Electron Spin Lattice Relaxation Rates for S = 1 2 Molecular Species in Glassy Matrices or Magnetically Dilute Solids at Temperatures between 10 and 300 K Yi Zhou, Bruce E. Bowler, Gareth R. Eaton, and Sandra S. Eaton Department of Chemistry and Biochemistry, University of Denver, Denver, Colorado 80208 Received December 30, 1998; revised March 12, 1999 The temperature dependence of X-band electron spin–lattice relaxation between about 10 and 300 K in magnetically dilute solids and up to the softening temperature in glassy solvents was analyzed for three organic radicals and 14 S  1 2 transition metal complexes. Contributions from the direct, Raman, local vibra- tional mode, thermally activated, and Orbach processes were con- sidered. For most samples it was necessary to include more than one process to fit the experimental data. Debye temperatures were between 50 and 135 K. For small molecules the Debye temperature required to fit the relaxation data was higherin 1:1 water:glycerol than in organic solvents. For larger molecules the Debye temper- ature was less dependent upon solvent and more dependent upon the characteristics of the molecule. The coefficients of the Raman process increased with increasing g anisotropy and decreasing rigidity of the molecule. For the transition metal complexes the data are consistent with major contributions from local modes with energies in the range of 185 to 350 K (130 to 240 cm 1 ). The coefficient for this contribution increases in the order 3d < 4d transition metal. For C 60  anions there is a majorcontribution from a thermally activated process with an activation energy of about 240 cm 1 . For low-spin hemes the dominant contribution at higher temperatures is from a local mode orthermally activated process with a characteristic energy of about 175 cm 1 . © 1999 Academic Press Key Words: Debye temperature;electron spin–lattice relaxation; local vibrational mode; Orbach process; Raman process; thermally activated process; transition metal. INTRODUCTION Electron spin relaxation rates reflect electronic structures of paramagnetic species and the dynamics of these species and their environment. Quantitative measures of electron spin re- laxation rates as a function of temperature for transition metals in molecular complexes and for organic radicals are required to interpret the effect of a more rapidly relaxing spin on the relaxation rate for a more slowly relaxing spin and thereby determine the distance between the two paramagnetic centers (1, 2). Thus, we seek to understand the relaxation processes that occur for molecular species in doped solids and in glassy solvents at temperatures between about 10 K and the softening temperature of the glass. Much of the classical work on electron spin–lattice relax- ation processes was performed on ions in ionic lattices and at temperatures below about 20 K (3, 4). We are aware of only a few cases in which processes have been characterized over a wider temperature range. Castle and Feldman (5, 6) analyzed relaxation rates for the E' defect in crystalline and vitreous quartz between 4.2 and about 250 K in terms of the direct process and two local modes. The relaxation for atomic hydro- gen in fused silica between 2 and 100 K could be modeled with either an Orbach process or a local mode (7). The data for atomic hydrogen in fused silica demonstrate that the similarity in temperature dependence predicted by some relaxation pro- cesses within limited temperature intervals requires that assign- ments be based not only on the temperature dependence of the relaxation rates, but also on the plausibility of the parameters obtained by fitting to various models. Hoffmann et al. (8) analyzed spin–lattice relaxation for Cu(II) in triglycine selenate between 4.2 and 90 K in terms of the direct process and the Raman process with a Debye temperature of 168 K. Gayda et al. (9) studied spin–lattice relaxation for a 2-iron–2-sulfur protein between 1.25 and 130 K. To fit the data several pro- cesses were required: below 3 K a phonon bottleneck, between about 3 and 30 K the Raman process, and near 100 K an Orbach process. Since the predicted temperature dependence of spin lattice relaxation (1/ T 1 ) is the same for the Orbach and local mode processes in the temperature range for which data were available, assignment of the relaxation processes required information beyond the EPR studies (10). These limited exam- ples suggest that more than one relaxation process may be required to fit the temperature dependence of electron spin– lattice relaxation between 10 K and the softening point of a glass. It has been proposed that modulation of nuclear hyperfine splitting contributes to electron 1/ T 1 (11). However, the fol- lowing observations have been made for magnetically dilute S = 1 2 species in the temperature range of about 30 to 150 K. For nitroxyl radicals in glassy solutions, 1/ T 1 is the same within experimental uncertainty for natural abundance and 15 N-enriched samples (12). For a chromium(V) complex in 1:1 Journal of Magnetic Resonance 139, 165–174 (1999) Article ID jmre.1999.1763, available online at http://www.idealibrary.com on 165 1090-7807/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.