopsin. This protein reveals a close correlation between proticity and polarity at the various label sites. The slope of the g xx versus A N zz dependence is affected strongly by polarity induced structural strains of the spin label.

Bacteriopurpurin is a macrocyclic compound at the saturation level of bacteriochlorins that was specifically synthesized as a potential photosensitizer in photodynamic therapy. It exhibits a long-wavelength Qy absorption band at 843 nm, which is a necessary prerequisite for a deep tissue penetration. Magnetic resonance spectroscopic properties of bacteriopurpurin have been examined by fluorescence-detected magnetic resonance (FDMR) and electron paramagnetic resonance (EPR) in conjunction with molecular orbital calculations. The electronic structure of the radical cation state obtained by oxidation of bacteriopurpurin with iodine is mapped by the determination of isotropic proton hyperfine coupling constants from electron−nuclear double-resonance spectroscopy at 298 K. A tentative assignment of the couplings to the various proton positions in the molecule is achieved by comparison of the experimental values with simulated ones based on semiempirical intermediate neglect of differential overlap calculations...

The conversion of solar light by the reaction center (RC) of purple bacteria proceeds through a construct of two identical pigment branches and a ferrous ion. The imperfect C 2 symmetry of the two branches has been a major issue in trying to understand the preference of only one branch for the energy migration process. In view of the significance of this imperfection, it is desirable to express this structural property on a quantitative scale. For this purpose we have applied on six different RC structures the continuous symmetry measure methodology, an approach which allows one to measure the degree of any symmetry group in any structure. For each structure, the C 2 content of the whole RC was calculated, as well as of the top special pair where it is believed that the initial charge separation occurs. Full analysis for all pairs was carried out for one of the RCs. It was found that the top pair of cofactors is the most symmetric and that the second pair is of the highest deviation.

The “Contracted Porphyrins” corrole and the recently synthesized isocorrole (as octaethyl derivatives) represent novel porphyrinoid macrocycles of biochemical interest. The radical cations of the free-bases of both corrole and its isomer are studied by EPR, ENDOR, and TRIPLE resonance in liquid solution to measure isotropic hyperfine couplings including signs. They yield detailed information of the electronic structure of the radical cations. The experimental findings are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/SP). The comparison shows that the free-bases of corrole and isocorrole undergo protonation when oxidized to cation radicals in CH2Cl2 solution. Excellent agreement of the measured and calculated spin density distributions is achieved for the protonated dication radicals, which exhibit the C2 symmetry observed for the hyperfine structure. The analysis of the hyperfine data discriminates against NH tautomerism as the sole source for an effective C2 symmetry of the macrocycle.

The bacteriochlorophyll (BGhl)a cation radical is studied by cw-EPR and multinuclear ENDOR/TRIPLE resonance techniques in liquid solution yielding the hyperfine coupling constants (hfcs) for 12 protons, all 4 nitrogens and the central magnesium nucleus. The H hfcs are assigned to specific molecular positions by various experimental techniques including isotope substitution, H/D exchange experiments and comparison with bacteriochlorophyll derivatives. The determined temperature dependences of the H hfcs are measured and related to dynamical properties of the molecule in solution. The experimental hfcs compare well with those obtained from semiempirical molecular orbital calculations of the RHF-INDO/SP type. The importance of these results for BChl speciesin vivo, i.e., in the protein matrix, is discussed.

The results of calculations of doublet state G tensors of organic radicals often show unsatisfactory agreement with the respective experimental data. This led us to reconsider the results of the Rayleigh–Schrodinger perturbation theory approach found in the literature. We came to the conclusion that neither the expressions given for restricted nor for unrestricted Hartree–Fock functions are fully correct. In this paper new expressions for the G tensor to be used with restricted Hartree–Fock functions will be introduced and results of calculations employing these new formulas in conjunction with molecular states from semiempirical Hartree–Fock-type calculations are discussed.

We present a model by which the efficiency of T 0 -S and T −1 -S mixing in a polyphyrin-quinone radical pair can be calculated. Rotational diffusion of the quinone relative to the porphyrin, causing a stochastic modulation of the exchange integral J , is included and contributes to the efficiency of triplet-singlet mixing. The model calculations can reproduce the mixing efficiencies extracted from time-resolved X-band EPR measurements.

