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A detailed experimental study on reversible photo-induced intramolecular charge separation is presented based on nuclear magnetic resonance detection of chemically induced dynamic nuclear polarization. From variation of such polarization with the external magnetic field, the coupling constants of isotropic and anisotropic hyperfine interactions at individual 13 C sites are measured in the short-lived charge separated state of dyad molecules composed of donor-bridge-acceptor parts. The objects of study were rigid donor-bridge-acceptor dyads, consisting of triarylamine as a donor, naphthalene diimide as an acceptor, and a meta-conjugated diethynylbenzene fragment as a bridge. By systematic variation of side groups in the bridging moiety, their influence on the electron withdrawing strength is traced. In combination with similar data for the 1 H positions obtained previously for the same compounds [I. Zhukov et al., J. Chem. Phys. 152, 014203 (2020)], our results provide a reliable basis for the determination of the spin density distribution in the charge separated state of such dyads.

The development of nuclear spins hyperpolarization, and the search for molecules that can be efficiently hyperpolarized is an active area in nuclear magnetic resonance. In this work we present a detailed study of SABRE SHEATH (signal amplification by reversible exchange in shield enabled alignment transfer to heteronuclei) experiments on 15 N 2 -azobenzene. In SABRE SHEATH experiments the nuclear spins of the target are hyperpolarized through transfer of spin polarization from parahydrogen at ultralow fields during a reversible chemical process. Azobenzene exists in two isomers, trans and cis. We show that all nuclear spins in cis-azobenzene can be efficiently hyperpolarized by SABRE at suitable magnetic fields. Enhancement factors (relative to 9.4 T) reach up to 3000 for 15 N spins and up to 30 for the 1 H spins. We compare two approaches to observe either hyperpolarized magnetization of 15 N/ 1 H spins, or hyperpolarized singlet order of the 15 N spin pair. The results presented here will be useful for further experiments in which hyperpolarized cis- 15 N 2 -azobenzene is switched by light to trans- 15 N 2 -azobenzene for storing the produced hyperpolarization in the long-lived spin state of the 15 N pair of trans- 15 N 2 -azobenzene., (© 2021 The Authors. ChemPhysChem published by Wiley-VCH GmbH.)

Flavin adenine dinucleotide (FAD) is an important cofactor in many light-sensitive enzymes. The role of the adenine moiety of FAD in light-induced electron transfer was obscured, because it involves an adenine radical, which is short-lived with a weak chromophore. However, an intramolecular electron transfer from adenine to flavin was revealed several years ago by Robert Kaptein by using chemically induced dynamic nuclear polarization (CIDNP). The question of whether one or two types of biradicals of FAD in aqueous solution are formed stays unresolved so far. In the present work, we revisited the CIDNP study of FAD using a robust mechanical sample shuttling setup covering a wide magnetic field range with sample illumination by a light-emitting diode. Also, a cost efficient fast field cycling apparatus with high spectral resolution detection up to 16.4 T for nuclear magnetic relaxation dispersion studies was built based on a 700 MHz NMR spectrometer. Site-specific proton relaxation dispersion data for FAD show a strong restriction of the relative motion of its isoalloxazine and adenine rings with coincident correlation times for adenine, flavin, and their ribityl phosphate linker. This finding is consistent with the assumption that the molecular structure of FAD is rigid and compact. The structure with close proximity of the isoalloxazine and purine moieties is favorable for reversible light-induced intramolecular electron transfer from adenine to triplet excited flavin with formation of a transient spin-correlated triplet biradical F ⚫ - -A ⚫ + . Spin-selective recombination of the biradical leads to the formation of CIDNP with a common emissive maximum at 4.0 mT detected for adenine and flavin protons. Careful correction of the CIDNP data for relaxation losses during sample shuttling shows that only a single maximum of CIDNP is formed in the magnetic field range from 0.1 mT to 9 T; thus, only one type of FAD biradical is detectable. Modeling of the CIDNP field dependence provides good agreement with the experimental data for a normal distance distribution between the two radical centers around 0.89 nm and an effective electron exchange interaction of - 2.0 mT., Competing Interests: The authors declare that they have no conflict of interest., (Copyright: © 2021 Ivan V. Zhukov et al.)

A comprehensive description of the spin dynamics underlying the formation of Ortho-Deuterium Induced Polarization (ODIP) is presented. ODIP can serve as a tool for enhancing Nuclear Magnetic Resonance (NMR) signals of 2 H nuclei, being important probes of molecular structure and dynamics. To produce ODIP, in the first step, the D 2 gas is brought to thermal equilibrium at low temperature, here 30 K, so that the ortho-component, corresponding to the total spin of the 2 H nuclei equal to 0 and 2, is enriched, here to 92%. In the second step, the orthodeuterium molecule is attached to a substrate molecule using a suitable hydrogenation catalyst such that the symmetry of the two 2 H nuclei is broken. As a result, the non-thermal spin order of orthodeuterium is converted into enhancement of observable NMR signals. In this work, we perform a theoretical study of ODIP and calculate the shape of ODIP spectra and their dependence on the magnetization flip angle. These results are compared with experiments performed for a number of substrates; good agreement between experimental and calculated ODIP spectra is found. We also discuss the performance of NMR techniques for converting anti-phase ODIP spectral patterns into in-phase patterns, which are more suitable for signal detection and for transferring ODIP to heteronuclei, here to 13 C spins. Experimental procedures reported here allowed us to reach signal enhancement factors of more than 1000 for 2 H nuclei in the liquid phase. These results are useful for extending the scope of spin hyperpolarization to the widely used 2 H nuclei.

