Chemistry Reference
In-Depth Information
Info Box 2
MD simulations can be used as a tool for the exploration of the actually populated confor-
mational space as a measure of time. In principle, the energy of a particular confi guration
of atoms that form molecules and molecular complexes can be treated as electronic energy
of the corresponding QM problem. This energy is a complicated function of atomic coordi-
nates, its spatial distribution being described by a potential energy surface. In almost all
practical cases, the dynamics of molecules can be described suffi ciently well as the dynamics
of nuclei, moving on a potential energy surface according to classical Newtonian equations
of motion. Although the origin of the potential energy is quantum mechanical, the fi nal
property of interest, energy
ER
, where
R
stands for coordinates of nuclei treated as classical
point masses, is a simple smooth hypersurface defi ned in a coordinate space. It is thus pos-
sible to approximate the shape of this surface by a purely empirical way, avoiding the need
for generally very costly QM calculations. In general, we are not interested in all possible
confi gurations, since only a very minor part of them is sampled under real experimental
conditions with signifi cant probability. Minima on a potential energy surface correspond to
stable molecular conformations, while the saddle points defi ne the transition states. They are
pivotal characteristics of the reaction path. The reaction path is an idealized route in the
confi gurational space describing the topological course of the reaction
()
- the transition from
one set of stable confi gurations (reactants) to another set of stable confi gurations (products).
The empirical description of the potential energy surface is written as a sum of terms express-
ing various physical contributions to the total energy of the molecular system. The most
common functional form can be given as:
()
=
∑
2
(
)
(
)
ER
K r
−
r
bond stretching terms
Bi
i
0
bonds
∑
2
+
K
(
ϑϑ
−
)
(
angular bending terms
)
Ai
i
0
angles
∑
∑
+
K
(
1cos
+
(
n
ωγ
−
)
)
(
torsion and wagging terms
)
τ
n
torsions
n
12
6
⎪
⎪
⎡
⎣
⎤
⎦
⎪
⎪
⎛
⎜
σ
⎞
⎟
−
⎛
σ
⎞
⎟
qq
<
∑
ij
ij
ij
+
4
ε
⎥
+
(
van der Waals and Coulomb terms
)
⎢
⎜
ij
r
r
4
πε
r
ij
ij
ij
0
ij
This expression is often called force fi eld (FF), because the forces acting on nuclei can be
easily calculated according
()
Fgr dER
=−
parameters of FF, i.e.
K
B
, r
i
0
,
K
A
,
ϑ
i
0
,
K
τ
n
,
γ
,
ε
ij
,
σ
ij
,
are called
force constants.
The actual confi guration of nuclei
R
is expressed in internal coor-
dinates, represented by
r
i
,
i
. Most biological molecules can access several nuclear
confi gurations and perform transitions between them without breaking chemical bonds.
Thus, there is a dynamic equilibrium between these key-like structures, with not yet well-
defi ned consequences for biological functions.
ϑ
i
, and
ω
