Real-World Predictions from Ab Initio Molecular Dynamics Simulations - Multiscale Molecular Methods in Applied Chemistry - page 122

Implementations using massively parallel algorithms are no longer restricted to
codes using plane wave basis sets. Atomic orbital based [ 27 ] or local basis sets
based on regular grids [ 28 ] were successfully adapted to modern computers. These
implementations are able to reduce scaling with system size and are therefore more
efficient to simulate larger systems. However, this also leads to more complex
algorithms and data structures which in turn make parallelization more difficult.
This increased complexity is also responsible for the fact that these codes typically
scale less efficiently to large numbers of processors.
Currently, reduced scaling methods using localized basis sets or the plane wave
method are both capable of performing AIMD simulations for systems of thousand
atoms at a rate of several picoseconds a week. The plane wave codes reach this
performance by making use of their excellent scaling while the localized basis set
codes profit from algorithmic efficiencies. In the future, plane wave codes will still
be of importance for system sizes up to a thousand atoms, but for considerably
larger systems the local basis set methods will dominate. For a further selection on
reviews about high performance computing on vector systems we refer the inter-
ested reader to [ 29 ] and references therein.
3.2 Basis Sets
Simulations using the plane wave-pseudopotential framework were completely
dominating the field of AIMD in the early years [ 3 ]. Plane waves are especially
suited to be used with the Car-Parrinello method and also have other advantages,
e.g., their orthogonality, control by a single parameter, or the absence of basis
set superposition errors [ 30 ]. However, the original plane wave approach has
an intrinsic cubic scaling with system size. For large system sizes, local basis set
methods are more advantageous as they can lead to a reduced and ultimately linear
scaling.
3.2.1 Finite Difference and Discrete Variable Representation Methods
Fattebert and Gygi proposed a real-space finite differences implementation for
O ( N ) density functional theory molecular dynamics simulations [ 31 ]. They showed
that the discretization error can be reduced systematically by adapting the mesh
spacing. Linear scalability was demonstrated with increasing system size using a
localized orbital scheme. The authors were able to demonstrate energy-conserving
AIMD with plane wave accuracy in O ( N ) operations. Similar achievements were
possible using spline function type basis sets within the CONQUEST code [ 32 ].
AIMD simulations at the complete basis set limit were demonstrated successfully
by Lee and Tuckerman [ 33 ]. The authors used a discrete variable representation
(DVR) approach. DVRs are local analytic functions defined at regular grid points.
In contrast to finite difference methods, the DVR is a basis set approach, and