Recent improvements of a 3 mm high-field/high-frequency CW EPR/ENDOR spectrometer [O. Burghaus, M. Rohrer, T. Gotzinger, M. Plate, and K. Mobius, Meas. Sci. Technol.3, 765 (1992)] are presented, making it possible for ENDOR measurements to be performed with NMR radiofrequeney fields of more than 2.5 mT (rotating frame) over a frequency range of 40 MHz. Applications of this setup to plastosemiquinone anion radicals are described which serve as a model for the secondary electron acceptor in plant photosystem II. The orientation-selected high-field ENDOR spectra of the plastoquinone anion radicals, recorded at different EPR field positions, are analyzed with the aid of computer simulations. The determination of hyperfine interactions of the radical in a perdeuterated solvent is described. The experiments demonstrate the potential of high-field/high-frequency EPR/ENDOR in structure determination including anisotropic interactions with the environment.

Semiempirical molecular orbital calculations of the electronic g-tensor have been performed on the primary donor cation radical P865+· of Rb. sphaeroides R-26 reaction centers (RCs). These calculations are based on Stone's theory for free radical doublet states and RHF-INDO wave functions and orbital energies. The result is in qualitative agreement with recent W-band (95 GHz) EPR measurements of the g-tensor in RC single crystals which show a breaking of C2 symmetry in the primary donor electronic structure.

The radical cations of two synthetic carotenoids, 7′-7′-dicyano-7′-apo-β-carotene (I) and 7′-phenyl-7′-apo-β-carotene (II), have been prepared by UV irradiation of samples adsorbed on silica gel. The methyl proton hyperfine coupling constants were deduced from ENDOR powder spectra and assigned by RHF-INDO/SP calculations. The powder EPR spectra of the carotenoid radical cations formed photolytically by electron transfer are unresolved, with a peak-to-peak linewidth of 15 ± 1 G, irrespective of the donor or acceptor character of the terminal substituents.

Cation radicals of the primary electron donor (D + ) in bacterial photosynthesis were investigated by high field, high frequency (95 GHz) EPR. Measurements on frozen solutions of D + , a dimeric π-cation radical, of various organisms ( Rps. viridis, Rb. sphaeroides, Chloroflexus aurantiacus and a heterodimer mutant) are reported, revealing differences in the principal values of the G -tensor. Elements of a theory relating the magnitudes of G principal values to the electronic structure are discussed.

Liquid solution ENDOR and TRIPLE resonance experiments have been performed on texaphyrin radical anions generated by sodium reduction in tetrahydrofuran. Six proton and two nitrogen hyperfine couplings could be determined, including their signs. The results were compared with theoretical isotropic hyperfine couplings. They were calculated for energy-minimized texaphyrin structures, including the sodium metallo-derivative, by state-of-the-art SCF-MO methods (RHF-INDO/SP). This comparison suggests that in the course of the alkali metal reduction of texaphyrin the acidic hydrogen in the macrocycle is replaced by sodium.

The electron spin density distribution of the cation radical of the primary donor, D+, a bacteriochlorophyll a dimer was determined by ENDOR and TRIPLE resonance experiments performed on single crystals of reaction centers (RCs) of Rhodobacter sphaeroides R-26. Nine isotropic proton hyperfine coupling constants (hfc's) were obtained and from the angular dependence of the hfc's in three crystallographic planes, five complete hyperfine (hf) tensors were determined. Theoretical hf tensors were calculated by the all-valence-electron SCF molecular orbital method RHF-INDO/SP using the X-ray structure data of the dimer D and its amino acid environment. A comparison of the directions of the principal axes of the experimental and calculated hf tensors enabled us to identify the hfc's with specific protons on the two bacteriochlorophyll halves DL and DM of the dimer. The result shows that the unpaired valence electron is unequally distributed over the dimer halves, favoring DL by approx. 2:1. This ratio has been obtained from the proton hfc's of rotating methyl groups, which directly reflect the π-spin densities at the corresponding positions in the two macrocycles, DL and DM. It was further confirmed by recent 15N-ENDOR experiments on RC single crystals (Lendzian, F., Bonigk, B., Plato, M., Mobius, K. and Lubitz, W. (1992) in The Photosynthetic Bacterial Reaction Center II (Breton, J. and Vermeglio, A., eds.), pp. 89–97, Plenum Press, New York). The observed asymmetry of D+ is attributed to the difference in energies of the highest filled molecular π-orbitals of the monomeric halves, DL and DM, which is caused by differences in the structure of the two bacteriochlorophylls and/or their environment. Possible implications of this asymmetry for the electron transfer in the RC are discussed.

