Computation of Electron Density Maps of a helical
structure
The fiber_refin-map-statement can be used to calculate
electron density maps, which can be calculated by a
Bessel-Fourier transform of ![$G$](img518.png)
:
![\begin{displaymath}
\rho (r, \phi, z) = \sum_{nlR_s} \mbox{\boldmath$G$}_{nl}(R)
2\pi R J_{n}(2\pi R r) \exp(n\phi-2\pi lz/c)i
\end{displaymath}](img520.png) |
(15.10) |
To reduce the computational time, a factorization method which is
similar to the Beevers-Lipson factorization method is applied to
the Bessel-Fourier transform. The first step is an
one-dimensional Bessel transform:
![\begin{displaymath}
\mbox{\boldmath$g$}_{nl} (r) = \sum_{R_s} \mbox{\boldmath
$G$}_{nl} (R)
2\pi R J_{n}(2\pi R r)
\end{displaymath}](img521.png) |
(15.11) |
Because the electron density map is usually rendered in the
orthogonal space, coefficient ![$g$](img522.png)
is
converted from the cylindrical space into the orthogonal space
in the Fourier transform:
The Fourier transform of ![$S$](img264.png)
in the final
step yields the electron density map:
![\begin{displaymath}
\rho (xyz) = \sum_l \mbox{\boldmath$S$}_l (xy) \exp (-2\pi lz/C)i
\end{displaymath}](img528.png) |
(15.13) |
Subsections
Xplor-NIH 2024-06-11