Subsections

Ri'(θ) gradients

A different partial derivative exists for the spectral density function parameter θj, the chemical exchange parameter ρex, CSA parameter Δσ, and bond length parameter r. In model-free analysis the spectral density parameters include both the parameters of the diffusion tensor and the parameters of the various model-free models.

θj partial derivative

The partial derivatives of the relaxation equations with respect to the spectral density function parameter θj are

\begin{subequations}\begin{align}\frac{\partial \mathrm{R}_1(\theta)}{\partial \...
... {J_d^{\sigma_{\scriptscriptstyle \mathrm{NOE}}}}'.\end{align}\end{subequations}

ρex partial derivative

The partial derivatives of the relaxation equations with respect to the chemical exchange parameter ρex are

\begin{subequations}\begin{align}\frac{\partial \mathrm{R}_1(\theta)}{\partial \...
...le \mathrm{NOE}}(\theta)}{\partial \rho_{ex}} &= 0.\end{align}\end{subequations}

Δσ partial derivative

The partial derivatives of the relaxation equations with respect to the CSA parameter Δσ are

\begin{subequations}\begin{align}\frac{\partial \mathrm{R}_1(\theta)}{\partial \...
...\mathrm{NOE}}(\theta)}{\partial \Delta\sigma} &= 0.\end{align}\end{subequations}

r partial derivative

The partial derivatives of the relaxation equations with respect to the bond length parameter r are

\begin{subequations}\begin{align}\frac{\partial \mathrm{R}_1(\theta)}{\partial r...
... d' J_d^{\sigma_{\scriptscriptstyle \mathrm{NOE}}}.\end{align}\end{subequations}

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