W-band EPR (λ ≈ 3 mm, ν ≈ 95 GHz) investigations of frozen solutions of various semiquinone anion radicals in vitro are presented. Among the quinones studied are ubiquinone-10 and the primary electron acceptors of photosystem I and II of plant photosynthesis, vitamin K, and plastoquinone-9, respectively. In addition, W-band spectra of the primary quinone Q and of the radical pair PQ Zn-substituted reaction centers of Rhodobacter sphaeroides R-26 are shown. The electron Zeeman interaction at resonant B fields in the W-band is increased by a factor of 10 as compared with conventional X-band, leading to almost completely resolved g-tensor components in all quinone radicals. By means of computer simulations of the EPR spectra of the immobilized radical ions, anisotropic g tensor components, anisotropic line width contributions, and, in some cases, hyperfine tensor information could be obtained. The data are partially interpreted by semiempirical MO methods including solvent effects. In all quinone radical anions studied, the measured g-tensor components are assigned to the molecular axes as follows: g > g > g, where x is along the C-O bond direction and z is perpendicular to the quinone plane.

We have used time-resolved electron-paramagnetic resonance (EPR) spectroscopy to investigate the triplet energy transfer in various covalently linked porphyrin dimers. For all these dimers the fine structure parameters are rather similar to the monomer values; thus according to the field-swept EPR spectra the triplet state appears to be localized on one monomeric subunit. However, for particular conformations, the time evolution of the EPR spectra reveals dynamic properties specific to a dimer. For these cases the hopping rates of the triplet exciton can be determined from the measured spin-lattice relaxation times. The values obtained for the different dimers can be related to structural parameters of the dimers and to the overlap of their electronic wavefunctions. Such overlap is essential for energy transfer via the exchange mechanism.

The triplet states of several substituted porphyrins (Tetraphenylporphyrin (H2TPP), Zinc-Tetramethylporphyrin (ZnTMP), Octaethylporphyrin (H2OEP) and the Dication of H2TPP (H4TPP2+)) and two covalently linked dimers with H2TPP-subunits in disordered solid solution were studied by EPR and ENDOR at liquid helium temperature. The measurement yields theAzz component of the hyperfine tensors of all α-protons in the reference frame of the zero field splitting tensor. Dipolar and isotropic contributions toAzz are discussed and spin densities derived. The spin densities are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/S). One of the dimers shows indications of triplet energy transfer between the porphyrin subunits. The order of magnitude of the transfer rate is estimated to be 5 · 105 s−1.

Porphycene is a structural isomer of porphyrin. The photoexcited triplet states of porphycene, 2,7,12,17-tetra-n-propylporphycene and 9,10,19,20-tetra-n-propylporphycene in disordered solid solution were studied by EPR and ENDOR. The ENDOR spectra yield the hyperfine tensor elementsA zz for each of the different groups of equivalent protons. The dipolar contribution toA zz is estimated and spin densities are derived from the isotropic contribution. They are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/SP and RHF-INDO/S).

Three millimeter (W band, 95 GHz) EPR meassurements were performed on single crystals of Rb. sphaeroides R-26 reaction centers at room temperature to determine the g tensor of the primary donor cation radical P 865 .+ . Due to the applied high magnetic field (3.4 T), the magnetically inequivalent sites in the unit cell of the crystals could be resolved. Some of the results are corroborated by additional measurements on P 865 .+ in perdeuterated reaction centers from fb. sphaeroides wild type 2.4. 1, which could be crystallized for the first time

Light-induced triplet electron transfer (ET) is observed in two isomeric cyclohexene-bridged porphyrin–quinones (P–Q) in highly viscous ethanol at temperatures between 130 and 150 K. Both the primary porphyrin triplet, TP–Q, and the triplet radical pair, T(P·+–Q·–), identified by their dipolar splittings and polarization patterns, are detected by time-resolved continuous-wave electron paramagnetic resonance (cw-EPR). A theoretical model is presented by which the kinetic traces at the turning points of the powder-type EPR spectrum of T(P·+–Q·–) are simulated. From the fits to the experimental data, values for the ET rate, kET, and the exchange integral, J, are estimated. At 150 K, for example, kET= 0.26 × 106 s–1(±0.02 × 106 s–1) and J=–1370 G (±60 G). The rates obtained for the charge recombination from the singlet radical pair to the ground state indicate that a distribution of J values has to be considered, even for P–Qs with a relatively rigid bridge.

