The model-free gradient of the original spectral density function (15.62) is the vector of partial derivatives of the function with respect to the geometric parameter
, the orientational parameter
, the order parameter *S*^{2}, and the internal correlation time *τ*_{e}.
The positions in the vector correspond to the model parameters which are being optimised.

The partial derivative of (15.62) with respect to the geometric parameter is

The partial derivative of (15.62) with respect to the orientational parameter is

= τ_{i} + . |
(15.63) |

The partial derivative of (15.62) with respect to the order parameter *S*^{2} is

= c_{i}τ_{i} - . |
(15.64) |

The partial derivative of (15.62) with respect to the correlation time *τ*_{e} is

= (1 - S^{2})c_{i}τ_{i}^{2}. |
(15.65) |

The relax user manual (PDF), created 2016-10-28.