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Université de Reims
CHAMPAGNE ARDENNE
INRA UMR FARE 614
Fractionnement des Agro Ressources
et Emballages,
CPCB Moulin de la Housse, BP 1039,
F 51687 REIMS cedex 2
MOLECULAR MODELING
at atomistic scale (I/II)
Ways to move on Energy Surface
Ways to move on Energy Surface
Newtonian and Quantum Mechanics
Newtonian and Quantum Mechanics
The force field expresses chemical interactions as potential
energy. A force field must be simple enough to be evaluated
quickly, but sufficiently detailed to reproduce the salient
features of the physical system being modeled. It includes
internal degrees of freedom of each molecule and terms
describing interactions between molecules.
Typical Energy Ranges
Force Fields
Newton's equation of motion
quantum
mechanical
classical
particles
Energy (heavy lines)
and probability (thin
lines) of a mechanical
and quantum particle in
a harmonic energy
described as an
oscillator.
Potential Functions
Potential Functions
The classical (mechanical)
probability is the highest when its
maximum potential energy is
maximal (zero velocity), and drops
to zero between these points. The
quantum mechanical probability is
the highest where the potential
energy is minimal. The probability to
find a particle outside the classical
limits is in pale vertical lines.
Correspondence of the Energy Minima
+0.6
+2.5
+2.0
+100
+20
+3.0
- 5.0
- 1.0
- 0.3
- 0.1
Energy to change a bond
angle by 10°
kT
Thermal energy at 300K
Energy to stretch a bond
length by 0.1A
Barrier to breaking a bond
Torsion barrier about
double bond C=C
Torsion barrier about
single bond C C
Hydrogen bond in vacuum
Hydrogen bond in water
van der Waals in vacuum
van der Waals in water
Energy
(kcal/mol)
Interaction
Van der Waals energy
Electrostatic energy
Bond stretching energy
Bond bending energy
Electrostatic repulsion
Electrostatic attraction
+
-
-
r
r
+
+
-
-
Electron overlap repulsion
Dispersion attraction
r
r
b
b
0
Bond length
"spring"
Bond angle
"spring"
ngles de liaiso
Different methods can be used to perturb atom
positions and thus explore the energy surface. They
can be combined to achieve speed convergence
accuracy, requirements. It is emphasized that only
MD and MC methods can sample the whole energy
landscape. Minimization and Normal Mode Analysis
are used to explore the configuration space around
local energy minima.
N H
O C
N H O C
E
tot
bonded
non bonded
b
vdW
elec
U
U
U U
U
U
U
-
=
+
+
+
b
U
U
vdW
U
elec
U
0
0
,
b
0
2
b
U
k b
=
2
U
k
=
12
0
repulsion
r
U
r
=
6
0
4
attraction
r
U
r
= -
2
elec
kqQ
U
r
= -
2
2
dU
d R
m
dR
dt
-
=
global
minimum
local
minima
Molecular Dynamics (MD)
U
Monte Carlo (MC)
random
U
Minimization
U
x
Normal Mode Analysis
harmonic
approximation
U
2
U
x
The minimization of a molecular structure often implements a calculation of the
"steepest descent" type with an aim of trimming calculations, followed by a
calculation of the "conjugate gradient" type allowing a fast convergence
towards the energy minimum nearest, then by a calculation of the "Newton
Raphson" type allowing a precise convergence towards this minimum.