Projector Augmented Wave Method
Ab-initio simulations describe materials and molecules on the nanometer scale. The goal is to understand how atoms hold together to make up a material, and what are its electronic, mechanic, chemical or optical properties. One can understand the processes that lead to a certain material or one can study its decay, such as corrosion processes. These ab-initio simulations provide quantitative predictions for real materials, so that they can be used to design materials with desired properties on the computer.
Ab-initio simulations have a sound basis and rely only on basic laws of nature. In order to describe the electrons, which are the glue to keep the atoms together in a material, one has to resort to quantum mechanics. More specifically, we use the Density-Functional Theory for which its inventor, Walter Kohn, was honored with the Nobel Price in 1998.
To solve the quantum mechanical equations for real systems is a considerable challenge: The mathematical problem is a system of often thousands of coupled differential equations with singularities and non-local couplings. Close to the nucleus, the electrons are so fast, that we need to describe them with Einstein's Theory of Relativity, another complication. We need to resolve energy differences that are only one-millionth of the total energy of the system.
In order to cope with these difficulties, physicists and chemists have developed a number of elaborate theoretical techniques, so-called "electronic structure methods". One of the most modern among these is the Projector Augmented Wave method, simply called PAW method, which has been developed by P. Blöchl in the early 1990s. The original paper is currently cited over thousand times per year.
The PAW method is based on a transformation theory which links the physical wave functions to auxiliary wave functions that can be treated well numerically. Thus it provides a general and rigorous framework for representing quantum mechanical expressions within the PAW formalism. Kinks and strong oscillations near the nucleus are augmented, i.e. attached to a numerically smooth auxiliary wave function, which is expanded into plane waves.
The original motivation for the development of the PAW method has been to port the ab-initio molecular dynamics method invented by R. Car and M. Parrinello into an all-electron framework, that allows to study a wider class of systems and properties than the previously used pseudopotential approach. Thus our methodology is well suited for studies, where the atomic trajectories are simulated from first principles.
The methodology has been implemented in the CP-PAW code. Electronic structure codes such as CP-PAW have a wide range of functionalities. The size of the source code is about 170000 lines of fairly compact code.
An incomplete selection of features in the CP-PAW package are the following:
- ab-initio molecular dynamics
- non-collinear magnetism
- full wave functions
- hyperfine parameters
- Electric field gradients,
- Isomer shifts,
- isotropic and anisotropic magnetic hyperfine constants
- Parrinello Rahman (Unit-cell dynamics)
- Mermin functional and Tetrahedron method
- Conductor like screening model (COSMO)
- Isolated molecules (Decoupling of periodic images)
For further details see:
- "Projector augmented wave method",
P.E. Blöchl, Phys. Rev. B 50 18953 (1994) - "The Projector Augmented Wave Method: Ab-initio Molecular Dynamics Simulations with Full Wave Functions",
P.E. Blöchl, C. Först and J. Schimpl, Bull. Mater. Sci. 26, 33 (2003).
http://www.arxiv.org/abs/cond-mat/0201015 - "Electronic structure methods: Augmented Waves, Pseudopotentials and the Projector Augmented Wave method",
Peter E. Blöchl, Johannes Kästner and Clemens J. Först, Book chapter in "Handbook of Materials Modeling" Vol.1, R.Catlow, H. Shercliff and S. Yip Eds., p.63 (Springer, 2005) - Projector augmented wave implementation, P. Blöchl, Presentation held on the CAMD Summer School 2010.