Per-Olof Westlund

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...

NMR lineshapes of I = 52 and I = 72 nuclei. Chemical exchange effects and dynamic shifts

Abstract Analytical expressions for NMR lineshapes of spin - 5 2 and - 7 2 nuclei are derived assuming quadrupolar relaxation and nonextreme narrowing conditions. The effects of both chemical exchange and dynamic shifts are included in the description. Also a fourth-order quadrupolar contribution to the relaxation is briefly discussed. The results are analyzed for some typical sets of parameters. It is found that the dynamic shifts can be substantial and sometimes account for experimentally observed shifts. In an intermediate range of correlation times the signal is slightly asymmetric. The linewidth at half-height Δν 1 2 , has a broad maximum as the correlation time is varied from long times to the extreme narrowing limit. With chemical exchange effects contributing to the transverse relaxation the behavior of Δν 1 2 is more complex. In general Δν 1 2 is less sensitive to the exchange rate than for a nucleus with an exponential relaxation in each site.

A study of vibrational dephasing of the A 1 modes of CH3CN in a computer simulation of the liquid phase

The vibrational dephasing of the four A 1 modes of CH3CN has been calculated for a simulation of the liquid phase at 288 K assuming that it is caused by generalized forces interacting with the cubic anharmonicities of each mode. The forces along each mode were resolved into electrostatic and Lennard-Jones components and the mean values, probability distributions and time autocorrelation functions were calculated. Line shifts in the liquid state were evaluated from the mean values. Line shapes are related to the shift-shift time correlation functions and hence to force-force correlation functions using the cumulant approximation. This was found to be a good approximation and the vibrational correlation functions (Fourier transforms of the line shapes) were computed using two sets of anharmonicity constants. The time scale of the shift fluctuations was never slow, so that the line shapes are nearly lorentzian in this model.

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...

Proton spin―lattice relaxation in aqueous solution of the nickel(II) ion

Abstract Spin-lattice relaxation rates for water protons in the presence of paramagnetic Ni(II) ions at high temperatures and low pH are reported as a function of the magnetic field up to 11.7 T. The data are analyzed using the conventional modified Solomon-Bloembergen equations and a theoretical model allowing for the slow-motion situation for the electron spin. The latter model is shown to describe the experimental data with a somewhat more reasonable set of parameters.

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.

The effects of pressure and temperature on vibrational dephasing in a simulation of liquid CH3CN

A principal cause of vibrational dephasing in molecules in liquids is the interaction of the components of intermolecular forces along normal modes with cubic anharmonicities. The amplitude and dynamics of the fluctuations in the forces along the two normal modes of CH3CN were compared for simulations of the liquid state at different densities and at different temperatures. In all cases the modes were homogeneously broadened. There are considerable differences in the amplitude and dynamics of the fluctuations in the forces along the two normal modes which can be attributed to the relative importance of the repulsive and electrostatic parts of the intermolecular forces. Comparisons are made with the predictions of isolated binary collision and density fluctuation theories for vibrational dephasing, as well as with published experimental data.

The effects of higher rank multipoles on relaxation measurements in isotropic high spin systems

Abstract The nuclear spin relaxation in isotropic spin systems with I = 3 2 , I = 5 2 , and I = 7 2 in the nonextreme narrowing regime is analyzed. The effect of the higher rank multipoles (rank ⩾3) of the spin density operator on a 180°-τi-Θ pulse experiment is twofold. The recorded NMR lineshape is τ1 and φ dependent. The multiexponentiality of the spin-lattice relaxation may be exaggerated by recording the amplitudes of the Lorentzian-like signals, instead of the full integrated signal. The influence of the detection pulse angle φ is discussed and we suggest that by choosing the detection angle φ = 63° the effects of the higher multipoles may be diminished.

Spin-lattice relaxation of a Spin-12 nucleus coupled to a quadrupolar spin-1 nucleus. The quadrupolar dip

Abstract A general theoretical formalism is presented for the discription of the so-called quadrupolar dip or the quadrupolar Zeeman cross-relaxation. We specifically apply the formalism to the problem of spin-lattice dipolar relaxation of a I = 1 2 nucleus coupled to a quadrupolar nucleus S = 1. The system is assumed to undergo isotropic rotational diffusion, and an expression for T1I is obtained over the motional regime, where the dipole-dipole interaction is motionally narrowed with no restrictions on the strength of the quadrupolar interaction. It is specifically shown how the dip in the relaxation time appears as the reorientational motion slows down. Furthermore, it is demonstrated that when the magnetogyric ratio for the S nucleus rises above the value for the I nucleus, the dip in the relaxation time disappears.