Analytical Expression for the Gradient

The derivative of $I_{ij}^{c}$ with respect to a coordinate $\mu$ (Eq. 12 of Yip and Case 1989) can be written as
{\bf\nabla}_{\mu} I_{ij}^{c} =
{\bf\nabla}_{\mu}[\exp(- {\bf...
...({\bf\nabla}_{\mu}{\bf R}) {\bf L} {\bf F}^{(ij)} {\bf L}^{T}]
\end{displaymath} (39.7)

where ${\bf F}^{(ij)}$ is defined as
{\bf F}_{ru}^{(ij)} \equiv
- {\...
...}^{T} \exp(-\lambda_{r} \tau) &\mbox{else}
\end{displaymath} (39.8)

L and ${\bf\Lambda}$ are the matrix of eigenvectors and eigenvalues of R, respectively. $\lambda_{r}$ is the rth eigenvalue of the relaxation matrix.

Xplor-NIH 2023-11-10