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## The UFF implementation

The uff implementation follows the paper by Rappé [7]. The energy expression in uff is as follows:

 E UFF = ⋅KIJ⋅r - rIJ (5.1) + + ⋅Vφ⋅1 - cosnφ0cos(nφ) + Vω⋅CI0 + CI1cosω + CI2cos 2ω + DIJ⋅ -2 + +

The Fourier coefficients CA0, CA1, CA2 of the general angle terms are evaluated as a function of the natural angle θ0:

 CA2 = (5.2) CA1 = - 4⋅CA2cosθ0 (5.3) CA0 = CA22 cos2θ0 + 1 (5.4)

The expressions in the engery term are:
NB, NA, NT, NI, Nnb
the numbers of the bond-, angle-, torsion-, inversion- and the non bonded-terms.
KIJ, KIJK
forceconstants of the bond- and angle-terms.
r, rIJ
bond distance and natural bond distance of the two atoms I and J.
θ, θ0
angle and natural angle for three atoms I - J - K.
CA0, CA1, CA2
Fourier coefficients of the general angle terms.
φ, φ0
torsion angle and natural torison angle of the atoms I - J - K - L.
Vφ
height of the torsion barrier.
n
periodicity of the torsion potential.
ω
inversion- or out-of-plane-angle at atom I.
Vω
height of the inversion barrier.
CI0, CI1, CI2
Fourier coefficients of the inversions terms.
x, xIJ
distance and natural distance of two non bonded atoms I and J.
DIJ
depth of the Lennard-Jones potential.
qI, ε
partial charge of atoms I and dielectric constant.
One major difference in this implementation concerns the atom types. The atom types in Rappé's paper have an underscore "_". In the present implementation an sp3 C atom has the name "C 3" instead of "C_3". Particularly the bond terms are described with the harmonic potential and the non-bonded van der Waals terms with the Lennard-Jones potential. The partial charges needed for electrostatic nonbond terms are calculated with the Charge Equilibration Modell (QEq) from Rappé [35]. There is no cutoff for the non-bonded terms.

The relaxation procedure distinguishes between molecules wih more than 90 atoms and molecules with less atoms. For small molecules it consists of a Newton step followed by a linesearch step. For big molecules a quasi-Newton relaxation is done. The BFGS update of the force-constant matric is done [36,37,30,38]. Pulay's DIIS procedure is implemented for big molecule to accelarate the optimization [39,29].

The coordinates for any single atom can be fixed by placing an 'f' in the third to eighth column of the chemical symbol/flag group. As an example, the following coordinates specify acetone with a fixed carbonyl group:

$coord 2.02693271108611 2.03672551266230 0.00000000000000 c 1.08247228252865 -0.68857387733323 0.00000000000000 c f 2.53154870318830 -2.48171472134488 0.00000000000000 o f -1.78063790034738 -1.04586399389434 0.00000000000000 c -2.64348282517094 -0.13141435997713 1.68855816889786 h -2.23779643042546 -3.09026673535431 0.00000000000000 h -2.64348282517094 -0.13141435997713 -1.68855816889786 h 1.31008893646566 3.07002878668872 1.68840815751978 h 1.31008893646566 3.07002878668872 -1.68840815751978 h 4.12184425921830 2.06288409251899 0.00000000000000 h$end


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