Previous transient absorption measurements using the magnetically affected reaction yield (MARY) technique for a series of rigidly linked electron donor/electron acceptor dyads (D-X-A) consisting of a triarylamine donor, a naphthalene diimide acceptor, and a meta-conjugated diethynylbenzene unit as a bridge had revealed the presence of electronic exchange interaction, J, in the photoexcited charge separated (CS) state. Here, we present results obtained by photochemically induced dynamic nuclear polarization (photo-CIDNP) that allows for determining the sign of J. By variation of the magnetic field from 1 mT to 9.4 T, pronounced absorptive maxima of CIDNP were detected for more than 20 1 H nuclei disregarding the sign of their hyperfine coupling constants in the transient charge separated state, with positions of maxima close to those found by the MARY technique. Quantitative comparison of the observed CIDNP signals for various D-X-A dyads reveals an increase in the CIDNP enhancement factor with increasing population of the triplet state determined by MARY spectroscopy at zero magnetic field. For CIDNP of the methyl groups of the TAA donor dyads, we found in all studies a good linear dependence between the CIDNP signal amplitude and the initial population of the CS triplet state. The linear relationship together with the absorptive CIDNP allows us to conclude that (i) the sign of the electronic exchange interaction J ex is positive, (ii) CIDNP is formed predominantly in the vicinity of level anticrossing between the T + and S electronic levels, and (iii) coherent triplet-singlet transitions are induced by hyperfine interaction and accompanied by simultaneous electron and nuclear spin flip, T + β→Sα.

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans- 15 N, 15 N'-azobenzene. The singlet state of the 15 N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the 15 N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of 15 N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization.

The magnetic field dependence of Chemically Induced Dynamic Nuclear Polarization (CIDNP) in solid-state systems is analyzed theoretically with the aim to explain the puzzling sign change of polarization found at low fields [D. Gräsing et al., Sci. Rep. 7, 12111 (2017)]. We exploit the analysis of polarization in terms of level crossings and level anti-crossings trying to identify the positions of features in the CIDNP field dependence with specific crossings between spin energy levels of the radical pair. Theoretical treatment of solid-state CIDNP reveals a strong orientation dependence of polarization due to the spin dynamics conditioned by anisotropic spin interactions. Specifically, different anisotropic CIDNP mechanisms become active at different magnetic fields and different molecular orientations. Consequently, the field dependence and orientation dependence of polarization need to be analyzed together in order to rationalize experimental observations. By considering both magnetic field and orientation dependence of CIDNP, we are able to explain the previously measured CIDNP field dependence in photosynthetic reaction centers and to obtain a good qualitative agreement between the experimental observations and theoretical results.

Signal amplification by reversible exchange (SABRE) is a promising hyperpolarization technique, which makes use of spin-order transfer from parahydrogen (the H 2 molecule in its singlet spin state) to a to-be-polarized substrate in a transient organometallic complex, termed the SABRE complex. In this work, we present an experimental method for measuring the magnetic field dependence of the SABRE effect over an ultrawide field range, namely, from 10 nT to 10 T. This approach gives a way to determine the complete magnetic field dependence of SABRE-derived polarization. Here, we focus on SABRE polarization of spin-1/2 hetero-nuclei, such as 13 C and 15 N and measure their polarization in the entire accessible field range; experimental studies are supported by calculations of polarization. Features of the field dependence of polarization can be attributed to level anticrossings in the spin system of the SABRE complex. Features at magnetic fields of the order of 100 nT-1 μT correspond to "strong coupling" of protons and hetero-nuclei, whereas features found in the mT field range stem from "strong coupling" of the proton system. Our approach gives a way to measuring and analyzing the complete SABRE field dependence, to probing NMR parameters of SABRE complexes and to optimizing the polarization value., (Copyright © 2017 John Wiley & Sons, Ltd.)

An experimental method is described allowing fast field-cycling Nuclear Magnetic Resonance (NMR) experiments over a wide range of magnetic fields from 5 nT to 10 T. The method makes use of a hybrid technique: the high field range is covered by positioning the sample in the inhomogeneous stray field of the NMR spectrometer magnet. For fields below 2 mT a magnetic shield is mounted on top of the spectrometer; inside the shield the magnetic field is controlled by a specially designed coil system. This combination allows us to measure T1-relaxation times and nuclear Overhauser effect parameters over the full range in a routine way. For coupled proton-carbon spin systems relaxation with a common T1 is found at low fields, where the spins are "strongly coupled". In some cases, experiments at ultralow fields provide access to heteronuclear long-lived spin states. Efficient coherent polarization transfer is seen for proton-carbon spin systems at ultralow fields as follows from the observation of quantum oscillations in the polarization evolution. Applications to analysis and the manipulation of heteronuclear spin systems are discussed.

We provide a detailed evaluation of nuclear magnetic resonance (NMR) parameters of the cis - and trans -isomers of azobenzene (AB). For determining the NMR parameters, such as proton-proton and proton-nitrogen J -couplings and chemical shifts, we compared NMR spectra of three different isotopomers of AB: the doubly 15 N labeled azobenzene, 15 N, 15 N'-AB, and two partially deuterated AB isotopomers with a single 15 N atom. For the total lineshape analysis of NMR spectra, we used the recently developed ANATOLIA software package. The determined NMR parameters allowed us to optimize experiments for investigating singlet long-lived spin states (LLSs) of 15 N spin pairs and to measure LLS lifetimes in cis -AB and trans -AB. Magnetization-to-singlet-to-magnetization conversion has been performed using the SLIC and APSOC techniques, providing a degree of conversion up to 17 and 24% of the initial magnetization, respectively. Our approach is useful for optimizing the performance of experiments with singlet LLSs; such LLSs can be exploited for preserving spin hyperpolarization, for probing slow molecular dynamics, slow chemical processes and also slow transport processes.

A consistent theoretical description of the spin dynamics underlying photo-PHIP (para-hydrogen induced polarization) experiments is given and validated experimentally: spectra from zero-quantum coherence (ZQC) "in-phase" and "out-of-phase" were obtained and evolution of ZQCs and the population of singlet spin state was tracked and modeled. Data from recent literature [O. Torres et al., J. Am. Chem. Soc., 2014] are reinterpreted. Advantages of using M2S sequences such as APSOC for detecting photo-PHIP are demonstrated. A sequence for 2D ZQ spectroscopy based on APSOC is proposed and the fundamental principles of ZQ spectroscopy are formulated. This investigation opens a new way to obtain information on the sign of J-couplings using ZQ spectroscopy. The proposed method is also useful to track the redistribution of the singlet spin population in various PHIP related experiments, which is essential for efficient polarization transfer to target nuclei.

