Potential shapes
****************

Setting the Verbosity to Verbose the engine prints the potential
formula and the parameters used.

The ForceField engine has a couple of potentials defined.

* Stretch: harmonic

   V^\text{stretch/harm} = \frac{1}{2} f_c (r-r_0)^2

* Angle: harmonic and cyclic

   V^\text{bend/harm} = \frac{1}{2} f_c (\phi-\phi_0)^2
   V^\text{bend/cycl} =  f_c \sum_{m=0}^n c_m \cos(m \phi)

* Torsions: cyclic, possibly linearly combined. The same torsion
  occurs more than once in the printed table, and the energies are
  added.

   V^\text{torsion/harm} = \frac{1}{2} f_c (\phi-\phi_0)^2
   V^\text{torsion/cycl} =  f_c \sum_{m=0}^n c_m \cos(m \phi)

* Inversions: either angle or distance based. The angle based one
  depends on the order of the three atoms connected to the central
  atom. UFF averages over the three permutations.

   V^\text{inversion/harm} = \frac{1}{2} f_c (\phi-\phi_0)^2
   V^\text{inversion/cycl} =  f_c \sum_{m=0}^n c_m \cos(m \phi)
   V^\text{inversion/amber} =  f_c  (1 + \cos(2 \phi- \phi_0))
   V^\text{inversion/dist} =  f_c  \; d^2

* Dispersion: Lennard-Jones. Neglect up to second neighbors, possibly
  scale contribution from third neighbors.

   V^\text{dispersion/LJ} = d \; (  (x/r)^{12} -2 * (x/r)^6 )

* Coulomb: Neglect up to second neighbors, possibly scale
  contributions from third neighbors.

In general which formula is used depends on the parameter files. Note
that the scaling of the third neighbors contributions is only possible
when using .ff parameter files.

See also: APPLE&P
