Chemistry Reference
In-Depth Information
simulations of condensed systems, Car and Parrinello kick started and dominated
the field. Their method stays at the beginning of all new developments in the field.
Section
2
provides a brief overview of the AIMD methodology mainly in the
representation of Car-Parrinello molecular dynamics simulations. Born-Oppenheimer
molecular dynamics (BOMD) simulations (time-independent electronic structure)
are introduced in a generalized formulation based on the work by Niklasson [
7
,
8
].
This will be followed (Sect.
3
) by some recent methodological advancements which
allow for computationally more efficient simulations with better statistical sampling
and which use more accurate electronic structure methods. After this, some
examples from applied chemistry studied from AIMD will be given in Sect.
4
.
2 Ab Initio Molecular Dynamics Simulations in a Nutshell
2.1 Molecular Dynamics Simulations: Basics
Molecular dynamics (MD) is an application of classical mechanics using computer
simulations. Good introductions can be found in many textbooks, for example the
excellent book by Tuckerman [
9
]. In order to carry out MD, equations describing
the motion of molecules are needed. These equations of motion can be derived for
example from the classical Lagrangian
L
, a function of the kinetic (
K
) and the
potential energy (
U
):
X
N
1
2
M
I
R
2
R
I
;
R
I
Þ¼
Lð
K
ð
energy
p
I
Þ
U
R
I
Þ
|
{z
}
potential
¼
ð
I
U
ð
R
I
Þ
(1)
|
{z
}
kin
I¼
1
:
with R
I
and
M
I
being position and mass of particle
I
. The momentum p
I
is related to
the velocity
R
p
I
/
M
I
. The equations of motion are then obtained from the
Euler-Lagrange relation:
¼
d
t
@L
d
@
R
I
¼
@L
R
I
:
(2)
@
This means that the nuclei (atoms) are treated as classical particles, a well
founded and tested approximation [
10
,
11
]. Applying the Euler-Lagrange equation
(2) to the Lagrangian
L
(1) leads to Newton's second law:
M
I
R
I
¼
F
I
:
(3)
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