Solomon-Bloembergen Equations Research Articles

Nuclear spin relaxation in paramagnetic systems ( S = 1) in the slow-motion regime for the electron spin. IV. Motional anisotropy and noncoinciding dipole-dipole and zero-field splitting tensors

In this work, a paramagnetic complex in which the interacting electron ( S) and nuclear ( I) spins are connected by a vector not coinciding with the principal coordinate system of the zero-field-splitting (ZFS) tensor of the electron spin is considered as a model system. It is shown that the behavior of the dipole-dipole (DD) nuclear spin relaxation in such a system changes drastically when the electron spin enters the slow-motion regime. The effect of the slow motion is shown to be strongly dependent on the angle between the DD vector and the z axis of the principal coordinate system of the ZFS tensor. The present theory is valid for all possible values of the experimental variables and gives the Solomon equations as a limit of lowest order. The relation of the new theory to the modified Solomon-Bloembergen (MSB) equations is also discussed. If the anisotropic reorientation is incoporated (coinciding ZFS and diffusion tensors), the present theory, to the lowest order, yields the same results for the DD interaction of two interacting spins as obtained by Woessner ( J. Chem. Phys. 37, 647 (1962) . The internal diffusion can also be easily incorporated. The differences between the traditional theory and the slow-motion results, as well as the effects on relaxation in some interesting experimental situations are demonstrated by appropriate diagrams.

1H-NMR study of the interaction of aminopyrine with purified rat liver microsomal cytochrome P-450

Longitudinal relaxation ( T 1) measurements for all lines (N(CH 3) 2, N(CH 3), (C(CH 3), phenyl) in the aminopyrine 1H-NMR spectrum were used to study the interaction of aminopyrine with purified microsomal cytochrome P-450 from livers of phenobarbital-treated rats. The paramagnetic contribution to the observed t 1 −1 values was determined from its dependence on aminopyrine concentration. The Solomon-Bloembergen equation was used to calculate between Fe 3+ and aminopyrine distances in the enzyme-substrate complex. For all protons these distances are about 8 Å.

Nuclear spin relaxation in a paramagnetic nickel(II) complex. An experimental test of new theoretical models

Paramagnetic relaxation enhancement data are reported for 15N and 1H in aniline in the presence of bis(2,2,6,6-tetramethylheptanedionato)nickel(II). For 15N, the spin-lattice as well as spin-spin relaxation rates are reported at two magnetic fields (2.35 and 5.875 T) and over a temperature range of 244 to 356 K. For 1H we report T 1 data at two fields (5.875 and 9.4 T) over a temperature range of 263 to 333 K. The experimental data are fitted to a new theoretical model, not invoking the concept of electron spin relaxation times, which is valid in the slow motion regime for the electron spin. The parameters obtained form a consistent set and have reasonable values, but the 15N results could not be fitted using the conventional model based on the modified Solomon-Bloembergen equations.

Dipole-dipole nuclear spin relaxation

The transverse spin relaxation of a spin I in a IS pair is analysed for the dipole-dipole relaxation mechanism. It is shown that, when for the S-spin there is an additional efficient relaxation mechanism, which is of a second order tensorial rank, there can exist substantial corrections to the Solomon-Bloembergen equation for T 2. The correction terms are found to be non-negligible in the non-extreme narrowing limit. The correction terms are due to a cross correlation effect between the dipole-dipole interaction and the interaction causing the efficient relaxation of the S spin. As shown in the Appendix the correction appears as a near divergence of a fourth order term in the Redfield type expansion of the equation of motion of the density matrix. The explicit expressions for T 2 are, however, derived using a Liouville operator formalism combined with a perturbation expansion. For the relaxation of the S-spin a zero field splitting term is considered for a paramagnetic system with S ≥ 1. Similarly for a nuclear spin S the quadrupolar interaction provides an efficient relaxation mechanism when S ≥ 1. For these cases explicit examples are worked out and for example if S = 1 and the principal axis system of the zero field splitting term or the quadrupolar interaction coincides with the dipole-dipole vector the cross correlation corrections are such that the high field value of T 2 is 2·5 times the value given by the Solomon-Bloembergen equation. It is also argued that a similar cross correlation effect can appear in spin one half systems if three or more spins are involved. It thus appears that the quantitative analysis of T 2 data for systems outside the extreme narrowing regime is even more complicated than has previously been appreciated.

