High-field ENDOR and the sign of the hyperfine coupling

Two different approaches for assigning electron nuclear double resonance (ENDOR) signals to their respectiveM _s manifolds by a controlled generation of asymmetric ENDOR spectra, are described and applied to a number of systems. This assignment then allows a straightforward determination of the sign of the hyperfine coupling. Both approaches rely on a high thermal polarization that is easily achieved at high fields and low temperatures. For high-spin systems, such asS = 5/2 the assignment is afforded by the selective inversion of the | ?3/2〉 → | ?1/2〉 electron paramagnetic resonance (EPR) transition which is highly populated as compared to its symmetric counterpart, the |1/2〉 → |3/2〉 EPR transition, and therefore is easily identified. ForS = 1/2 the determination of the sign of the hyperfine coupling becomes possible when the cross- and nuclear-spin relaxation rates are much slower than the electron-spin relaxation rate and variable mixing time pulse ENDOR is used to measure the spectrum. Under these conditions the signals of theM _s = 1/2 (α) manifold become negative when the mixing time is on order of the electron-spin relaxation time, whereas those of theM _s =?1/2 (β) manifold remain positive. Under partial saturation of the nuclear transitions and short mixing time the opposite behavior is observed. Pulse W-band¹H ENDOR experiments demonstrating these approaches were applied and the signs of the hyperfine couplings of the water ligands in Mn(H₂O) ₆ ²⁺ , the H_α and H_β histidine protons in the Cu(histidine)₂ complex, the imidazole protons in Cu(imidazole) ₄ ²⁺ and the cysteine β-protons in nitrous oxide reductase were determined.     

Pulsed EPR and ENDOR on the Peridinin Triplet State Involved in the Photoprotective Mechanism in Peridinin–Chlorophyll a–Proteins

The photoexcited triplet state of the carotenoid peridinin in the peridinin–chlorophyll a–protein (PCP) of the dinoflagellate Heterocapsa pygmaea has been investigated by pulsed electron paramagnetic resonance (EPR) and pulsed electron-nuclear double resonance (ENDOR) spectroscopies. The α- and β-protons hyperfine couplings of the peridinin-conjugated chain have been derived from Davies and Mims ENDOR experiments. The spectroscopic results have been compared to those obtained for the main form of the PCP complex and for the high-salt PCP form from Amphidinium carterae. The EPR features of the peridinin triplet state are very similar in the antenna complexes belonging to the two different dinoflagellate species, proving that the triplet formation pathway and the triplet localization on one specific peridinin per subcluster are common features of different PCP antennas. No significant variation of the hyperfine couplings of the peridinin triplet state has been detected between the main form of the PCP complex from A. carterae and H. pygmaea. The spectroscopic results confirm the close relationship between the Amphidinium PCP and the corresponding Heterocapsa complex at least in terms of mutual arrangement of the chlorophyll a–peridinin pair involved in photoprotection and in terms of conformation of the peridinin-conjugated chain.     

Angle-selective measurements of spin soliton in ladder polydiacetylene by pulsed 94 GHz EPR

Angle-selection experiments of a spin soliton in randomly oriented ladder polydiacetylene were carried out by pulsed electron paramagnetic resonance (EPR) at W-band. EPR measurement using 94 GHz microwaves increased the difference in the resonance field due tog anisotropy of the spin soliton to allow the orientation dependence of transient nutation, electron nuclear double resonance (ENDOR) and spin relaxations to be investigated. The shape of theg anisotropy-resolved nutation spectrum was discussed on the basis of the EPR transition moments and the differences between spin relaxation times. Reliable assignments of hyperfine couplings to the β protons (H_β) of the alkyl side chains were achieved with the support of W-band ENDOR measurements. No significant orientational dependence in theT ₁ andT ₂ processes was found in terms of isotropy of the H_β-hyperfine interaction.     

Absolute signs of hyperfine coupling constants as determined by pulse ENDOR of polarized radical pairs

A novel method that allows the determination of absolute signs of hyperfine coupling constants in polarized radical pair (RP) pulse electron-nuclear double resonance (ENDOR) spectra is presented, The variable mixing time (VMT) ENDOR method used here leads to a separation of ENDOR transitions originating from different electron spin manifolds by employing their dependence on the time-dependent parameters of the pulse sequence. The simple kinetic model of the RP VMT ENDOR experiment shows very good agreement with the experiments performed on the P ₇₀₀ ^.+ A ₁ ^.- RP in photosystem I. This method relies on the selective excitation of absorptive or emissive lines of one radical in the RP EPR spectrum and therefore requires high spectral resolution. This condition was fulfilled for the system studied at the low-field edge of the RP EPR spectrum obtained at Q-band. The method presented here has a very high sensitivity and does not require any equipment additional to the one used for RP pulse ENDOR. The VMT ENDOR method offers the possibility for selective suppression of signals from different electron spin manifolds.     

