Calculating NMR paramagnetic relaxation enhancements without adjustable parameters: the spin‐3/2 complex Cr(III)(AcAc)₃

Abstract

NMR paramagnetic relaxation enhancement (NMR-PRE) produced by the electron spin S = 3/2 complex Cr(III)(acac) 3 (acac = acetylacetonato) has been simulated by spin dynamic (SD) simulation methods in order to test current theory of NMR-PRE. This system provides a particularly demanding test of theory, since the Zeeman and zero field splitting (zfs) contributions to the electron spin Hamiltonian are of comparable magnitude in the range of magnetic field variation of the data, and Brownian reorientation of both the zfs tensor and the interspin vector play important roles in the relaxation mechanism. For Cr(III)(acac) 3 , all of the sensitive parameters of theory were known from independent experiments, so that a calculation was possible without variation of parameters. The

Electron spin relaxation due to reorientation of a permanent zero field splitting tensor

“…When a permanent zfs interaction is present, however, H S (t) and the spin wavefunctions are timedependent, which introduces considerable complexity into the theory. The SD simulation methods described above 27,30,33,35 and the stochastic Liouville formalism developed in Sweden 36 -39 can be used in the general situation.…”

“…͑2͒. 30,45,46 This procedure is intended to describe the motion of the interspin vector r ជ IS while neglecting the motion of H S (t). The approach is attractive in that it permits relatively rapid and simple calculations of the NMR-PRE while accounting in part for both the zfs interaction and reorientational motion.…”

“…The approach is attractive in that it permits relatively rapid and simple calculations of the NMR-PRE while accounting in part for both the zfs interaction and reorientational motion. Prior work 30,44 has indicated that these contributions are substantial.…”

Four complementary theoretical approaches for the analysis of NMR paramagnetic relaxation

“…Spin dynamics simulations [20][21][22] evaluate the TCF of Eq. (14) in the time domain as an ensemble average of Brownian trajectories of the spin motion, using the hamiltonian of Eq.…”

“…This paper describes four theoretical approaches currently used at Michigan to analyze NMR paramagnetic relaxation enhancement. These are: (1) spin dynamics (SD) simulation [20][21][22], (2) the ''constant H S '' LF (laboratory frame) formulation, (3) the ''constant H S '' MF (molecular frame) formulation, and (4) the ''constant H S '' zfs-limit formulation [5]. These four formulations are implemented in a computer program, Parelax2, which has evolved from an earlier program, Parelax [23].…”