NMR, EPR, and INDO Studies on the complexes of dopamine with Cu 2+, Mn 2+, and Fe 3+ in aqueous solution

The spin-lattice relaxation rates of dopamine in the presence of Cu 2+, Mn 2+, and Fe 3+ have been investigated by FT NMR spectroscopy in aqueous solution. The Solomon-Bloembergen equation is found to hold in the case of Mn 2+ complex while a failure of its applicability was observed in Cu 2+ and Fe 2+ complexes. Rationalization of the relaxation rates with the aid of EPR spectroscopy allowed the estimation of the pertinent molecular correlation time. Furthermore INDO MO calculations furnished detailed information on the mechanism of spin density onto the ligand.

Nuclear spin relaxation in paramagnetic systems

A theory of nuclear spin relaxation in paramagnetic systems, allowing for the electron spin relaxation to be in the slow motion regime, is presented. The formulation is general and can, for example, be used to derive formally the modified Solomon-Bloembergen equations. The theory is applied to the specific problem of nuclear spin lattice relaxation caused by the dipole-dipole interaction between the nuclear spin and an electron spin (S = 1). The lattice is described in terms of the electron Zeeman interaction, a zero field splitting of cylindrical symmetry and isotropic rotational diffusion. The resulting equations are solved numerically for a range of parameter values of practical interest and limiting cases are discussed. In the slow motion regime for the electron spin relaxation (that is, where the zero field splitting is larger than the rotational diffusion constant), the behaviour of the nuclear spin-lattice relaxation rate predicted using the present formalism differs qualitatively from the predicti...

Ambiguities in the proton NMR studies involving Cu(II) ions as paramagnetic relaxation centres

The theory of nuclear spin relaxation induced by paramagnetic ions in solution has been given great relevance in delineating structural and kinetic parameters of bioinorganic reactions. Although several criticism and corrections have been worked out, the original form of the Solomon-Bloembergen-Morgan equitions [1, 2] still represents the most suitable starting point for interpreting experimental paramagnetic rates. t001 Paramagnetic Proton Relaxation Rates of Imidazole H 4, pH = 7.0; T = 300 K. His ( M) Cu 2+ (m M) T −1 1p (sec −1) T −1 2p(sec −1) (sec −1) T − 2p/T − 1p 0.1 0.01 0.02 0.32 16 0.1 0.02 0.03 0.45 15 0.1 0.03 0.06 0.65 11 0.1 0.04 0.14 1.27 7 0.1 0.05 0.18 1.41 10 When dealing with Cu(II) ions as relaxation reagents, the scalar interaction was shown to give significant contributions to NMR line broadening, and T 1 measurements were therefore designed for getting structural information from the dipolar term. In this report we suggest that asymmetric coordination to Cu(II) ions, resulting in large g tensor anisotropies, make the Solomon-Bloembergen equations meaningless, since unreasonable answers are obtained in well defined Cu(II) complexes. The Cu(His) 2 complex was taken as a model complex, since the X-ray structure of crystals obtained from aqueous solution has been reported [3]. The experimental paramagnetic contributions T −1 ip = T −1 i(obs) − T t-1 i (blank) are reported in Table I for H 4 of the imidazole moiety at different [Cu ++] tot/ [His] tot ratios. In these conditions CuA 2 (His = H 3A) is almost exclusively present in solution [4] and the T − 2p/T − 1p values are consistent with fast exchange of His molecules from the metal coordination sphere. The correlation time of the dipolar interaction was approximately by measuring that of water protons bound in the complex and the Cu(II)H 4 distance was taken rom crystallorgraphic structure. Calculations based on the Solomon-Bloembergen equations give values of the coordination number ranging between 0.039 and 0.054, which is nonsense. Since the correlation time of the complex is not rapid enough compared with the electron spin anisotropy energy, that is h τ −1 c ⪡|g∥ − g⊥|βB o no theoretical model is available to allow quantitative interpretation of nuclear relaxation. Combined ESR and NMR experiments are therefore suggested to build up a novel theoretical approach.