Elektronen-Kern-Doppelresonanz-Untersuchung vonU 2-Zentren in Kaliumchlorid

U ₂-centers in alkali halides are neutral hydrogen atoms in interstitial lattice sites, as has been shown by EPR measurements. The hyperfine interactions with the proton and with the four nearest halogen nuclei are resolved in the EPR spectrum. In order to resolve hyperfine interactions with further nuclei of the surrounding lattice ENDOR measurements have been performed onU ₂-centers in KCl at 77 °K. The analysis of the ENDOR spectra gave precise values for the hyperfine and quadrupole interaction constants of the nearest neighbour chlorine and potassium nuclei. The isotropic hyperfine constant of the chlorine neighbours is 24 times larger than that of the potassium neighbours although both nuclei are on equivalent first shell lattice positions. The hyperfine interactions of second shell potassium nuclei [(1/2, 1/2, 3/2)-position] show an unexpectedly large isotropic hyperfine constant. One expects a pure magnetic dipole-dipole interaction for the outer shell nuclei because of the concentrated hydrogen wave function. Two further chlorine shells could be approximately analysed. A theoretical estimate of the hyperfine and quadrupole interaction constants was made by orthogonalizing the 1s hydrogen wave function to the cores of the surrounding ions. If one takes into account the mutual overlap of neighbouring potassium and chlorine ions, one gets the right order of magnitude of the measured constants and a value of 10.4∶1 for the ratio of the isotropic hyperfine constants of the first shell chlorine and potassium nuclei. The relatively large isotropic constant of the second shell potassium nuclei can also be explained on this basis.     

A pulsed EPR study of the catalytic oxidation of CO over Cu/SnO2

The role of the Cu(II) in the catalytic oxidation of CO over Cu/SnO₂ with low Cu(II) content was studied by continuous wave EPR, electron spin echo envelope modulation (ESEEM) and hyperfine sublevel correlation (HYSCORE) spectroscopes. Three methods were employed for introducing the copper: (i) by coprecipitation, (ii) impregnation onto SnO₂ gel and (iii) impregnation onto calcined SnO₂. Two types of Cu(II) species were identified in these calcined Cu/SnO₂ materials. Those belonging to the first type, termed B and C, exhibit highly resolved EPR spectra with well defined EPR parameters and are located within the bulk of the oxide. The other group comprises a distribution of surface Cu(II) species with unresolved EPR features and are referred to as S. While the latter were readily reduced by CO the former required long exposures at high temperatures (> 673 K). The specific interactions of the different Cu(II) species with CO were investigated through the determination of the¹³C hyperfine coupling of enriched¹³CO. The ESEEM spectra of calcined samples, generated either by coprecipitation or impregnation, show after the adsorption of CO signals at the Larmor frequencies of^{117, 119}Sn and¹³C and at twice these Larmor frequencies. Although these signals indicate that^{117, 119}Sn and¹³C are in the close vicinity of Cu(II), they cannot provide the hyperfine couplings of these nuclei. This problem was overcome by the application of the HYSCORE experiment. The 2D HYSCORE spectra show well resolved cross peaks which provide the hyperfine interaction of these nuclei. Simulations of the HYSCORE spectra yield for^{117, 119}Sn an isotropic hyperfine constant,a _iso, of ±4.0 MHz and an anisotropic component,T _?, of ±2.0 MHz. Pulsed ENDOR spectra also showed^{117, 119}Sn signals which agree with the above values. The¹³C cross peaks yielda _iso=±1.0 MHz andT _?=±2.0 MHz. Similar C cross peaks were observed in spectra of calcined Cu/SnO₂ after the adsorption of CO₂. Based on the same hyperfine couplings in the samples exposed to¹³CO and¹³CO₂ the signals were assigned to surface carbonate species generated by part of the Cu(II) S type species rather then by species B and the role of the Cu(II) in the oxidation process is discussed.     

Single crystal 63Cu and 65Cu ENDOR of bis(2,4-pentanedionato)copper(II)

ENDOR spectra were obtained from ⁶³Cu and ⁶⁵Cu nuclei in bis(2,4-pentanedionato)copper(II) doped in bis(2,4-pentanedionato)palladium(II) single crystals. The copper hyperfine and nuclear quadrupole coupling constants determined from the ENDOR spectra are compared to those obtained previously by EPR. The nuclear quadrupole coupling tensor obtained from ENDOR reveals deviation from the axial symmetry. It is shown that the asymmetry may arise from interaction with the field gradient attributable to the charges on the ligand.     