The oxidized primary electron donor P865+ in reaction center single crystals of Rb. sphaeroides wild type 2.4.1 has been investigated by electron-nuclear-nuclear TRIPLE resonance techniques. The measured anisotropic and isotropic hyperfine couplings have been compared with data from the carotenoidless mutant R-26 of the same organism. There is no detectable structural difference of the dimer P865+ in both strains and its orientation in the crystal unit cell axes is the same within ±3°. However, a small shift of spin density towards the L-half of the dimer is observed due to the presence of the carotenoid.

The last decade witnessed a tremendous growth in combined efforts of biologists, chemists and physicists to understand the dominant factors determining the specificity and directionality of transmembrane transfer processes in proteins. A large variety of experimental techniques is being used including X-ray and neutron diffraction, but also time-resolved optical, infrared and magnetic resonance spectroscopy. This is done in conjunction with genetic engineering strategies to construct site-specific mutants for controlled modification of the proteins. As a general perception of these efforts, the substantial influence of weak interactions within the protein and its membrane interfaces is recognized. The weak interactions are subject to subtle changes during the reaction cycle owing to the inherent flexibility of the protein-membrane complex. Specific conformational changes accomplish molecular-switch functions for the transfer process to proceed with optimum efficiency. Characteristic examples of time varying non-bonded interactions are specific H-patterns and/or polarity effects of the microenvironment. The present perception has emerged from the coupling of newly developed spectroscopic techniques – and advanced EPR certainly deserves credit in this respect – with newly developed computational strategies to interpret the experimental data in terms of protein structure and dynamics. By now, the partners of this coupling, particularly high-field EPR spectroscopy and DFT-based quantum theory, have reached a level of sophistication that applications to large biocomplexes are within reach. In this review, a few large paradigm biosystems are surveyed which were explored lately in our laboratory. Taking advantage of the improved spectral and temporal resolution of high-frequency/high-field EPR at 95 GHz/3.4 T and 360 GHz/12.9 T, as compared to conventional X-band EPR (9.5 GHz/0.34 T), three biosystems are characterized with respect to structure and dynamics: (1) Light-induced electron-transfer intermediates in wild-type and mutant reaction-centre proteins from the photosynthetic bacterium Rhodobacter sphaeroides, (2) light-driven proton-transfer intermediates of site-specifically nitroxide spin-labelled mutants of bacteriorhodopsin proteins from Halobacterium salinarium, (3) refolding intermediates of site-specifically nitroxide spin-labelled mutants of the channel-forming protein domain of Colicin A bacterial toxin produced in Escherichia coli. The detailed information obtained is complementary to that of protein crystallography, solid-state NMR, infrared and optical spectroscopy techniques. A unique strength of high-field EPR is particularly noteworthy: it can provide highly desired detailed information on transient intermediates of proteins in biological action. They can be observed and characterized while staying in their working states on biologically relevant time scales. The review introduces the audience to origins and basic experiments of EPR in relation to NMR, describes the underlying strategies for extending conventional EPR to high-field/high-frequency EPR, and highlights those details of molecular information that are obtained from high-field EPR in conjunction with genetic engineering and that are not accessible by “classical” spectroscopy. The importance of quantum-chemical interpretation of the experimental data by DFT and advanced semiempirical molecular-orbital theory is emphasized. A short description of the laboratory-built 95 GHz and 360 GHz EPR/ENDOR spectrometers at FU Berlin is also presented. The review concludes with an outlook to future opportunities and challenges of advanced bio-EPR in interdisciplinary research.

Austin model 1 (AMI) geometry-optimized coordinates were used as input to an INDO and an RHF-INDO/SP molecular orbital calculation. Comparison to ENDOR-derived methyl proton hyperfine coupling of the carotenoid cation radical formed photolytically on Nafion film and the second-moment-deduced EPR linewidth of the electrochemically prepared carotene cation in solution showed excellent agreement with the RHF-INDO/SP-derived proton hyperfine couplings. The INDO-derived solution linewidth was calculated to be 60% larger than that found experimentally due to the calculated INDO methyl protons being larger by 64%.

The EPR g -factor rotation pattern of the primary donor cation radical in the x  y plane of illuminated reaction center single crystals of Rb. sphaeroides R-26 near room temperature was measured at 3 mm wavelength (W-band, 95 GHz). In contrast to earlier X-band (9.5 GHz) EPR experiments, the two magnetically inequivalent sites of the four reaction centers per unit cell were well resolved. in frozen reaction center solution was also measured by 3 mm EPR. The analysis of both the frozen-solution spectrum and the single-crystal rotation pattern yields the principal values of the g -tensor and the phase angle between the two magnetically inequivalent sites in the x  y plane.

