A general approach to the electronic spin relaxation of Gd(III) complexes in solutions. Monte Carlo simulations beyond the Redfield limit

The time correlation functions of the electronic spin components of a metal ion without orbital degeneracy in solution are computed. The approach is b ased on the numerical solution of the time-dependent Schrodinger equation f or a stochastic perturbing Hamiltonian which is simulated by a Monte Carlo algorithm using discrete time steps. The perturbing Hamiltonian is quite ge neral, including the superposition of both the static mean crystal field co ntribution in the molecular frame and the usual transient ligand field term . The Hamiltonian of the static crystal field can involve the terms of all orders, which are invariant under the local group of the average geometry o f the complex. In the laboratory frame, the random rotation of the complex is the only source of modulation of this Hamiltonian, whereas an additional Ornstein-Uhlenbeck process is needed to describe the time fluctuations of the Hamiltonian of the transient crystal field. A numerical procedure for c omputing the electronic paramagnetic resonance (EPR) spectra is proposed an d discussed. For the [Gd(H2O)(8)](3+) octa-aqua ion and the [Gd(DOTA)(H2O)] (-) complex [DOTA=1,4,7,10-tetrakis(carboxymethyl)-1,4,7,10-tetraazacyclo d odecane] in water, the predictions of the Redfield relaxation theory are co mpared with those of the Monte Carlo approach. The Redfield approximation i s shown to be accurate for all temperatures and for electronic resonance fr equencies at and above X-band, justifying the previous interpretations of E PR spectra. At lower frequencies the transverse and longitudinal relaxation functions derived from the Redfield approximation display significantly fa ster decays than the corresponding simulated functions. The practical inter est of this simulation approach is underlined. (C) 2001 American Institute of Physics.