Time resolved measurements of Optical Nuclear Polarization (ONP) have been performed on hyperpolarized triplet states in molecular crystals created by light excitation. Transfer of the initial electron polarization to nuclear spins has been studied in the presence of radiofrequency excitation; the experiments have been performed with different pulse sequences using different doped molecular systems. The experimental results clearly demonstrate the dominant role of coherent mechanisms of spin order transfer, which manifest themselves in well pronounced oscillations. These oscillations are of two types, precessions and nutations, having characteristic frequencies, which are the same for the different molecular systems and the pulse sequences applied. Hence, precessions and nutations constitute a general feature of polarization transfer in ONP experiments. In general, coherent manipulation of spin order transfer creates a powerful resource for improving the performance of the ONP method, which paves the way to strong signal enhancement in nuclear magnetic resonance.

We propose a robust and highly efficient NMR technique to create singlet spin order from longitudinal spin magnetization in coupled spin-½ pairs and to perform backward conversion (singlet order)→magnetization. In this method we exploit adiabatic ramping of an RF-field in order to drive transitions between the singlet state and the T ± triplet states of a spin pair under study. We demonstrate that the method works perfectly for both strongly and weakly coupled spin pairs, providing a conversion efficiency between the singlet spin order and magnetization, which is equal to the theoretical maximum. We anticipate that the proposed technique is useful for generating long-lived singlet order, for preserving spin hyperpolarization and for analyzing singlet spin order in nearly equivalent spin pairs in specially designed molecules and in low-field NMR studies., (Copyright © 2016 Elsevier Inc. All rights reserved.)

We describe an NMR method to generate singlet order in spin pairs from longitudinal spin magnetization and suppress residual background signals. This method can also be used for generating and observing long-lived spin states. A singlet order selection (SOS) filter is proposed, which allows us to find signals of the spin pair of interest buried in a crowded NMR spectrum. Likewise, SOS filtering enables proton NMR measurements in H 2 O without pulse sequences for solvent suppression. We demonstrate that the method works perfectly for both weakly and strongly coupled spin pairs. Furthermore, it can be combined with standard NMR pulse sequences: in this way, T 1 - and T 2 -relaxation times for spin pairs of interest can be measured. The power of the SOS-filter is demonstrated by relaxation studies in biomolecules.

Photo-oxidation of seven cyclic dipeptides containing methionine, Met, and/or S-methylcysteine, Cys(Me) by electron transfer from the sulfur atom was studied in aqueous solution by time-resolved and field dependent CIDNP (chemically induced dynamic nuclear polarization). Hyperpolarized high resolution NMR spectral patterns of the starting peptides detected immediately after pulsed laser excitation show signals of all protons that are bound to carbons neighboring the sulfur atom, thus proving the involvement of sulfur-centered cation radicals. The magnetic field dependence of CIDNP shows a pronounced maximum that is determined by the g-factors and hyperfine coupling constants of the transient radical species. From simulation of the experimental data obtained for the magnetic field dependences of CIDNP, three types of radical structures were characterized: (1) a linear sulfur-centered cation radical of the methionine (Met) residue (g = 2.0107 ± 0.0010) for cyclo-(d-Met-l-Met) (trans-configuration), cyclo-(d-Met-l-Cys(Me)) (trans-configuration), and cyclo-(Gly-Met); (2) a cyclic radical (S∴O)(+) (g = 2.0088 ± 0.0010) with a two-center three-electron bond (2c-3e) structure between the sulfur atom of the Cys(Me) residue and the oxygen atom of cyclo-(d-Met-l-Cys(Me)) and cyclo-(Gly-Cys(Me)); (3) a cyclic radical (S∴S)(+) (g = 2.013 ± 0.0020) with a two-center three-electron bond structure between the two sulfur atoms of the peptides cyclo-(l-Met-l-Met), cyclo-(l-Met-l-Cys(Me)), and cyclo-(l-Cys(Me)-l-Cys(Me)). In contrast, no indication of any type of cyclic radicals with a two-center three-electron bond between sulfur and nitrogen atoms was found. In addition, the hyperfine coupling constants (HFCCs) were determined.

Chemically Induced Dynamic Nuclear Polarization (CIDNP) is an efficient method of creating non-equilibrium polarization of nuclear spins by using chemical reactions, which have radical pairs as intermediates. The CIDNP effect originates from (i) electron spin-selective recombination of radical pairs and (ii) the dependence of the inter-system crossing rate in radical pairs on the state of magnetic nuclei. The CIDNP effect can be investigated by using Nuclear Magnetic Resonance (NMR) methods. The gain from CIDNP is then two-fold: it allows one to obtain considerable amplification of NMR signals; in addition, it provides a very useful tool for investigating elusive radicals and radical pairs. While the mechanisms of the CIDNP effect in liquids are well established and understood, detailed analysis of solid-state CIDNP mechanisms still remains challenging; likewise a common theoretical frame for the description of CIDNP in both solids and liquids is missing. Difficulties in understanding the spin dynamics that lead to the CIDNP effect in the solid-state case are caused by the anisotropy of spin interactions, which increase the complexity of spin evolution. In this work, we propose to analyze CIDNP in terms of level crossing phenomena, namely, to attribute features in the CIDNP magnetic field dependence to Level Crossings (LCs) and Level Anti-Crossings (LACs) in a radical pair. This approach allows one to describe liquid-state CIDNP; the same holds for the solid-state case where anisotropic interactions play a significant role in CIDNP formation. In solids, features arise predominantly from LACs, since in most cases anisotropic couplings result in perturbations, which turn LCs into LACs. We have interpreted the CIDNP mechanisms in terms of the LC/LAC concept. This consideration allows one to find analytical expressions for a wide magnetic field range, where several different mechanisms are operative; furthermore, the LAC description gives a way to determine CIDNP sign rules. Thus, LCs/LACs provide a consistent description of CIDNP in both liquids and solids with the prospect of exploiting it for the analysis of short-lived radicals and for optimizing the polarization level.

A device for performing fast magnetic field-cycling NMR experiments is described. A key feature of this setup is that it combines fast switching of the external magnetic field and high-resolution NMR detection. The field-cycling method is based on precise mechanical positioning of the NMR probe with the mounted sample in the inhomogeneous fringe field of the spectrometer magnet. The device enables field variation over several decades (from 100μT up to 7T) within less than 0.3s; progress in NMR probe design provides NMR linewidths of about 10(-3)ppm. The experimental method is very versatile and enables site-specific studies of spin relaxation (NMRD, LLSs) and spin hyperpolarization (DNP, CIDNP, and SABRE) at variable magnetic field and at variable temperature. Experimental examples of such studies are demonstrated; advantages of the experimental method are described and existing challenges in the field are outlined., (Copyright © 2016 Elsevier Inc. All rights reserved.)

