Next: Molecular Dynamics Calculations
Up: Force Field Calculations
Previous: How to Perform a
Contents
Index
The uff implementation follows the paper by Rappé [7].
The energy expression in uff is as follows:
E _{UFF} = 
⋅K_{IJ}⋅r  r_{IJ} 
(5.1) 
+ 


+ 
⋅V_{φ}⋅1  cosnφ_{0}cos(nφ) 

+ 
V_{ω}⋅C^{I}_{0} + C^{I}_{1}cosω + C^{I}_{2}cos 2ω 

+ 
D_{IJ}⋅ 2 + 

+ 


The Fourier coefficients
C^{A}_{0}, C^{A}_{1}, C^{A}_{2} of the general angle terms
are evaluated as a function of the natural angle θ_{0}:
C^{A}_{2} 
= 
(5.2) 
C^{A}_{1} 
=  4⋅C^{A}_{2}cosθ_{0} 
(5.3) 
C^{A}_{0} 
= C^{A}_{2}2 cos^{2}θ_{0} + 1 
(5.4) 
The expressions in the engery term are:

N_{B}, N_{A}, N_{T}, N_{I}, N_{nb}
 the numbers of the bond,
angle, torsion, inversion and the non bondedterms.

K_{IJ}, K_{IJK}
 forceconstants of the bond and
angleterms.
 r, r_{IJ}
 bond distance and natural bond
distance of the two atoms I and J.

θ, θ_{0}
 angle and natural angle for
three atoms I  J  K.

C^{A}_{0}, C^{A}_{1}, C^{A}_{2}
 Fourier coefficients of the general
angle terms.

φ, φ_{0}
 torsion angle and natural torison
angle of the atoms I  J  K  L.
 V_{φ}
 height of the torsion barrier.
 n
 periodicity of the torsion potential.
 ω
 inversion or outofplaneangle at atom I.
 V_{ω}
 height of the inversion barrier.

C^{I}_{0}, C^{I}_{1}, C^{I}_{2}
 Fourier coefficients of the
inversions terms.
 x, x_{IJ}
 distance and natural distance of two
non bonded atoms I and J.
 D_{IJ}
 depth of the LennardJones potential.

q_{I}, 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 sp^{3} C atom has the name "C 3" instead of
"C_3". Particularly the bond terms are described with the harmonic
potential and the nonbonded van der Waals terms with the
LennardJones 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
nonbonded 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 quasiNewton relaxation is done. The BFGS
update of the forceconstant 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
Next: Molecular Dynamics Calculations
Up: Force Field Calculations
Previous: How to Perform a
Contents
Index
TURBOMOLE 15888