Subsections

Ri'(θ) Hessians

Again different second partial derivatives with respect to the spectral density function parameters θj and θk, the chemical exchange parameter ρex, CSA parameter Δσ, and bond length parameter r. These second partial derivatives are the components of the Ri'(θ) Hessian matrices.

θj - θk partial derivative

The second partial derivatives of the relaxation equations with respect to the spectral density function parameters θj and θk are

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
...{J_d^{\sigma_{\scriptscriptstyle \mathrm{NOE}}}}''.\end{align}\end{subequations}

θj - ρex partial derivative

The second partial derivatives of the relaxation equations with respect to the spectral density function parameter θj and the chemical exchange parameter ρex are

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
...}{\partial \theta_j \cdot \partial \rho_{ex}} &= 0.\end{align}\end{subequations}

θj - Δσ partial derivative

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

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
...partial \theta_j \cdot \partial \Delta\sigma} &= 0.\end{align}\end{subequations}

θj - r partial derivative

The second partial derivatives of the relaxation equations with respect to the spectral density function parameter θj and the bond length parameter r are

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
... {J_d^{\sigma_{\scriptscriptstyle \mathrm{NOE}}}}'.\end{align}\end{subequations}

ρex - ρex partial derivative

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

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{{\partia...
...mathrm{NOE}}(\theta)}{{\partial \rho_{ex}}^2} &= 0.\end{align}\end{subequations}

ρex - Δσ partial derivative

The second partial derivatives of the relaxation equations with respect to the chemical exchange parameter ρex and the CSA parameter Δσ are

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
...artial \rho_{ex} \cdot \partial \Delta\sigma} &= 0.\end{align}\end{subequations}

ρex - r partial derivative

The second partial derivatives of the relaxation equations with respect to the chemical exchange parameter ρex and the bond length parameter r are

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
...\theta)}{\partial \rho_{ex} \cdot \partial r} &= 0.\end{align}\end{subequations}

Δσ - Δσ partial derivative

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

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{{\partia...
...hrm{NOE}}(\theta)}{{\partial \Delta\sigma}^2} &= 0.\end{align}\end{subequations}

Δσ - r partial derivative

The second partial derivatives of the relaxation equations with respect to the CSA parameter Δσ and the bond length parameter r are

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{\partial...
...eta)}{\partial \Delta\sigma \cdot \partial r} &= 0.\end{align}\end{subequations}

r - r partial derivative

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

\begin{subequations}\begin{align}\frac{\partial^2 \mathrm{R}_1(\theta)}{{\partia...
...d'' J_d^{\sigma_{\scriptscriptstyle \mathrm{NOE}}}.\end{align}\end{subequations}

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