Chemistry Reference
In-Depth Information
computed from first principles. The coefficients for new eighth-order dispersion
terms are computed, and system (geometry) dependent information is used for a
DFT-D type approach by employing the new concept of fractional coordination
numbers. They are used to interpolate between dispersion coefficients of atoms in
different chemical environments. The method only requires adjustment of two
global parameters for each density functional. Three-body non-additivity terms
are considered. Benchmark calculations showed an improvement by 15-40% com-
pared to previous DFT-D functionals. An approach which combines the simplicity
of the semi-empirical formalism with the accuracy of the first principles methods
has been developed by Silvestri [
77
]. This approach is based on the use of the
maximally localised Wannier functions.
A general scheme for systematically modelling long-range corrected (LC)
hybrid density functionals has been proposed by Chai and Head-Gordon [
78
,
79
].
Adapted to B3LYP functionals the LC hybrid functionals are quite accurate
in thermo-chemistry, kinetics and non-covalent interactions, when compared to
common hybrid density functionals.
There are also problems if one deals with the chemistry of an oxide surface and
its role in the reactivity with adsorbed species [
80
].
Here, only a few papers on recent developments of including vdW forces into the
DFT scheme could be mentioned.
As soon as one knows the molecular wave function, one can calculate any
property of the molecule like dipole moment, chemical shift, force constants, etc.
Of particular importance is the PES, which will be used in the statistical mechanics
procedures discussed below.
2.2 Monte Carlo, Molecular Dynamics
Quantum chemical approaches give results for the absolute zero temperature
(
T
0). In fact, systems in chemical engineering are ensembles at higher tempe-
ratures. In order to compute properties of systems of many particles at any temper-
ature and pressure, one has to refer to statistical mechanics [
15
-
18
]. As most
systems occurring in practice are very complicated, computational methods have
to be employed. The most prominent ones are MC and MD approaches.
The first MC scheme was developed by Metropolis et al. [
81
]. The MC methods
follow a Markov process to evolve a system towards equilibrium, regardless of
pathway. In principle one starts with an initial configuration of molecules. The total
potential energy of the initial configuration is calculated. Then several thousand
random moves of the particles are executed. After each move it is checked whether
the energy goes down. If it does, the move is accepted. If not, the energy is com-
pared with a random number. If the energy is lower or higher than the random
number, the movement is accepted or rejected. MC methods do generate states that
are correlated owing to the sequential Markov process. In detail the so-called
Metropolis algorithm works as in Fig.
4a
.
ΒΌ
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