MOLECULA R PHYSICS, 1998, VOL. 95, NO. 6, 1325±1332 Multi-frequency EPR determination of zero ®eld splitting of high spin species in liquids: Gd(III ) chelates in water R. B. CLARKSON 1, 2 , ALEX I. SMIRNOV 1 , T. I. SMIRNOVA 3 , H. KANG 1, 3 , R. L. BELFORD 1, 3 , K. EARLE 4 , and JACK H. FREED 4 Departments of 1 Medical Information Science, 2 Veterinary Clinical Medicine, 3 Chemistry, and the Illinois EPR Research Center, University of Illinois, Urbana, IL 61801, USA 4 Department of Chemistry, Cornell University, Ithaca, NY 14853, USA ( Received 25 April 1998; revised version accepted 8 July 1998 ) Multi-frequency EPR spectroscopy at 9.5, 35, 94, and 249 GHz has been employed to inves- tigate the zero ®eld splitting (ZFS) of high spin ions in liquids. In particular, experiments are reported on aqueous solutions of DTPA and DOTA chelates of Gd(III), and on the uncom- plexed ion, which are relevant to the eectiveness of paramagnetic contrast agents for mag- netic resonance imaging (MRI). The ®eld dependence of the centroid of the resonance line, characterized by an eective g factor, g e, has been analysed in order to determine ¢ 2 , the trace of the square of the ZFS matrix. Analysis of the variation in transverse electron spin relaxation T 2e with experimental frequency provides yet another route to measure ¢ 2 from EPR data. This analysis also gives ¿ v , a correlation time describing the time-dependent ZFS eect. The ZFS parameters so obtained agree well with results obtained by the analysis of proton nuclear magnetic relaxation dispersion. At 94 GHz, partially resolved spectra from chelated and unchelated Gd(III) were observed. The shifts in resonance ®eld for Gd(III) in these two compounds are due primarily to dierences in the magnitude of ZFS. The spectral resolution as a function of frequency exhibits a maximum in the range of our experiments; the resolution disappeared at either higher or lower resonance frequency. Study of ZFS by EPR at multiple high ®elds oers a new and sensitive route to probe water interactions and chelate dynamics in biologically relevant systems having high spin ions. 1. Introduction As pointed out by Abragam and Bleaney [1], the ground state of the Gd(III) ion 4f 7 is nearly pure 8 S7/2, with a slight admixture of 6 P 7/2 through inter- mediate coupling. Perturbations from ligands cause a splitting of the electronic states, producing a ®ne struc- ture in the resonance spectrum that can be represented by a simpli®ed spin Hamiltonian of the form spin b B g S m , n B M n O m n , 1 where the second term describes the ®ne structure in terms of spin operators characterizing the eects of the ligand ®elds. While we may anticipate a number of higher-order terms for the 4f 7 (ground state S 7 /2) ion, the very small orbital angular momentum in this system causes terms of higher degree to become rapidly smaller [1], and for this discussion they will be neglected. In single crystals, the expansion in m , n often can be evaluated for speci®c ligand symmetries; in solutions, this term is less well de®ned, and generally is time depen- dent. Odelius, et. al. [2], discussing the analogous prob- lem for Ni(II) 3d 8 , 3F 1 , re-write the Hamiltonian as spin Zeeman ZFS b B g S S D ZFS t S , 2 where D ZFS is the time dependent zero ®eld splitting (ZFS) tensor, which describes the second-order coupling of the electron spins with the orbital angular momentum, and which removes some of the degeneracy in the spin states even in the absence of a magnetic ®eld. For many years the time dependent ¯uctuations of the ZFS term have been thought to dominate electron spin relaxation in Gd(III) systems [3±8]. Prior workers have adopted a form of Bloch±Wangsness±Red®eld (BWR) theory [9] to characterize the time dependent ¯uctua- tions of D ZFS by means of an exponentially decaying correlation function, which de®nes a correlation time ¿ v for the modulation of the ZFS. This approach requires that ¿ v T 2e , a condition which Slichter char- acterizes as not asking for information over time inter- vals comparable with ¿ v [9]. The inequality is not 0026±8976/98 $12 . 00 Ñ 1998 Taylor & Francis Ltd.