Phase-sensitive NOESY/EXSY experiments have been utilized to measure the rates of axial ligand rotation for (tetramesitylporphyrinato)iron(m) and -cobalt(III) bis(2-methylimidazole), [(TMP)Fe(2-MeImH)(2)]+ClO4- and [(TMP)Co(2-MelmH)(2)]+BF4-, and several related complexes at various low temperatures. The derivations of the expressions for EXSY cross-peak volumes (Ernst, R. R.; Bodenhausen, G.; Wokaun, A, Principles of Magnetic Resonance in One and Two Dimensions; Clarendon Press : Oxford, U.K., 1992; chapters 6 and 9) as a function of mixing time tau(m), longitudinal relaxation time T-1, and chemical exchange rate constant, k, have been extended to the case of cyclic four-site chemical exchange having a single rate constant. Cross-peak volumes were fit to the expressions, and the rate constants were calculated using a computer fitting program developed in this laboratory. The dependence of the reliability of the rate constant on T-1, tau(m), and other experimental factors is discussed. The temperature dependence of the rate constants was used to calculate the activation enthalpy and entropy for these complexes and two others, [tetrakis(2,6- dichlorophenyl)porphyrinato]iron bis(2-methylimidazole) perchlorate, [(2,6-Cl-2)(4)(TPP)Fe(2-MeImH)(2)]+ClO4- and its 2,6-dibromophenyl analog, [(2,6-Br-2)(4)(TPP)Fe(2-MelmH)(2)]+ClO4-, as well as the bis(1,2-dimethylimidazole) complexes of(TMP)Co-III. The values of Delta H-double dagger are very similar for all Fe(III) complexes (46-51 kJ/mol), and Delta S-double dagger values are close to zero. Nevertheless, the combined differences in these activation parameters led to rate constants for ligand rotation at 25 degrees C ranging from 1.1 x 10(5) (2,6-Br-2) to 1 x 10(4) (TMP) s(-1). For the [(TMP)CoL(2)]+BF4- complexes where L = 2-MeImH and 1,2-Me(2)Im, the values of Delta H-double dagger are very similar but slightly smaller than those for the low-spin Fe(m) complexes, but the values of Delta S-double dagger are rather negative (-63 and -84 J/(mol K), respectively), which lead to rate constants at 25 degrees C of 14 and 5 s(-1), respectively. The difference in Delta S-double dagger and thus the 10(3) difference in the rate constants for Fe(III) and Co(III) complexes probably indicates either steric hindrance to rotation of the 2-methyl group of the "hindered" ligand in the Co(III) complexes, where the Co-N-ax bond lengths are expected to be somewhat shorter than the corresponding Fe-N-ax bonds, or differences in solvation of the Co(III) complexes (BF4- anion) that lead to a more highly structured transition state than for those of the Fe(III) complexes (ClO4- anion). The methods developed for analysis of the EXSY data are general and could be used for any case of four-site chemical exchange with a single rate constant.