NMR and INDO study of the Ni(II) complexes of some bidentate ligands

The joint use of NMR spectroscopy and quantum mechanical calculations proved a powerful tool for investigating the conformational and electronic properties of various ligands complexes to paramagnetic metal ions. It is well known that the spin–lattice relaxation rates cannot often be rationalized in terms of the Solomon-Bloembergen equation, in its original form, because of the important contribution arising from the unpaired spin density onto the ligand molecule [1]. Thus a modified S.B. equation, where both the metal-centered and ligand-centered dipolar contributions are taken into account, must be employed. In this work the Ni(II) complexes of dopamine [2], a molecule of biological relevance, phthalic acid [3], maleic and succinic acid [4] were examined. The common feature of these differently flexible ligands is a potential bidentate binding site. ▪ From the analysis of the proton and carbon paramagnetic shifts, induced on the nuclei of the different ligands bound to Ni 2+, a delocalization mechanism was hypothesized with the aid of an INDO M.O. analysis, performed on suitable radical models of the ligand. The radical model giving hyperfine coupling constants in the best agreement with the experimental shifts was then used to obtain a complexation model. The reliability of the model chosen was tested introducing the metal–nucleus distances in the reduced and modified S.B. equation and veryfying whether the calculated total unpaired spin densities and correlation times satisfy the experimental nuclear relaxations. In the case of ligands having a partially rigid skeleton (dopamine, phthalic and maleic acids) the approach led to a unique complexation model, consistent with the experimental data, while for the more flexible succinic acid the result were not so encouraging.

C-13 magnetic relaxation rates and H-1 and C-13 paramagnetic shifts of Co(II) complex of dopamine

Abstract The importance of unpaired spin distribution in the Co(II)-Dopamine complex in aqueous solution, was investigated. From the analysis of the H-1 and C-13 isotropic shifts and with the aid of an INDO M.O. calculation on a dopamine radical a prevalent σ-type delocalization mechanism of the spin density was evidentiated, even if a contribution from π-electrons cannot be completely excluded. The analysis of the spin-lattice relaxation rates revealed the importance of ligand-centered dipolar interactions. The introduction of the spin densities, calculated from the INDO method, in the modified Solomon-Bloembergen equation, allowed to estimate the correlation time of the complex which can be identified with the electronic relaxation time.

1H-NMR spectroscopic study on the binding of alcohols to soybean lipoxygenase-1

The line-shape of the EPR signal around g 6 of yellow lipoxygenase-1, obtained upon addition of I molar equivalent of 13- l s- hydroperoxy-9-cis ,11- trans-octadecadienoic acid to the native enzyme (linoleate:oxygen oxidoreductase, EC 1.13.11.12), is strongly affected by alcohols. NMR spectra of solutions of alcohols to which lipoxygenase has been added show a line-broadening of the proton resonances which is due to proton relaxation enhancement from magnetic interaction between iron and protons. This can be taken as direct evidence for binding of alcohols in the vicinity of iron. For unbranched alcohols the line-broadening gradually increases, going from the methyl protons to the protons on carbon atom 1, indicating that the latter are closer to iron. Titrations of yellow lipoxygenase with ethanol, 1-butanol and 1-hexanol reveal that the affinity of the alcohols increases with longer carbon chain length; their binding constants were found to be 260, 30 and approx. 3 mM respectively. The distances between protons of bound alcohol and iron were calculated with the Solomon-Bloembergen equation, leading to values of approx. 6 Å, for the distance between iron and the methyl protons. A hydrophobic binding of the alcohols to the enzyme is proposed in line with the mode of binding of the natural substrates, polyunsaturated fatty acids.

C-13 magnetic relaxation rates and H-1 and C-13 paramagnetic shifts of Ni(II) complex of dopamine

The 1H and 13C isotropic contact shifts and the 13C relaxation times of dopamine in aqueous solution have been measured in the presence of the Ni(II) ion. The pD dependence of the 1H and 13C paramagnetic shifts was also investigated. From the analysis of the shifts at pD = 6.5 and from the INDO MO calculations on selected models of dopamine radicals, a dominant σ delocalization mechanism of the spin density is proposed. From the spin distribution on the ligand carbon atoms, the metal centered as well as the ligand centered dipolar contributions of the modified Solomon—Bloembergen equation were calculated and an estimate of the correlation time τ c was given.

