Subsections

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 S2, and the internal correlation time τe. The positions in the vector correspond to the model parameters which are being optimised.

### partial derivative

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

### partial derivative

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

 = τi + . (15.63)

### S2 partial derivative

The partial derivative of (15.62) with respect to the order parameter S2 is

 = ciτi - . (15.64)

### τe partial derivative

The partial derivative of (15.62) with respect to the correlation time τe is

 = (1 - S2)ciτi2. (15.65)

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