Chemistry Reference
In-Depth Information
characterized by several quantum/classic states but the same thermodynamics
parameters. Thermodynamic properties obtained experimentally are represented
by thermodynamic averages. The distribution of probability of the ensemble
considered is used for sampling the configurations of the system.
Regarding the ensemble types, for fixed number of atoms (N), fixed volume (V)
and fixed temperature (T) we have a Canonical Ensemble (NVT). For fixed
number of atoms, fixed V and fixed energy E we have a Microcanonical
Ensemble (NVE). For fixed chemical potential (µ), fixed volume and a fixed
temperature (T) we have a Grand Canonical Ensemble (NVT). For fixed number
of atoms, fixed pressure (P) and fixed temperature we have an Isothermal-Isobaric
Ensemble (NPT). For fixed number of atoms, fixed pressure, and fixed enthalphy
(H) we have an Isoenthalpic-Isobaric Ensemble (NPH) [564].
MD are widely applied and extremely versatile for studying biological
macromolecules by doing simulations of the dynamics of systems of atoms. This
is done using series of infinitesimal time increments and chosen force fields. From
the potential energy function for all atoms of the system, it is possible to generate
trajectories (time evolution of the molecular motion) of the molecular system by
simultaneous integration of Newton's equation of motion.
Calculation of the gradient of the potential energy V(r), yields F
i
,the vector of
forces acting on the i-th atom (F
i
= m
i
a
i,
i-1,2,3.N) where m
i
is the mass of each
atom, a
i
is the corresponding acceleration, and N is the number of atoms. The
numerical integration of Newton's equations of motion is performed in minor
steps (femtoseconds,
i.e.
10
-15
seconds).
Finite difference methods are often used in time integration algorithms. In these
methods, the integration is partitioned into small steps (Δt). It is also expected to
require little memory, be fast, duplicate the classical trajectory as closely as
possible, permit usage of long time steps, be simple, easy to program, be time-
reversible and conserve momentum and energy.
The Verlet algorithm [565] uses the accelerations (a) at time t, atomic positions ( r )
as well as positions from prior steps in order to determine new positions at time
