Biomedical Engineering Reference
In-Depth Information
All structures described in this chapter have been fully relaxed
using an efficient matrix-diagonalization routine based on a
sequential band-by-band residual minimization method of single-
electron energies [49], with direct inversion in the iterative subspace,
to a total energy convergence of 10
-4
eV. During the relaxations ultra-
soft, gradient-corrected Vanderbilt-type pseudopotentials (US-PP)
[50, 51] and real-space projected wave function character were used,
to decrease the computational cost. Each relaxation was followed by
higher precision static single point calculations to determine the
adsorption energies and ECD.
Figure 7.1
Two-dimensional electron charge density (ECD) profiles for
ethane (top left) and ethylene (bottom left), along with the
three-dimensional total bonding iso-surfaces ethane (centre),
and sp
2
iso-surfaces (right). Reproduced with permission from
Ref. [12]. Copyright American Scientific Publishing, 2005.
These were performed using the projected augmented wave
(PAW) potentials [52], with a basis set increased by 30% and
reciprocal-space projected wave function character, also to a
convergence of 10
−4
eV. PAW potentials are generally considered to
be more accurate than the ultra-soft pseudopotentials [53], since
the radial cutoffs (core radii) are smaller than the radii used for the
ultrasoft pseudopotentials, and the PAW potentials reconstruct the
exact valence wave function with all nodes in the core region.
