Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field

Abstract

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.

Quadrupole-enhanced proton spin relaxation for a slow reorienting spin pair: (I)–(S). A stochastic Liouville approach

“…Several experimental studies of 1 H NMRD profiles obtained for different paramagnetic systems have been reported [12]- [15], and various computational methods have been developed to describe these systems [16]- [19].…”

Multiple‐Frequency and Variable‐Temperature EPR Study of Gadolinium(III) Complexes with Polyaminocarboxylates: Analysis and Comparison of the Magnetically Dilute Powder and the Frozen‐Solution Spectra

“…While the molecular factors influencing (1) and (2) are rather well understood [2][3][4][5] , the electronic spin relaxation of Gd(III) complexes relevant for MRI remains the subject of much discussion [6][7][8][9][10][11][12][13][14][15] .…”

Joint analysis of ESR lineshapes and 1H NMRD profiles of DOTA-Gd derivatives by means of the slow motion theory

“…The three NMRD models compared above 33 are based on the same description of the ZFS interactions. The ZFS coupling is split into a permanent (static) part modulated by the molecular tumbling and a fluctuating (transient) part varying in time mostly by the distortional (vibrational) motion of the complex.…”

“…In this context, one should mention somewhat different implementations of the slow motion theory, SLE-L, (stochastic Liouville equation in Langevin form) presented by Åman and Westlund. 31,32 Predictions of the slow motion theory 30 were recently compared 33 with two other treatments, referred to as the Grenoble, 21,34 and Ann Arbor approaches, [35][36][37] respectively. It was found that the "Swedish slow motion theory" and the Grenoble approach agreed very well with each other, while some discrepancies were observed when compared to the Ann Arbor method, which was explained by a somewhat different description of the electron spin dynamics.…”