A method for precise manipulation of non-thermal nuclear spin polarization by switching a RF-field is presented. The method harnesses adiabatic correlation of spin states in the rotating frame. A detailed theory behind the technique is outlined; examples of two-spin and three-spin systems prepared in a non-equilibrium state by Para-Hydrogen Induced Polarization (PHIP) are considered. We demonstrate that the method is suitable for converting the initial multiplet polarization of spins into net polarization: compensation of positive and negative lines in nuclear magnetic resonance spectra, which is detrimental when the spectral resolution is low, is avoided. Such a conversion is performed for real two-spin and three-spin systems polarized by means of PHIP. Potential applications of the presented technique are discussed for manipulating PHIP and its recent modification termed signal amplification by reversible exchange as well as for preparing and observing long-lived spin states.

We have investigated the magnetic field dependence of Signal Amplification By Reversible Exchange (SABRE) arising from binding of para-hydrogen (p-H2) and a substrate to a suitable transition metal complex. The magnetic field dependence of the amplification of the (1)H Nuclear Magnetic Resonance (NMR) signals of the released substrates and dihydrogen, and the transient transition metal dihydride species shows characteristic patterns, which is explained using the theory presented here. The generation of SABRE is most efficient at low magnetic fields due to coherent spin mixing at nuclear spin Level Anti-Crossings (LACs) in the SABRE complexes. We studied two Ir-complexes and have shown that the presence of a (31)P atom in the SABRE complex doubles the number of LACs and, consequently, the number of peaks in the SABRE field dependence. Interestingly, the polarization of SABRE substrates is always accompanied by the para-to-ortho conversion in dihydride species that results in enhancement of the NMR signal of free (H2) and catalyst-bound H2 (Ir-HH). The field dependences of hyperpolarized H2 and Ir-HH by means of SABRE are studied here, for the first time, in detail. The field dependences depend on the chemical shifts and coupling constants of Ir-HH, in which the polarization transfer takes place. A negative coupling constant of -7Hz between the two chemically equivalent but magnetically inequivalent hydride nuclei is determined, which indicates that Ir-HH is a dihydride with an HH distance larger than 2Å. Finally, the field dependence of SABRE at high fields as found earlier has been investigated and attributed to polarization transfer to the substrate by cross-relaxation. The present study provides further evidence for the key role of LACs in the formation of SABRE-derived polarization. Understanding the spin dynamics behind the SABRE method opens the way to optimizing its performance and overcoming the main limitation of NMR, its notoriously low sensitivity., (Copyright © 2015 Elsevier Inc. All rights reserved.)

A method is proposed to create Long-Lived spin States (LLSs) from longitudinal spin magnetization, which is based on adiabatic switching of a Radio-Frequency (RF) field with proper frequency. The technique is simple to implement with standard Nuclear Magnetic Resonance (NMR) equipment, providing an excellent conversion of population from the triplet T+ (or T-) state to the singlet state of a pair of spins and back. The method has been tested for the amino acid tyrosine and its partially deuterated isotopomer; for the deuterated compound, we have achieved a LLS lifetime, which exceeds the longitudinal relaxation time by a factor of 21. Furthermore, by slightly modifying the method, an enhanced contrast with respect to LLSs in NMR spectra is achieved; contrast enhancements of more than 1200 are feasible. This enables efficient suppression of longitudinal spin magnetization in NMR allowing one to look selectively at LLSs. Using this method we have demonstrated that not only spectral but also spatial contrast can be achieved: we have obtained spatial NMR images with strongly improved contrast originating from the difference of LLS lifetimes at different positions in the sample., (Copyright © 2015 Elsevier Inc. All rights reserved.)

A new technique is developed that allows one to carry out the signal amplification by reversible exchange (SABRE) experiments at high magnetic field. SABRE is a hyperpolarization method, which utilizes transfer of spin order from para-hydrogen to the spins of a substrate in transient iridium complexes. Previously, it has been thought that such a transfer of spin order is only efficient at low magnetic fields, notably, at level anti-crossing (LAC) regions. Here it is demonstrated that LAC conditions can also be fulfilled at high fields under the action of a RF field. The high-field RF-SABRE experiment can be implemented using commercially available nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) machines and does not require technically demanding field-cycling. The achievable NMR enhancements are around 100 for several substrates as compared to their NMR signals at thermal equilibrium conditions at 4.7 T. The frequency dependence of RF-SABRE is comprised of well pronounced peaks and dips, whose position and amplitude are conditioned solely by the magnetic resonance parameters such as chemical shifts and scalar coupling of the spin system involved in the polarization transfer and by the amplitude of the RF field. Thus, the proposed method can serve as a new sensitive tool for probing transient complexes. Simulations of the dependence of magnetization transfer (i.e., NMR signal amplifications) on the frequency and amplitude of the RF field are in good agreement with the developed theoretical approach. Furthermore, the method enables continuous re-hyperpolarization of the SABRE substrate over a long period of time, giving a straightforward way to repetitive NMR experiments.

The magnetic field dependence of Chemically Induced Dynamic Nuclear Polarization (CIDNP) was studied for the amino acids N-acetyl histidine, N-acetyl tryptophan and N-acetyl tyrosine. It is demonstrated that at low field CIDNP is strongly affected by polarization redistribution in the diamagnetic molecules. Such a polarization transfer is of coherent nature and is due to spin coherences formed together with non-equilibrium population of the spin states. These coherences clearly manifest themselves in an oscillatory time dependence of polarization. Polarization transfer effects are most pronounced at nuclear spin Level Anti-Crossings (LACs), which also result in sharp features in the CIDNP field dependence. Thus, polarization transfer is an important factor, which has to be taken into account in order to interpret low-field CIDNP data on both qualitative and quantitative level. Possible applications of polarization transfer phenomena are also discussed in the paper. In particular, the role of LACs in spin order transfer is highlighted: LACs provide a new tool for precise manipulation of spin hyperpolarization and NMR enhancement of selected target spins., (Copyright © 2015 Elsevier Inc. All rights reserved.)

