  The simplified Lennard-Jones (LJ) potential minimization problem is minimize
f(x)=4\sum_{i=1}^N \sum_{j=1,j<i}^N (\tau_{ij}^{-6} -\tau_{ij}^{-3}) subject to
x\in \mathbb{R}^n, where $\tau_{ij}=(x_{3i-2}-x_{3j-2})^2
+(x_{3i-1}-x_{3j-1})^2+(x_{3i} -x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the
coordinates of atom $i$ in $\mathbb{R}^3$, $i,j=1,2,...,N(\geq 2 \quad
\text{integer})$, $n=3N$ and $N$ is the whole number of atoms. The nonconvexity
of the objective function and the huge number of local minima, which is growing
exponentially with $N$, interest many mathematical optimization experts. The
global minimizer should be just at the point of the bottom of the LJ potential
well. Based on this point, this paper tackles this problem illuminated by
amyloid fibril molecular model building. The 3nhc.pdb, 3nve.pdb, 3nvf.pdb,
3nvg.pdb and 3nvh.pdb of PDB bank are used for the successful molecular
modeling.
