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Coulomb restraint


$\displaystyle c$ $\textstyle =$ $\displaystyle \frac{q_i q_j}{f} s(f,f_1,f_2)$ (7.58)
$\displaystyle s(f,f_1,f_2)$ $\textstyle =$ $\displaystyle \left\{ \begin{array}{ll} 1 \; ;
& f \leq f_1 \\
\frac{(f_2 - f)...
...f_2-f_1)^3}\; ;
& f_o < f \leq f_2 \\
0 \; ;
& f > f_2 \\
\end{array} \right.$ (7.59)

where $q_i$ and $q_j$ are the atomic charges of atoms $i$ and $j$, obtained from the CHARMM topology file, that are at a distance $f$. Function $s(f,f_1,f_2)$ is a switching function that smoothes the potential down to zero in the interval from $f_1$ to $f_2$ ($f_2> f_1$). The total Coulomb energy of a molecule is a sum over all pairs of atoms that are not in the same bonds or bond angles. 1-4 energy for the 1-4 atom pairs in the same dihedral angle corresponds to the ELEC14 MODELLER term; the remaining longer-range contribution corresponds to the ELEC term.

The first derivatives are:

$\displaystyle \frac{ \; {d}c}{ \; {d}f}$ $\textstyle =$ $\displaystyle -\frac{c}{f} + \frac{c}{s} \frac{ \; {d}s}{ \; {d}f}$ (7.60)
$\displaystyle \frac{ \; {d}s}{ \; {d}f}$ $\textstyle =$ $\displaystyle \left\{ \begin{array}{ll} 0 \; ;
& f \leq f_1 \\
\frac{6 (f_2-f)...
..._2-f_1)^3} \; ;
& f_1 < f \leq f_2 \\
0 \; ;
& f > f_2 \\
\end{array} \right.$ (7.61)


next up previous contents index
Next: Lennard-Jones restraint Up: Restraints and their derivatives Previous: Cosine restraint   Contents   Index
Bozidar BJ Jerkovic 2001-12-21