A new technique is proposed to carry out Signal Amplification By Reversible Exchange (SABRE) experiments at high magnetic fields. SABRE is a method, which utilizes spin order transfer from para-hydrogen to the spins of a substrate in transient complexes using suitable catalysts. Such a transfer of spin order is efficient at low magnetic fields, notably, in the Level Anti-Crossing (LAC) regions. Here it is demonstrated that LAC conditions can also be fulfilled at high fields in the rotating reference frame under the action of an RF-field. Spin mixing at LACs allows one to polarize substrates at high fields as well; the achievable NMR enhancements are around 360 for the ortho-protons of partially deuterated pyridine used as a substrate and around 700 for H2 and substrate in the active complex with the catalyst. High-field SABRE effects have also been found for several other molecules containing a nitrogen atom in the aromatic ring.

Nuclear Magnetic Relaxation Dispersion (NMRD) of protons was studied in the pentapeptide Met-enkephalin and the amino acids, which constitute it. Experiments were run by using high-resolution Nuclear Magnetic Resonance (NMR) in combination with fast field-cycling, thus enabling measuring NMRD curves for all individual protons. As in earlier works, Papers I-III, pronounced effects of intramolecular scalar spin-spin interactions, J-couplings, on spin relaxation were found. Notably, at low fields J-couplings tend to equalize the apparent relaxation rates within networks of coupled protons. In Met-enkephalin, in contrast to the free amino acids, there is a sharp increase in the proton T1-relaxation times at high fields due to the changes in the regime of molecular motion. The experimental data are in good agreement with theory. From modelling the relaxation experiments we were able to determine motional correlation times of different residues in Met-enkephalin with atomic resolution. This allows us to draw conclusions about preferential conformation of the pentapeptide in solution, which is also in agreement with data from two-dimensional NMR experiments (rotating frame Overhauser effect spectroscopy). Altogether, our study demonstrates that high-resolution NMR studies of magnetic field-dependent relaxation allow one to probe molecular mobility in biomolecules with atomic resolution.

A method is proposed to transfer spin order from para-hydrogen, that is, the H2 molecule in its singlet state, to spin-1/2 heteronuclei of a substrate molecule. The method is based on adiabatic passage through nuclear spin level anticrossings (LACs) in the doubly rotating frame of reference; the LAC conditions are fulfilled by applying resonant RF excitation at the NMR frequencies of protons and the heteronuclei. Efficient conversion of the para-hydrogen-induced polarization into net polarization of the heteronuclei is demonstrated; the achieved signal enhancements are about 6400 for (13)C nuclei at natural abundance. The theory behind the technique is described; advantages of the method are discussed in detail.

A method of transferring hyperpolarization among scalar-coupled nuclear spins is proposed, which is based on spin mixing at energy Level Anti-Crossing (LAC) regions. To fulfill LAC conditions a resonant RF-field was applied with properly set frequency and amplitude. In this situation LACs occur between the nuclear spin levels in the rotating doubly tilted reference frame. The validity of the approach is demonstrated by taking as an example the transfer of para-hydrogen induced polarization in a symmetric molecule, whose coupled spin network can be modeled as a four-spin AA'MM'-system with two pairs of 'isochronous' spins. For this spin system LAC positions have been identified; rules for the sign of spin polarization have been established. The dependence of the polarization transfer efficiency on the RF-field parameters and on the time profile of switching off the RF-field has been studied in detail; experimental results are in excellent agreement with the theory developed. In general, exploiting LACs in the rotating doubly tilted frame is a powerful tool for manipulating hyperpolarization in multispin systems.

Nuclear spin hyperpolarization is an important resource for increasing the sensitivity of NMR spectroscopy and MRI. Signal enhancements can be as large as 3-4 orders of magnitude. In hyperpolarization experiments, it is often desirable to transfer the initial polarization to other nuclei of choice, either protons or insensitive nuclei such as (13)C and (15)N. This situation arises primarily in Chemically Induced Dynamic Nuclear Polarization (CIDNP), Para-Hydrogen Induced Polarization (PHIP), and the related Signal Amplification By Reversible Exchange (SABRE). Here we review the recent literature on polarization transfer mechanisms, in particular focusing on the role of Level Anti-Crossings (LACs) therein. So-called "spontaneous" polarization transfer may occur both at low and high magnetic fields. In addition, transfer of spin polarization can be accomplished by using especially designed pulse sequences. It is now clear that at low field spontaneous polarization transfer is primarily due to coherent spin-state mixing under strong coupling conditions. However, thus far the important role of LACs in this process has not received much attention. At high magnetic field, polarization may be transferred by cross-relaxation effects. Another promising high-field technique is to generate the strong coupling condition by spin locking using strong radio-frequency fields. Here, an analysis of polarization transfer in terms of LACs in the rotating frame is very useful to predict which spin orders are transferred depending on the strength and frequency of the B1 field. Finally, we will examine the role of strong coupling and LACs in magnetic-field dependent nuclear spin relaxation and the related topic of long-lived spin-states., (Copyright © 2014 Elsevier B.V. All rights reserved.)

Magnetic field dependence of long-lived spin states (LLSs) of the β-CH2 protons of aromatic amino acids was studied. LLSs are spin states, which are immune to dipolar relaxation, thus having lifetimes far exceeding the longitudinal relaxation times; the simplest example of an LLS is given by the singlet state of two coupled spins. LLSs were created by means of the photo-chemically induced dynamic nuclear polarization technique. The systems studied were amino acids, histidine and tyrosine, with different isotopomers. For labeled amino acids with the α-CH and aromatic protons substituted by deuterium at low fields the LLS lifetime, TLLS, for the β-CH2 protons was more than 40 times longer than the T1-relaxation time. Upon increasing the number of protons the ratio TLLS/T1 was reduced; however, even in the fully protonated amino acids it was about 10; that is, the long-lived mode was still preserved in the system. In addition, the effect of paramagnetic impurities on spin relaxation was studied; field dependencies of T1 and TLLS were measured. LLSs were also formed in tyrosine-containing dyads; a TLLS/T1 ratio of ∼7 was found, usable for extending the spin polarization lifetime in such systems.

