The weights of the spheroid


The direction cosine defining the XH bond vector within the spheroidal diffusion frame is

δz = $\displaystyle \widehat{{XH}}$$\displaystyle \widehat{{\mathfrak{D}_z}}$. (15.148)

Let the set of geometric parameters be

$\displaystyle \mathfrak{G}= \{\mathfrak{D}_{iso}, \mathfrak{D}_a\},$ (15.149)

and the set of orientational parameters be the spherical angles

$\displaystyle \mathfrak{O}= \{\theta, \phi\}.$ (15.150)

The weights

The three spheroid weights ci in the correlation function of the Brownian rotational diffusion of a spheroid (15.169) are

c_{-1} &= \tfrac{1}{4}(3\delta_z^2 - 1)^2,\\
c_{1} &= \tfrac{3}{4}(\delta_z^2 - 1)^2.\end{align}\end{subequations}

The relax user manual (PDF), created 2020-08-26.