From time-resolved direct detection cw EPR with pulsed laser excitation, the photoinduced electron transfer and spin dynamics (CIDEP) in mixed zinc-tetraphenylporphyrin (ZnTPP)/benzo-1,4-quinone (BQ) ethanol solutions were determined as functions of temperature and BQ concentration. At lower temperatures the EPR spectra reveal that mixing of the S and T−1 states in the charge separated radical pair gains in importance relative to the ST0 mixing. Furthermore, at lower temperatures, the EPR spectra of the spin-correlated radical pairs of ZnTPP+ and BQ7 could also be observed. From the temperature/viscosity dependence of the electron transfer rates and of the polarization contributions from the triplet and radical pair mechanisms, deviations from a macroscopic diffusion behaviour are inferred at lower temperatures.

Porphycenes are novel structural isomers of porphyrins. The radical anions of several porphycenes were studied by ESR, ENDOR, and TRIPLE resonance in liquid solution yielding the isotropic hyperfine coupling constants including signs. For the unsubstituted free-base porphycene, the 2,7,12,17-tetra-n-propylporphycene, and the 9,10,19,20-tetra-n-propylporphycene, the experimental findings are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/SP).

The spin density distributions in the cation radicals of various covalently linked tetraphenyl porphyrin dimers and of their monomeric constituents have been studied by liquid-phase EPR, ENDOR and TRIPLE resonance methods to find out whether the dimer systems show intramolecular electron delocalization. Such delocalization is known to occur in the bacteriochlorophyll dimer (‘special pair’) in photosynthetic reaction centres. The dimers studied in this work are derived from zinc meso-tetraphenylporphyrin (ZnTPP) moieties linked either by a phenyl ring at para and meta positions or by a —CH2— bridge at para positions. 1H and 14N hyperfine coupling constants were measured for the dimer and ZnTPP cation radicals. By comparing the hyperfine data it was concluded that in the phenyl-bridged porphyrin dimers the unpaired electron is delocalized over the dimer halves (similar to the ‘special pair’) whereas in the CH2-bridged dimer the unpaired electron is localized on one porphyrin unit.

International audience; In the last decade, joint efforts of biologists, chemists and physicists have helped in understanding the dominant factors determining specificity and directionality of transmembrane transfer processes in proteins. In this endeavor, electron paramagnetic resonance (EPR) spectroscopy has played an important role. Characteristic examples of such determining factors are hydrogen-bonding patterns and polarity effects of the microenvironment of protein sites involved in the transfer process. These factors may undergo characteristic changes during the reaction and, thereby, control the efficiency of biological processes, e.g. light-induced electron and proton transfer across photosynthetic membranes or ion-channel formation of bacterial toxins. In case the transfer process does not involve stable or transient paramagnetic species or states, site-directed spin labeling with suitable nitroxide radicals still allows EPR techniques to be used for studying structure and conformational dynamics of the proteins in action. By combining site-directed spin labeling with high-field/high-frequency EPR, unique information on the proteins is revealed, which is complementary to that of X-ray crystallography, solid-state NMR, FRET, fast infrared and optical spectroscopic techniques. The main object of this publication is twofold: (i) to review our recent spin-label high-field EPR work on the bacteriorhodopsin light-driven proton pump from Halobacterium salinarium and the Colicin A ion-channel forming bacterial toxin produced in Escherichia coli, (ii) to report on novel high-field EPR experiments for probing site-specific pK(a) values in protein systems by means of pH-sensitive nitroxide spin labels. Taking advantage of the improved spectral and temporal resolution of high-field EPR at 95 GHz/3.4 T and 360 GHz/12.9 T, as compared to conventional X-band EPR (9.5 GHz/0.34 T), detailed information on the transient intermediates of the proteins in biological action is obtained. These intermediates can be observed and characterized while staying in their working states on biologically relevant timescales. The paper concludes with an outlook of ongoing high-field EPR experiments on site-specific protein mutants in our laboratories at FU Berlin and Osnabrück.

For an efficient charge separation in quinones coupled covalently with porphyrin, the MO coefficient in the HOMO of the porphyrin at the site of coupling should be as small as possible and the orientation of the quinone to the cyclohexane bridge as orthogonal as possible