Coherent polarization transfer effects in a coupled spin network have been studied over a wide field range. The transfer mechanism is based on exciting zero-quantum coherences between the nuclear spin states by means of non-adiabatic field jump from high to low magnetic field. Subsequent evolution of these coherences enables conversion of spin order in the system, which is monitored after field jump back to high field. Such processes are most efficient when the spin system passes through an avoided level crossing during the field variation. The polarization transfer effects have been demonstrated for N-acetyl histidine, which has five scalar coupled protons; the initial spin order has been prepared by applying RF-pulses at high magnetic field. The observed oscillatory transfer kinetics is taken as a clear indication of a coherent mechanism; level crossing effects have also been demonstrated. The experimental data are in very good agreement with the theoretical model of coherent polarization transfer. The method suggested is also valid for other types of initial polarization in the spin system, most notably, for spin hyperpolarization.

Various hyperpolarization methods are able to enhance the sensitivity of nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) by several orders of magnitude. Among these methods are para-hydrogen-induced polarization (PHIP) and signal amplification by reversible exchange (SABRE), which exploit the strong nuclear alignment of para-hydrogen. Several SABRE experiments have been reported but, so far, it has not been possible to account for the experimentally observed sign and magnetic-field dependence of substrate polarization. Herein, we present an analysis based on level anti-crossings (LACs), which provides a complete understanding of the SABRE effect. The field-dependence of both net and anti-phase polarization is measured for several ligands, which can be reproduced by the theory. The similar SABRE field-dependence for different ligands is also explained. In general, the LAC concept allows complex spin dynamics to be unraveled, and is crucial for optimizing the performance of novel hyperpolarization methods in NMR and MRI techniques., (Copyright © 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim.)

Spin hyperpolarization can be coherently transferred to other nuclei in field-cycling NMR experiments. At low magnetic fields spin polarization is redistributed in a strongly coupled network of spins. Polarization transfer is most efficient at fields where level anti-crossings (LACs) occur for the nuclear spin-states. A further condition is that field switching to the LAC positions is non-adiabatic in order to convert the starting population differences into spin coherences that cause time-dependent mixing of states. The power of this method has been demonstrated by studying transfer of photo-Chemically Induced Dynamic Nuclear Polarization (photo-CIDNP) in N-acetyl-tryptophan. We have investigated the magnetic field dependence and time dependence of coherent CIDNP transfer and directly assessed nuclear spin LACs by studying polarization transfer at specific field positions. The proposed approach based on LACs is not limited to CIDNP but is advantageous for enhancing NMR signals by spin order transfer from any type of hyper-polarized nuclei.

We propose a technique for transferring the multiplet spin polarization (CIDNP or PHIP, or one created by any other method), which is the mutual entanglement of spins, into net hyper-polarization with respect to the direction of a high magnetic field by slowly (adiabatically) switching-off a strong external RF-field with a specially selected frequency. The net hyper-polarized molecules can then be used in NMR spectroscopy or imaging for strong signal enhancement.

We have investigated the mechanism of para-hydrogen-induced polarization (PHIP) transfer from the original strongly aligned protons to other nuclei at low external magnetic fields. Although it is known that PHIP is efficiently transferred at low fields, the nature of the transfer mechanism, that is, coherent spin mixing or cross-relaxation, is not well established. Polarization transfer kinetics for individual protons of styrene was, for the first time, measured and modeled theoretically. Pronounced oscillations were observed indicating a coherent transfer mechanism. Spin coherences were excited by passing through an avoided level crossing of the nuclear spin energy levels. Transfer at avoided level crossings is selective with respect to spin order. Our work provides evidence that the coherent PHIP transfer mechanism is dominant at low magnetic fields.

Effects of spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of protons were studied in a situation where spin ½ hetero-nuclei are present in the molecule. As in earlier works [K. L. Ivanov, A. V. Yurkovskaya, and H.-M. Vieth, J. Chem. Phys. 129, 234513 (2008); S. E. Korchak, K. L. Ivanov, A. V. Yurkovskaya, and H.-M. Vieth, ibid. 133, 194502 (2010)], spin-spin interactions have a pronounced effect on the relaxivity tending to equalize the longitudinal relaxation times once the spins become strongly coupled at a sufficiently low magnetic field. In addition, we have found influence of (19)F nuclei on the proton NMRD, although in the whole field range, studied protons and fluorine spins were only weakly coupled. In particular, pronounced features in the proton NMRD were found; but each feature was predominantly observed only for particular spin states of the hetero-nuclei. The features are explained theoretically; it is shown that hetero-nuclei can affect the proton NMRD even in the limit of weak coupling when (i) protons are coupled strongly and (ii) have spin-spin interactions of different strengths with the hetero-nuclei. We also show that by choosing the proper magnetic field strength, one can selectively transfer proton spin magnetization between spectral components of choice.

We have shown that long-lived spin states (LLS) can be selectively populated by photogenerated chemically induced dynamic nuclear polarization (CIDNP) over a wide range of magnetic fields. Relaxation times of LLS of the β-CH2 protons in N-acetyl histidine and partially deuterated histidine have been measured. Our experiments demonstrate that CIDNP enables creating LLS in the amino acid in a field range of up to a few Tesla and that their lifetimes can be 45 times longer than T1. The advantage of the method is thus two-fold: it allows one to accumulate high levels of spin hyperpolarization and to preserve them for periods of time far exceeding T1. Therefore, photo-CIDNP is a technique suitable for creating long-lived spin order in biologically relevant molecules.

