Biomedical Engineering Reference
In-Depth Information
reliable modeling of the chemical interactions and an accurate
description of the electronic properties of the structures involved,
are based on advanced quantum chemistry techniques, such as the
configuration interaction (CI) theory or similar [24, 120], or total
energy
ab initio
calculations based on the Density Functional Theory
(DFT) [51, 58].
Accurate quantum chemistry models can be used also to treat
equilibrium configurations of physisorbed molecules in carbon
nanopores and nanostructures. Collective studies on gas adsorption
are usually addressed by classical analytical potentials in the
framework of statistical mechanics techniques such as the Metropolis
scheme in various statistical ensembles.
As mentioned before, also continuum theory models have been
developed to support the interpretation of gas storage experiments
in carbon porous materials. However a detailed description of
these techniques and of the obtained results is beyond the scope
of the present chapter and thus, part of the literature concerning,
for instance, porosimetry has been omitted. Moreover, it must be
emphasized that the methods treated in this chapter should not
be considered as an exhaustive list of the suitable schemes for gas
adsorption in carbonaceous materials but, rather, a collection of
theoretical frameworks that are close to the expertise of the present
authors.
8.3.1
Density Functional Theory Based
ab initio
Calculations
DFT based
) calculations have become
very popular in the last three decades, thanks to the enormous
improvement of the computational resources and to the relative
accessibility of this method. The total energy of a
ab initio
(or
first principles
-particles system
(that contains nuclei and electrons) can be considered as a functional
of the electron density only. Since the publication of the Hohenberg-
Kohn theorems [45] and the Kohn-Sham method [54], a route was
indicated to calculate the electronic structure and the total energy
of an atomistic system and then, in principle, to study the reaction
dynamics involving molecules, nanostructures, and solids.
Following Hohenberg and Kohn, the total energy of an atomistic
system is, in the frame of the adiabatic approximation, a functional
of the electron density
N
