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Lennard-Jones restraint

Usually used for non-bonded distances:

\begin{displaymath}
c = \left[(\frac{A}{f})^{12} - (\frac{B}{f})^6 \right] s(f,f_1,f_2)
\end{displaymath} (7.62)

The parameters $f_1$ and $f_2$ of the switching function can be different from those in Eq. 5.59. The parameters $A$ and $B$ are obtained from the CHARMM parameter file (NONBOND section) where they are given as $E_i$ and $r_j$ such that $E_{ij}(f) = -4
\sqrt{E_i E_j} [(\rho_{ij}/f)^{12} - (\rho_{ij}/f)^6]$ in kcal/mole for $f$ in angstroms and $\rho = (r_i + r_j)/2^{1/6}$; the minimum of $E$ is $-\sqrt{E_i E_j}$ at $f=(r_i + r_j)$, and its zero is at $f=\rho$. The total Lennard-Jones energy should be evaluated over all pairs of atoms that are not in the same bonds or bond angles. The parameters $A$ and $B$ for 1-4 pairs in dihedral angles can be different from those for the other pairs; they are obtained from the second set of $E_i$ and $r_i$ in the CHARMM parameter file, if it exists. 1-4 energy corresponds to the LJ14 MODELLER term; the remaining longer-range contribution corresponds to the LJ term.

The first derivatives are:

$\displaystyle \frac{ \; {d}c}{ \; {d}f}$ $\textstyle =$ $\displaystyle \frac{C s}{f} - C \frac{ \; {d}s}{ \; {d}f}$ (7.63)
$\displaystyle C$ $\textstyle =$ $\displaystyle -12 (\frac{A}{f})^{12} + 6 (\frac{B}{f})^6$ (7.64)


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