EPR and ENDOR Study of a series of free base porphycenes in the photoexcited triplet state

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).     

Effects of pressure on magnetic properties of F-centers in rubidium halides

Room temperature magnetic resonance measurements have been made on additively colored RbCl and RbBr and on X-irradiated RbH at pressures up to 8 kbar. In RbCl and RbH pressure shifts of the F-center isotropic coupling constant a₁ were obtained from changes in the resolved EPR hyperfine structure. Pressure shifts of first and second shell hyperfine coupling constants of F-centers in RbBr were found from high pressure ENDOR spectra. Effects of the pressure induced polymorphic phase transformations in RbCl and RbBr are discussed. No evidence was found for a structure transformation in RbH. Room pressure ENDOR measurements on additively colored RbI were made at 77°K. The first and second shell hyperfine coupling constants are reported. All results accord well with the behavior of F-centers in other alkali halides.     

Liquid-phase EPR, ENDOR, and TRIPLE resonance studies on corrole and isocorrole cation radicals

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.     

Local31P and distant31P and195Pt ENDOR studies of powdered samples of Bis(O,O′-disubstituted-dithiophosphato)copper(II) complexes magnetically diluted in the corresponding Pd(II) and Pt(II) host lattices

ENDOR studies on bis(dithiophosphato)copper(II) complexes magnetically diluted in the corresponding Pd(II) and Pt(II) host lattices performed with the use of the method of “polycrystalline ENDOR crystallography” are reported. In these samples well resolved local³¹P (A_iso ca. 29 MHz and A_aniso ca. 0.9 MHz) as wel1 as distant³¹P (A _iso ca. 1.3 and 5.5 MHz and A_aniso ca. 0.2 and 0.4 MHz) and¹⁹⁵Pt (A_iso ca. 3.1 MHz and A_aniso ca. 0.2 MHz) ENDOR transitions are recorded. It is shown that the directions of the main values of A_aniso for all local³¹P and distant³¹P and¹⁹⁵Pt ENDOR transitions are parallel. Comparison of these results with those reported about the same complexes but diluted in other host lattices shows that there is no difference in the EPR and local³¹P ENDOR parameters thus suggesting that the structure of the paramagnetic complex remains unchanged. It is found that distant ENDOR transitions appear only in the case when the host lattice contains one molecule in the unit cell, i.e., when all molecules are parallel to each other. Using the obtained data from local and distant³¹P ENDOR transitions some structural features of Cu(dtp)₂ as well as Pd(dtp)₂ and Pt(dtp)₂ complexes are found for the first time.     

EPR and ENDOR Investigation of Rhodosemiquinone in Bacterial Reaction Centers Formed by B-Branch Electron Transfer

In photosynthetic bacteria, light-induced electron transfer takes place in a protein called the reaction center (RC) leading to the reduction of a bound ubiquinone molecule, Q_B, coupled with proton binding from solution. We used electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) to study the magnetic properties of the protonated semiquinone, an intermediate proposed to play a role in proton coupled electron transfer to Q_B. To stabilize the protonated semiquinone state, we used a ubiquinone derivative, rhodoquinone, which as a semiquinone is more easily protonated than ubisemiquinone. To reduce this low-potential quinone we used mutant RCs modified to directly reduce the quinone in the Q_B site via B-branch electron transfer (Paddock et al. in Biochemistry 44:6920–6928, 2005). EPR and ENDOR signals were observed upon illumination of mutant RCs in the presence of rhodoquinone. The EPR signals had g values characteristic of rhodosemiquinone (g _x  = 2.0057, g _y  = 2.0048, g _z  ~ 2.0018) at pH 9.5 and were changed at pH 4.5. The ENDOR spectrum showed couplings due to solvent exchangeable protons typical of hydrogen bonds similar to, but different from, those found for ubisemiquinone. This approach should be useful in future magnetic resonance studies of the protonated semiquinone.     

Studies of EPR and ENDOR spectra of14N and15N label bis(2-hydroxyacetophenyl ketoxime)-63Cu(II) and-65Cu(II) complexes in disordered system

The EPR spectra of isotopic label bis(2-hydroxyacetophenyl ketoxime)-Cu(II) [N?Cu-HAP] complexes, such as¹⁴N?⁶³Cu-HAP,¹⁵N?⁶³Cu-HAP and¹⁴N?⁶⁵Cu-HAP in frozen THF solution below 77 K, and their ENDOR spectra in frozen DMSO/EtOH (5∶1) solution below 20 K were studied. The exact values of the components ofg-tensor, of hyperfine tensors of copper isotopes, and of superhyperfine interaction tensors of copper with nuclei of nitrogen isotopes and¹H nuclei, and of the¹⁴N nuclear quadrupolar moment coupling tensor were obtained. The bond parameters α, β, δ, γ and the corresponding energy levels of N?Cu-HAP complexes were calculated by using EPR and ENDOR data. It was shown that the unpaired, electron is delocalized not only to the nearest N atom but also to the H atom, of ligands, which is more far from the Cu ion.     

