Nikolas P. Benetis

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...

Paramagnetic proton nuclear magnetic relaxation in the Ni2+ hexa-aquo complex

The nuclear magnetic relaxation of the protons in the Ni2+(H2O)6 complex is analysed using a previously developed formalism (Benetis et al. 1983, Molec. Phys., 48, 329) for the description of paramagnetic nuclear spin relaxation in systems with a complex electron spin relaxation. The nuclear spin relaxation can be described within the Redfield theory and the transverse relaxation rate is expressed in terms of a spectral density K 1, -1(ωI), which is the Fourier-Laplace transform of a complex correlation function. In the Ni2+(H2O) complex the electron spin relaxation is caused by the zero field splitting (ZFS) and to evaluate the correlation function it is necessary to specify the dynamics of the ZFS. Three models are considered for this motion: (i) modulation of the ZFS by quantized vibrations, (ii) a classical pseudo-rotation of the ZFS at constant amplitude and (iii) a classical motion of the ZFS in an harmonic potential governed by the Smoluchowski equation.

Dipole-dipole nuclear spin relaxation: A cross correlation correction to the Solomon-Bloembergen equation forT2

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 n...

Nuclear spin-lattice and spin-spin relaxation in paramagnetic systems in the slow-motion regime for the electron spin. III. Dipole-dipole and scalar spin-spin interaction for S = 32 and S = 52

Abstract The theory for nuclear spin relaxation in paramagnetic complexes, where the electron spin relaxation is allowed to be in the slow-motion regime, [Mol. Phys. 48, 329 (1983)] is generalized to spin states of multiplicity higher than triplet. Numerical calculations of nuclear spin-spin and nuclear spin-lattice relaxation rates are reported for electron spin systems ( S = 3 2 , S = 5 2 ), coupled to the nuclear spin system via dipole-dipole and scalar spin-spin interaction. Analogous to the S = 1 case, in the region when the zero-field splitting interaction is larger than the electron Zeeman interaction, the spectral densities show qualitatively different behavior than that described by the Solomon-Bloembergen (SB) theory. Furthermore, the spectral densities show an additional structure, a “soft plateau,” compared to the S = 1 case. This extra structure is a characteristic feature for half-integer electron spin systems ( S ⩾ 3 2 ). It is shown that this structure is mainly due to the lifting of the Kramers degeneracy of the |S ± 1 2 〉 level. The results show that the interference spectral density at zero frequency K0,0DD-SC(0), i.e., the contribution to the nuclear spin-spin relaxation due to the interference term when both dipole-dipole and scalar coupling are present, does not vanish in the Redfield region for the electron spin system.

Nuclear spin relaxation in paramagnetic systems (S = 1) in the slow-motion regime for the electron spin. II. The dipolar T2 and the role of scalar interaction

The previously presented theory (Mol. Phys. 48, 329 (1983)) for the dipolar contribution to the spin-lattice relaxation in paramagnetic systems is extended. The theory, which allows the electron spin relaxation to be in the slow motion regime, is generalized to cover both the longitudinal and the transverse relaxation and to include both the dipole-dipole (DD) and the scalar interaction in the Hamiltonian coupling the nuclear spin to the lattice. The lattice is described in terms of the electron Zeeman interaction, a zero-field splitting (ZFS) of cylindrical symmetry and the isotropic rotational diffusion. It is shown that the spectral densities at the nuclear Larmor frequency and at zero frequency consist of three terms. Besides the usual DD and scalar components, a cross-term is shown to contribute to nuclear spin relaxation rates for certain parameter ranges. In the absence of exchange, the numerical calculations for S = 1 show that the DD and cross term spectral densities at zero frequency are independent of the magnetic field and the ZFS parameter. This is traced to the cross correlation between the DD and ZFS interactions. A formal way to include chemical exchange in the model is sketched. The effect of including exchange is that the DD-ZFS cross correlation is reduced.

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

Abstract 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.

Conformation and Bioactivity. Design and Discovery of Novel Antihypertensive Drugs

Peptidomimitism is applied to the medicinal chemistry in order to synthesize drugs that devoid of the disadvantages of peptides. AT1 antagonists constitute a new generation of drugs for the treatment of hypertension designed and synthesized to mimic the C-terminal segment of Angiotensin II and to block its binding action on AT1 receptor. An effort was made to understand the molecular basis of hypertension by studying the conformational analysis of Ang II and its derivatives as well as the AT1 antagonists belonging to SARTANs class of molecules. Such studies offer the possibility to reveal the stereoelectronic factors responsible for bioactivity of AT1 antagonists and to design and synthesize new analogs. An example will be given which proves that drugs with better pharmacological and financial profiles may arise based on this rational design.

Intramolecular dynamics of the C4H8NH radical cation. An application of the anisotropic exchange theory for powder ESR lineshapes

Abstract The temperature variation of ESR spectra attributed to the heterocyclic radical cation C4H8NH+ stabilised in a CFCl3 matrix is shown to be due to intramolecular dynamics of the ring. Two new methods for simulating anisotropic exchange broadened ESR spectra, the secular and nonperturbative, were utilised to investigate the dynamics of C4H8NH+. The powder ESR lineshape exhibits overall anisotropic features and a differentiated broadening with respect to the nuclear spin quantum numbers, which could be explained by simultaneously including the g- and hyperfine tensor anisotropies in the model for the dynamical motion. The motion was described by an interconversion of the ring between two isodynamic twisted structures having C2 symmetry. It was concluded that the major changes of the ESR lineshape were governed by the exchange of the isotropic hyperfine coupling constants. The anisotropic interactions were shown to account for the overall anisotropic features and the differentiated broadening of the spectra.

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

Abstract 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 T1 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.

Theoretical comparison and experimental test of the secular and nonperturbative approaches on the ESR lineshapes of randomly oriented, anisotropic systems undergoing internal motion

Abstract The nuclear Zeeman and the electronic nonsecular parts of the spin Hamiltonian complicate the ESR lineshape of exchanging anisotropic spin systems by introducing, at high field, “forbidden” transitions and, at low field, additional shift and splitting. We compare the nonperturbative with the secular approach for such systems. The exchange is treated within the Kaplan-Alexander limit and both A and g tensors are included, resulting in spectrum asymmetry, in contrast to previous separate treatments. The two approaches are then used to simulate the powder spectrum of OCH 2 COO − and compare the results to experimental spectra of an irradiated powder of ZnAc. The powder X-band spectra simulations using the secular approach appear to be accurate. For both the low-field (20 to 200 G) and the high-field (Q-band) regions, however, the nonsecular part of the electronic term and the nuclear Zeeman term, respectively, cannot be neglected. On the other hand, the approximate approach is much faster and consequently more appropriate for treating large, multisite exchanging systems.