A theoretical approach is proposed to describe Overhauser-type Dynamic Nuclear Polarization (DNP) for pulsed EPR pumping by application of a train of short pulses with a duration on the nanosecond time scale. We obtained an elegant general expression for the NMR enhancement provided by the DNP effect. The expression for the enhancement is similar to that known for cw-pumping except for the saturation factor, which is re-defined as the deviation of the electron spin magnetization from its equilibrium value averaged over the cycle of the pulse sequence. It is shown that one can achieve the maximal theoretically allowed NMR enhancement for pulsed pumping even when the duty cycle of pumping is low. This becomes possible because coherent motion of the electron spins in the B(1)-field is exploited, a key feature of the pulsed DNP experiment also enabling optimization of the achievable NMR enhancement. The dependence of the effect on the duty cycle, pulse duration and electron spin relaxation times has been studied in detail. Once the lines in the EPR spectrum are inhomogeneously broadened, higher DNP effects are expected in the pulsed pumping mode than in the cw-mode for the same total power of microwave irradiation. The theoretical results are in good agreement with experimental data obtained for the pumping frequencies of 300 MHz and 1.4 GHz., (This journal is © the Owner Societies 2012)

The cis-trans isomerisation of N-benzylideneaniline (NBA) and derivatives containing a central C=N bond has been investigated experimentally and theoretically. Eight different NBA molecules in three different solvents were irradiated to enforce a photochemical trans--(hnu)-->cis isomerisation and the kinetics of the thermal backreaction cis--(Δ)-->trans were determined by NMR spectroscopy measurements in the temperature range between 193 and 288 K. Theoretical calculations using density functional theory and Eyring transition-state theory were carried out for 12 different NBA species in the gas phase and three different solvents to compute thermal isomerisation rates of the thermal back reaction. While the computed absolute rates are too large, they reveal and explain experimental trends. Time-dependent density functional theory provides optical spectra for vertical transitions and excitation energy differences between trans and cis forms. Together with isomerisation rates, the latter can be used to identify "optimal switches" with good photochromicity and reasonable thermal stability., (Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Chemically Induced Dynamic Nuclear Polarization (CIDNP) of the diamagnetic products of radical reactions is exploited for the purpose of determination of the hyperfine coupling constants (HFCCs) of the radical intermediates. A simple proportionality relation between geminate CIDNP of a nucleus and its HFCC at the radical stage is established. The applicability range of this relation is determined: the relation is fulfilled in the case of a large difference in g-factor between the radicals involved and for the situation where the number of magnetic nuclei in the system is sufficiently large. The validity of the relation was confirmed by CIDNP experiments on radical pairs with precisely known HFCCs. Using the proportionality relation we were able to measure the HFCCs in various short-lived radicals of the amino acids histidine and tryptophan and of the S-N-centered cyclic radical of methionine derived from the methionine-glycine dipeptide in aqueous solution.

Effects of scalar spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of coupled multispin systems were analyzed. Taking spin systems of increasing complexity we demonstrated pronounced influence of the intramolecular spin-spin couplings on the NMRD of protons. First, at low magnetic fields where there is strong coupling of spins the apparent relaxation times of the coupled spins become equal. Second, there are new features, which appear at the positions of the nuclear spin level anticrossings. Finally, in coupled spin systems there can be a coherent contribution to the relaxation kinetics present at low magnetic fields. All these peculiarities caused by spin-spin interactions are superimposed on the features in NMRD, which are conditioned by changes of the motional regime. Neglecting the effects of couplings may lead to misinterpretation of the NMRD curves and significant errors in determining the correlation times of molecular motion. Experimental results presented are in good agreement with theoretical calculations.

A theoretical description of para-hydrogen-induced polarization (PHIP) is developed, applicable to coupled multi-spin systems that are polarized at an arbitrary magnetic field. Scalar spin-spin interaction is considered to be the leading factor governing PHIP formation and transfer. At low magnetic fields, these interactions make the spins strongly coupled and cause efficient, coherent re-distribution of spin polarization. We describe the effects of strong coupling and field cycling for a three-spin system and compare calculated spectra with the experimental examples available. By using a fast field-cycling device, which shuttles the whole NMR probe, and thereby makes high-resolution NMR detection at high field possible, we studied PHIP patterns for a set of different fields between 0.1 mT and 7 T. PHIP spectra were measured for ethylbenzene as the product of a catalytic reaction between para-hydrogen and styrene. Additionally, the polarizations of ethylbenzene bound to the catalyst, and of the starting styrene molecule were analyzed. This is the first time that the full field dependence of PHIP has been determined experimentally. The spectra obtained are in perfect agreement with the simulations for the CH(2) and CH(3) protons of ethylbenzene and even for its weakly-polarized aromatic protons. Analysis of styrene polarization shows that the time profile of the field variation has pronounced effects on the PHIP pattern. Our study gives evidence that scalar spin-spin interactions determine the PHIP patterns. Possible applications of the theory are discussed.

Time-resolved chemically induced dynamic nuclear polarization (CIDNP) was applied to the investigation of the photo-oxidation of two sulfur containing peptides, glycylmethionine (Gly-Met) and methionylglycine (Met-Gly). It was established that the reaction of Gly-Met with a photosensitizer, triplet 4-carboxybenzophenone, occurs via electron transfer from the sulfur atom and also from the terminal amino group in its uncharged state. The latter process leads to the formation of nuclear polarization of the alpha-protons of the glycine residue. The sulfur-centered cation radical of Gly-Met formed as a result of triplet quenching participates in the degenerate electron exchange reaction with the parent molecule. The rate constant of this reaction obtained from a simulation of the CIDNP kinetics is 2x10(8) M(-1) s(-1). Two channels of triplet quenching were also found for the Met-Gly peptide at pH values above the pKa of the terminal amino group: electron transfer from the amino group and from the sulfur atom. On the basis of the analysis of the CIDNP spectra and kinetics, it was found that at pH below pKa of the terminal amino group photo-oxidation of Met-Gly leads to the formation of an open-chain S-centered cation radical, which releases a proton from its N-terminal amino group to form a five-membered cyclic radical structure with a three electron bond between the S and N atoms. The rate constant of deprotonation obtained to be 1.8x10(5) s(-1) is in agreement with the pKa=4.7 of the S-centered radical of Met-Gly determined from the pH dependence of nuclear polarization. At pH>pKa, the aminium radicals formed in both peptides as a result of electron transfer from the lone pair of N-terminal amino group undergo deprotonation to the neutral aminyl radical on the submicrosecond time scale. The involvement of the different radicals was confirmed by the dependence of CIDNP on the external magnetic field ranging from 0.1 T to 7 T.

