The influence of positional errors on the Debye effects

The relation between a Gaussian perturbation of the atomic positional parameters and the average squared structure-factor amplitude is presented. Using an error-dependent radial distance distribution of an atomic protein model, it can be shown that the Debye effects diminish exponentially as a function of increasing positional errors. These relations can be used to estimate the quality of an atomic model and the corresponding phases. The limiting case of equal atoms with an infinitely large coordinate error results in the classical Wilson model.