Temperature dependent g-shift and exchange interaction in β: BIS(N-methyl salicylaldimine) copper (II)

EPR Studies have been performed on β: bis(N-methyl salicylaldimine) copper (II) in the temperature range 300–1.5 K and are compared with EPR of other two isomers α and λ. Only in β-form g_∥ increases and g_⊥ decreases continuously with lowering temperature. This is explained in terms of temperature dependent vibronic mixing of d_z2 state with ground d_x²?y² state.Only at 1.5 K some structures appear. These may be identified as hyperfine structures. Also linewidths increases gradually at low temperatures. These observations show the existence of a positive temperature coefficient of exchange interaction in this salt.     

Combining steady-state and dynamic methods for determining absolute signs of hyperfine interactions: pulsed ENDOR Saturation and Recovery (PESTRE)

The underlying causes of asymmetric intensities in Davies pulsed ENDOR spectra that are associated with the signs of the hyperfine interaction are reinvestigated. The intensity variations in these asymmetric ENDOR patterns are best described as shifts in an apparent baseline intensity that occurs dynamically following on-resonance ENDOR transitions. We have developed an extremely straightforward multi-sequence protocol that is capable of giving the sign of the hyperfine interaction by probing a single ENDOR transition, without reference to its partner transition. This technique, Pulsed ENDOR Saturation and Recovery (PESTRE) monitors dynamic shifts in the 'baseline' following measurements at a single RF frequency (single ENDOR peak), rather than observing anomalous ENDOR intensity differences between the two branches of an ENDOR response. These baseline shifts, referred to as dynamic reference levels (DRLs), can be directly tied to the electron-spin manifold from which that ENDOR transition arises. The application of this protocol is demonstrated on (57)Fe ENDOR of a 2Fe-2S ferredoxin. We use the (14)N ENDOR transitions of the S = 3/2[Fe(II)NO](2+) center of the non-heme iron enzyme, anthranilate dioxygenase (AntDO) to examine the details of the relaxation model using PESTRE.     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

Local structure of titanium pair centers in SrF2 crystals: EPR and ENDOR spectroscopic studies

The local structure of titanium pair centers in SrF₂: Ti crystals is investigated using electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy. It is found that titanium pair centers with spin moment S=2 and tetragonal symmetry of the magnetic properties are formed in SrF₂: Ti cubic crystals under certain growth conditions and during annealing. The tensor components of the fine and ligand hyperfine structures in the EPR and ENDOR spectra are determined. A model of the Ti⁺-Ti³⁺ paramagnetic dimer is proposed. This model provides an adequate interpretation of both the ferromagnetic nature of the exchange interaction and the observed displacements of four ligands in the first coordination sphere of titanium impurity ions in directions perpendicular to the impurity ion-ligand bonds.     

High-Frequency EPR and ENDOR Spectroscopy on Semiconductor Quantum Dots

It is shown that high-frequency electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy are excellent tools for the investigation of the electronic properties of semiconductor quantum dots (QDs). The great attractions of these techniques are that, in contrast to optical methods, they allow the identification of the dopants and provide information about the spatial distribution of the electronic wave function. This latter aspect is particularly attractive because it allows for a quantitative measurement of the effect of confinement on the shape and properties of the wave function. In this contribution EPR and ENDOR results are presented on doped ZnO QDs. Shallow donors (SDs), related to interstitial Li and Na and substitutional Al atoms, have been identified in this material by pulsed high-frequency EPR and ENDOR spectroscopy. The shallow character of the wave function of the donors is evidenced by the multitude of ENDOR transitions of the ⁶⁷Zn nuclear spins and by the hyperfine interaction of the ⁷Li, ²³Na and ²⁷Al nuclear spins that are much smaller than for atomic lithium, sodium and aluminium. The EPR signal of an exchange-coupled pair consisting of a shallow donor and a deep Na-related acceptor has been identified in ZnO nanocrystals with radii smaller than 1.5 nm. From ENDOR experiments it is concluded that the deep Na-related acceptor is located at the interface of the ZnO core and the Zn(OH)₂ capping layer, while the shallow donor is in the ZnO core. The spatial distribution of the electronic wave function of a shallow donor in ZnO semiconductor QDs has been determined in the regime of quantum confinement by using the nuclear spins as probes. Hyperfine interactions as monitored by ENDOR spectroscopy quantitatively reveal the transition from semiconductor to molecular properties upon reduction of the size of the nanoparticles. In addition, the effect of confinement on the g-factor of SDs in ZnO as well as in CdS QDs is observed. Finally, it is shown that an almost complete dynamic nuclear polarization (DNP) of the ⁶⁷Zn nuclear spins in the core of ZnO QDs and of the ¹H nuclear spins in the Zn(OH)₂ capping layer can be obtained. This DNP is achieved by saturating the EPR transition of SDs present in the QDs with resonant high-frequency microwaves at low temperatures. This nuclear polarization manifests itself as a hole and an antihole in the EPR absorption line of the SD in the QDs and a shift of the hole (antihole). The enhancement of the nuclear polarization opens the possibility to study semiconductor nanostructures with nuclear magnetic resonance techniques.     

