Real-World Predictions from Ab Initio Molecular Dynamics Simulations - Multiscale Molecular Methods in Applied Chemistry - page 124

orbital transformation technique resulted in good parallel performance
outperforming traditional diagonalization methods. The efficiency of this method
enabled the use of large Gaussian basis sets. Energy conserving Born-Oppenheimer
dynamics were shown to be possible, and a highly efficient scheme was obtained
using an extrapolation of the density matrix [ 27 ].
A comparison of plane waves and Gaussian basis sets was carried out in 2007
[ 30 ]. This was conducted in the framework of density functional theory for the
hydrogen bond description with the water dimer as an example. Molecular dynam-
ics simulations enforcing the self-dissociation reaction of the water dimer to study
the influence of the basis set onto the reaction showed strongly varying results of the
calculated forces for a chosen cutoff along the reaction coordinates. The basis set
superposition errors of the dimer interaction energy was analyzed along the free-
energy surface. Based on the analysis along the trajectories a qualitative and
quantitative estimate depending on the particular point of the free-energy surface
was provided.
In 2008, Artacho et al. presented developments and applicability of the Siesta
method for a large variation of systems [ 37 ]. Within the Siesta code the plane wave
basis for the electron density is combined with numerical atomic orbitals of finite
support. In their article, Artacho et al. demonstrate linear scalability of the Siesta
program using a system with more than 4,000 atoms [ 37 ].
Blum et al. suggested the application of numerically tabulated atom-centered
orbitals (NAOs) in AIMD. These basis sets are implemented in the ab initio
molecular simulations package FHI-aims. In benchmark calculations the authors
showed an O ( N ) scalability and a good parallelization [ 38 ].

3.3 New Developments in Accuracy

Real-world predictions do not just rely on a sufficiently large system size and fast
calculations. Accuracy of the calculations plays an equally important role in
applications. As most of the AIMD codes are carried out within the framework of
density functional theory, the errors connected with this electronic structure method
have to be reduced. For instance, frequencies calculated by Gaigeot et al. using the
BLYP functional had to be down shifted by up to 100 cm 1 compared to
frequencies calculated with hybrid functionals (e.g., B3LYP) or with wavefunction
based ab initio calculations [ 39 ]. Gaigeot et al. stated that 5-10% underestimation
of frequencies is typical for the BLYP functional. The amplitudes of methyl groups
d (C-H) bands were underestimated in their calculations which they attributed to

C-H-water interactions being more sensitive to dispersion than to electrostatics
forces. Therefore they estimated that this deficiency could be related to the lack of a
proper dispersion term in DFT calculations. In 2008, Cohen et al. discussed the
deficiencies of DFT in a short communication [ 40 ]. Approximations to the
unknown exchange-correlation functional lead to major failures in DFT, e.g.,
underestimation of chemical reaction barriers and band gaps, errors in dissociation