The theory of the Fe2+–Fe3+ electron exchange in water

The rate constant for the Fe2+–Fe3+ electron exchange is formulated as k23= ∫ 0∞g23(r) k̂23(r) 4πr2 dr, a form which also is used to analyze the data for the nuclear spin relaxation in Al3+ induced by collision with Ni2+. It is assumed that the equilibrium pair correlation function g23(r) is the same function of ionic composition and temperature in the two cases and that in the spin relaxation process the local rate constant k̂23(r) has the form that may be deduced from the Solomon–Bloembergen equations. In the case of the exchange reaction the theory of k̂23(r) is developed with respect to the contributions from slow inner shell or outer shell reorganization (activation) dynamics. It is concluded that in the present case these complications are not important and that the controlling dynamics is the crossing from the reactant to the product diabatic Born– Oppenheimer surface. Neither the exchange nor the spin relaxation data can be accounted for if the smallest metal–metal distance in collisions is that given by the closest approach of the envelopes of the M(H2O)6n+ complexes. However, allowing for overlap of the envelopes as one complex pokes into the interstices of the other reduces the distance of closest approach from 6.9 to 4.5 Å. Then one can find Gurney type models for the ion–ion forces in solution such that the model calculations are in good agreement with the experimental exchange and relaxation rate constants and their dependence on temperature and ionic strength, as far as the limited data for the last allow.

Applicability of the Solomon-Bloembergen equation to the study of paramagnetic transition metal-water complexes. An ab initio SCF-MO study

Applicability of the Solomon-Bloembergen equation to the study of paramagnetic transition metal-water complexes. An ab initio SCF-MO study

A nonempirical SCF–MO study of the validity of the Solomon–Bloembergen equation for the hexa-aquonickel (II) ion

Nonempirical SCF–MO calculations of the effective distance between the ligand nuclei and the unpaired electron spins in the triplet ground state (3Ag) of the hexa-aquonickel (II) ion are presented and the validity of the point dipole approximation in the Solomon–Bloembergen equation is discussed. The calculations show that the effective distance between the oxygen atom and the unpaired electron is significantly shorter than the internuclear oxygen–nickel distance. For the case of the hydrogen atom, the point dipole approximation functions very well. Calculations of the isotropic hyperfine coupling constants are also reported.

Interactions of some nitrogen, oxygen, and sulphur heterocycles with gadolinium and nickel chelates. A carbon-13 nuclear magnetic resonance spin–lattice relaxation study

Electron–nuclear spin–lattice relaxation times for 13C in natural abundance are determined for six saturated and aromatic heterocyclic compounds containing nitrogen, oxygen, and sulphur in the presence of the metal chelates [Gd(tmhd)3] and [Ni(tmhd)2](tmhd = 2,2,6,6-tetramethylheptane-3,5-dionate). The measurements provide evidence of complex formation between [Gd(tmhd)3] and pyrrolidine and tetrahydrofuran, and between [Ni-(tmhd)2] and pyrrolidine, tetrahydrofuran, and tetrahydrothiophen. The relative affinities of the metal chelates for different ligands have been studied in a series of competition experiments, yielding the affinity order N > O > S for [Gd(tmhd)3] and N > O ≈ S for [Ni(tmhd)2]. For the case of [Ni(tmhd)2] complexes it is found that the relaxation rates deviate largely from the predictions of the Solomon–Bloembergen equation. Comparisons with contact shifts are employed in order to rationalize these deviations.