Using high resolution solid state (15)N and (2)H spectroscopy and longitudinal relaxometry we have studied the tautomerism of porphycene in the solid state, corresponding to a double proton transfer in two cooperative hydrogen bonds. The tautomerism is degenerate above 225 K but the degeneracy is lifted below this temperature, indicating a phase transition. Thus, the high-temperature phase is characterized by a dynamic proton disorder and the low-temperature phase by a dynamic proton order. (15)N magnetization transfer experiments obtained under cross polarization (CP) and magic angle spinning (MAS) conditions reveal the presence of two nonequivalent molecules A and B in the unit cell of phase II, exhibiting slightly different equilibrium constants of the tautomerism. Rate constants of the tautomerism in phase I could be obtained by the analysis of the longitudinal (15)N and (2)H relaxation times. The former, obtained at 9.12 MHz, exhibit a T(1) minimum around 270 K and are consistent with proton transfer induced dipolar (1)H-(15)N relaxation mechanism. The latter, obtained at 46.03 MHz, exhibit a minimum around 330 K and arise from quadrupole relaxation. Within the margin of error, the rate constants of the HH and of the HD/DD tautomerism are the same, exhibiting a barrier of about 30 kJ mol(-1), as expected for an overbarrier reaction in a configuration with two compressed hydrogen bonds. By contrast, in the low-temperature phase a switch of the DD transfer kinetics into the nanosecond time scale is observed, exhibiting a non-Arrhenius temperature dependence which is typical for tunneling. This increase of the rate constants by lowering the temperature is discussed in terms of a switch from a concerted HH transfer in phase I to a stepwise transfer in phase II, where intermolecular interactions lower the energy of one of the cis-intermediates.

The (2)H solid-state NMR spectra of the transition metal complexes Tp*RuD(THT)(2) (1a), Tp*RuD(D(2))(THT) (1b), Tp*RuD(D(2))(2) (1c), Cp*RuD(3)(PPh(3)) (2) and RuD(2)(eta(2)-D(2))(2)(PCy(3))(2) (3) have been measured in a wide temperature range. These compounds were chosen as potential model systems for hydrogen surface species in Ru-nanoparticles. The deuterium quadrupolar coupling constants Q(cc) and asymmetry parameters were extracted by (2)H NMR line-shape analysis. The Q(cc) values of the deuterons bound to the metal vary between 13 kHz and 76 kHz. In addition all spectra show that some of the deuterium is incorporated into carbon positions exhibiting quadrupolar coupling constants in the range of 134 kHz to 192 kHz. The room temperature spectra contain an additional weak very narrow line which was assigned to deuterons exhibiting a high mobility. These deuterons are attributed to crystallographic impurity and partially to D(2) molecules which lost by the complexes. The temperature where their motion is quenched and the types of these motions depend on the chemical structure. We propose to use the values of the quadrupolar coupling constants measured in order to characterize different hydrogen species on the surface of Ru-nanoparticles.

A theoretical approach to the description of longitudinal (T(1)) relaxation in scalar coupled systems of spin 1/2 nuclei at arbitrary magnetic field is developed, which is based on the Redfield theory. The consideration is addressed to field-cycling relaxometry experiments with high-resolution NMR detection, in which the field dependence of T(1)-relaxation times, the nuclear magnetic relaxation dispersion (NMRD), can be studied for individual spins of the molecule. Our study reveals well-pronounced effects of spin-spin couplings on the NMRD curves. First, coupled spins having completely different high-field T(1) times tend to relax at low field with a common relaxation time. Second, the NMRD curves exhibit sharp features at the fields corresponding to the positions of nuclear spin level anticrossings. Such effects of spin-spin couplings show up not only for individual spins but also for the T(1)-relaxation of the total spin magnetization of the molecule. The influence of spin-spin coupling is of importance as long as the coupling strength J is larger than the inverse T(1)-relaxation times of the spins. Around J x T(1) = 1 there is also a coherent contribution to the relaxation kinetics resulting in an oscillatory component of the kinetic curves. Application of the theory to experimental examples will be described in subsequent publications.

Using solid-state NMR spectroscopy, we have detected and characterized ultrafast intramolecular proton tautomerism in the N-H-N hydrogen bonds of solid N, N'-diphenyl-6-aminofulvene-1-aldimine ( I) on the microsecond-to-picosecond time scale. (15)N cross-polarization magic-angle-spinning NMR experiments using (1)H decoupling performed on polycrystalline I- (15)N 2 and the related compound N-phenyl- N'-(1,3,4-triazole)-6-aminofulvene-1-aldimine ( II) provided information about the thermodynamics of the tautomeric processes. We found that II forms only a single tautomer but that the gas-phase degeneracy of the two tautomers of I is lifted by solid-state interactions. Rate constants, including H/D kinetic isotope effects (KIEs), on the microsecond-to-picosecond time scale were obtained by measuring and analyzing the longitudinal (15)N and (2)H relaxation times of I- (15)N 2, I- (15)N 2- d 10, and I- (15)N 2- d 1 over a wide temperature range. In addition to the microcrystalline modification, a novel amorphous modification of I was found and studied. In this modification, proton transfer is much faster than in the crystalline form. For both modifications, we observed large H/D KIEs that were temperature-dependent at high temperatures and temperature-independent at low temperatures. These findings are interpreted in terms of a simple quasiclassical tunneling model proposed by Bell and modified by Limbach. We obtained evidence that a reorganization energy is necessary in order to compress the N-H-N hydrogen bond and achieve a molecular configuration in which the barrier for H transfer is reduced and tunneling or an over-barrier reaction can occur.

By combining magnetic field cycling in the range from 0.1mT to 7T with high-resolution NMR detection the T(1) relaxation dispersion (nuclear magnetic relaxation dispersion (NMRD)) of protons in the nucleotides adenosine mono-phosphate and guanosine mono-phosphate was measured in a site-specific way. While at high field the individual spins have distinctly different T(1) times, their scalar spin-spin interaction fulfills at low field the condition of strong coupling and leads to convergence of their T(1) dispersion curves. In addition, the spin-spin coupling can lead to oscillatory components in the relaxation kinetics traceable to a coupling between spin polarization and coherence in the relaxation process. As a consequence the NMRD curves do not directly reflect the spectral density function of the motional processes, but the effects of motion and spin coupling must be separated for a reliable evaluation. A theoretical approach is described allowing such an analysis.