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From the Modelfree4 manual:
{{quote|text='''Modelfree''' (version 4.0) is a program to fit the extended model free spectral density function to NMR spin relaxation data. The program can analyze the spin-lattice relaxation rate constant ({{:R1}}), the spin-spin relaxation rate constant ({{:R2}}), and the heteronuclear steady -state {1H}-X nuclear Overhauser effect (NOE) for any combination of <sup>13</sup>C and <sup>15</sup>N spins at up to five static magnetic fields. The algorithm assumes dipolar and chemical shift anisotropy (CSA) relaxation mechanisms for {{:R1}}, {{:R2}}, and the NOE and includes an additive term to account for chemical exchange broadening of {{:R2}}. The exchange broadening parameter is scaled quadratically with respect to the static magnetic field if data for more than one field is available. Descriptions of the main principles utilized in the program for model selection, optimization and error analysis using Monte Carlo simulations have been published previously (Palmer et al., 1991; Mandel et al., 1995).
'''Modelfree''' incorporates three models for rotational diffusion. Brent's method is used to optimize a single global {{:tau_m}} for an isotropic overall diffusion model. Either Powell's method (as implemented by Brent) or a simulated annealing protocol (based on the downhill simplex method) is used to optimize a global rotational diffusion tensor for an axially symmetric diffusion model. A local rotational correlation time, τ<sub>mi</sub>, for each spin can be optimized by non-linear least squares regression.