EPR relaxations of aqueous Ni2+ ion

The experimental data for proton NMR relaxation and shifts in aqueous Ni2+ solutions at 25°C have been extended, especially to high fields (8.4 T). Infinite-order perturbation theory for the EPR relaxation in the Ni2+ and a generalized set of Solomon–Bloembergen equations for the proton–electron spin–spin interaction are applied to deduce the rms value Δ and the correlation time τv for the tensor D(t) in the zero field splitting or SDS term of the electron spin Hamiltonian. Both the Brownian rotation of the Ni(H2O)62+, with correlation time τϑ, and the mean lifetime τp of protons in this complex, before exchanging with the bulk, are very important in determining the functional relation of the proton relation times and shift to the corresponding EPR quantities. The best fit of the theory to the data implies the following values for the parameters for assumed values τϑ=25 psec and τp=32 μsec: Δ=2.6 cm−1, τv=2.2 psec, TlS=T2S=2.9 psec at zero magnetic field, proton contact shift in the complex=14 ppm, proton dynamical shift in the complex at zero field=2.1 ppm. The proton dynamical shift is a second-order effect in the dipolar electron–proton spin–spin interaction. The discussion includes the comparison of some of these parameters with earlier determinations as well as a summary of additional effects that might be included in a more realistic model.

A magnetic resonance study of the coenzyme A--manganese(II) complex in solution.

Proton and 31P magnetic resonance experiments were employed in the study of the weak, stoichiometric, one-to-one complex that is formed between coenzyme A and manganese-(II). The distances in solution between the three phosphorus atoms and the manganese(II) ion are obtained at 287 K and at 298 K. The experiments are carried out over a pH range of 6.3 to 7.7. The correlation time τc of the water molecules bound to the Mn(II) ion in the CoA–Mn(II) complex was calculated using the Solomon–Bloembergen equation from the T1M value obtained for the water protons for solutions where most of the Mn(II) ions are complexed. Paramagnetic spin-lattice relaxation rates for all three phosphorus atoms in the CoA molecule were obtained using proton decoupled Fourier transform 31P nmr techniques. For most probable values of two or three water molecules in the CoA–Mn(II) complex, the distances between the manganese (II) ion and the three phosphorus nuclei are 4.0 ± 0.4 Å (1 Å = 0.1 nm) or 3.7 ± 0.4 Å respectively for 0.062 M CoA solutions. For experiments carried out on 0.010 M CoA, a correlation time which has been determined previously for propionyl CoA was used for the distance calculations and the distances remain unchanged within experimental error. These results indicate that the Mn(II) ion coordinates equally with the oxygens of the three phosphate groups in the CoA–Mn(II) complex.

31P NMR spectra of paramagnetic MBr 2 (OPPh 3) 2 complexes. A breakdown in the validity of the Solomon-Bloembergen equations

31P NMR spectra of paramagnetic MBr 2 (OPPh 3) 2 complexes. A breakdown in the validity of the Solomon-Bloembergen equations

Ligand-centered 1H and 13C electron-nuclear dipolar relaxation in a Ni(II) Complex. Breakdown of the Solomon-Bloembergen equation

Ligand-centered 1H and 13C electron-nuclear dipolar relaxation in a Ni(II) Complex. Breakdown of the Solomon-Bloembergen equation

The calcium ion binding site in bovine chymotrypsin A

The effect of Gd 3+ on the nuclear magnetic resonance (nmr) relaxation rates, T 1 m −1 and T 2 m −1, of inhibitor protons in metal-inhibitor-α-chymotrypsin ternary complexes has been measured. The Solomon-Bloembergen equations were used to calculate the distance from the methyl protons of p-toluamidine (a competitive inhibitor) to the Gd 3+ binding site which is 9.2 ± 0.5 Å. Calcium ion and gadolinium ion compete for the same binding site on α-chymotrypsin. Distances from the specificity pocket of α-chymotrypsin to the metal binding site have been measured by fluorescence energy transfer experiments. By observing energy transfer between proflavine and Nd 3+, Pr 3+, or Ho 3+, we have been able to calculate a distance of approximately 10 Å between the two chromophores. This agrees well with the data obtained by nmr techniques and also gives nearly identical values to those obtained for trypsin (Darnall, D., Abbott, F., Gomez, J. E., and Birnbaum, E. R., Biochemistry 15, 5017, 1976). This is consistent with the calcium ion binding sites being composed of the same residues in both trypsin and α-chymotrypsin.