Influence of photoexcitation on the EPR spectra of Mo5+ in Li2Zn2(MoO4)3: Ce3+,Cu2+ crystals annealed in a CO2 atmosphere

The influence of recovery annealing in a CO₂ atmosphere at 700°C on the properties of Li₂Zn₂(MoO₄)₃ crystals doped with cerium and copper ions has been studied. The EPR investigation of Li₂Zn₂(MoO₄)₃ crystals annealed in a CO₂ atmosphere has revealed that the annealing leads to the formation of oxygen vacancies in positions adjacent to the oxygen octahedron of lithium, M3, and the oxygen tetrahedron of molybdenum, Mo1. In this case, the charge state of molybdenum becomes Mo⁵⁺ and appears in the EPR spectra in the form of one magnetically nonequivalent position. The analysis of the angular dependence of the EPR spectrum of Mo⁵⁺ made it possible to calculate the spectral parameters g _∥ = 1.862, g _⊥ = 1.933, A _∥ = 71.8 G, and A _⊥ = 34.1 G. The cross relaxation on the hyperfine structure from the molybdenum isotope ⁹⁷Mo is found in the EPR spectra. The photoexcitation of Li₂Zn₂(MoO₄)₃ crystal doped with cerium ions leads to the saturation of the EPR spectrum of Mo⁵⁺ and to the formation of the hyperfine structure from one lithium ion with a hyperfine structure constant of 14 G. For Li₂Zn₂(MoO₄)₃ crystals doped with copper ions, a very weak EPR spectrum of Mo⁵⁺ is observed in the initial crystals. As a result of the photoexcitation, an increase in the intensity of this spectrum by an order of magnitude and manifestation of the EPR spectrum of Cu²⁺ ions take place. It is assumed that such a behavior of the EPR spectra of molybdenum ions in Li₂Zn₂(MoO₄)₃ crystals doped with cerium and copper ions under photoexcitation is caused by different positions of the energy levels of cerium and copper ions with respect to the energy level of the molybdenum ion.     

2D TRIPLE in orientationally disordered samples--a means to resolve and determine relative orientation of hyperfine tensors

The two-dimensional (2D) TRIPLE experiment provides correlations between electron-nuclear double resonance (ENDOR) frequencies that belong to the same electron-spin manifold, M(S), and therefore allows to assign ENDOR lines to their specific paramagnetic centers and M(S) manifolds. This, in turn, also provides the relative signs of the hyperfine couplings. So far this experiment has been applied only to single crystals, where the cross-peaks in the 2D spectrum are well resolved with regular shapes. Here we introduce the application of the 2D TRIPLE experiment to orientationally disordered systems, where it can resolve overlapping powder patterns. Moreover, analysis of the shape of the cross-peaks shows that it is highly dependent on the relative orientation of the hyperfine tensors of the two nuclei contributing to this particular peak. This is done initially through a series of simulations and then demonstrated experimentally at a high field (W-band, 95 GHz). The first example concerned the (1)H hyperfine tensors of the stable radical alpha,gamma-bisdiphenylene-beta-phenylallyl (BDPA) immobilized in a polystyrene matrix. Then, the experiment was applied to a more complex system, a frozen solution of Cu(II)-bis(2,2':6',2' terpyridine) complex. There, the 2D TRIPLE experiment was combined with the variable mixing time (VMT) ENDOR experiment, which determined the absolute sign of the hyperfine couplings involved, and orientation selective ENDOR experiments. Analysis of the three experiments gave the hyperfine tensors of a few coupled protons.