Subsections

The weights of the ellipsoid

Definitions

The three direction cosines defining the XH bond vector within the diffusion frame are

\begin{subequations}\begin{align}\delta_x &= \widehat{XH} \cdot \widehat{\mathfr...
..._z &= \widehat{XH} \cdot \widehat{\mathfrak{D}_z}. \end{align}\end{subequations}

Let the set of geometric parameters be

$\displaystyle \mathfrak{G}= \{\mathfrak{D}_{iso}, \mathfrak{D}_a, \mathfrak{D}_r\},$ (15.112)

and the set of orientational parameters be the Euler angles

$\displaystyle \mathfrak{O}= \{\alpha, \beta, \gamma\}.$ (15.113)

The weights

The five weights ci in the correlation function of the Brownian rotational diffusion of an ellipsoid (15.132) are

\begin{subequations}\begin{align}c_{-2} &= \tfrac{1}{4}(d - e),\\ c_{-1} &= 3\de...
...elta_x^2\delta_y^2,\\ c_{2} &= \tfrac{1}{4}(d + e),\end{align}\end{subequations}

where

d = 3$\displaystyle \left(\vphantom{ \delta_x^4 + \delta_y^4 + \delta_z^4 }\right.$δx4 + δy4 + δz4$\displaystyle \left.\vphantom{ \delta_x^4 + \delta_y^4 + \delta_z^4 }\right)$ - 1, (15.115)
e = $\displaystyle {\frac{{1}}{{\mathfrak{R}}}}$$\displaystyle \bigg[$(1 + 3$\displaystyle \mathfrak{D}_r) \left(\delta_x^4 + 2\delta_y^2\delta_z^2\right) +...
...^2\delta_z^2\right) - 2 \left(\delta_z^4 + 2\delta_x^2\delta_y^2\right) \bigg].$ (15.116)

The factor $ \mathfrak{R}$ is defined as

$\displaystyle \mathfrak{R} = \sqrt{1 + 3\mathfrak{D}_r^2}.$ (15.117)

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