1. In 1985, Car and Parrinello published the work in which they proposed to solve the equations of motions of the coupled many-atom, many electron system via a dynamical simulated annealing strategy. The Car-Paarinello (P) method was designed to replace the traditional approach consisting of the iterative self-consistent solution of the Kohn-Sham equations for the electrons, the calculation of the fores acting on the atoms via Hellmann-Feynman theorem, and the integration of the Newtonian equations of the motions of the ions-the procedure having to be repeated after each ionic integration step until the ground state of the many-atom, many-electron system had been reached.
2. Strong Point of CP: CP paper introduced several other important innovations. One which is very important for the methodology is the use of Fast Fourier Transforms to switch between real-space and momentum-space representations of the wave function because different parts of the calculation can be done most efficiently in one space or another. The Kinetic Energy has a diagonal representation in momentum space while the Potential Energy is diagonal in real space. The second step forward was based on the observation that it is inefficient to do one part of the calculation with very high accuracy while one other part is still far from convergence. This led immediately to the bold idea--already referred to above-- that the total energy of a system could be minimized simultaneously with respect to both the electronic and ionic degrees of freedom.
3. Weakness of CP: Although much of recent development was undoubtedly triggered by the CP paper, it is a bit ironical that the development of modern DFT calculations is characterized by a rather quick return to the more traditional approach. The reason is twofold: First, the CP method of a dynamical updating of electronic degrees of freedom requires electrons and ions to be decoupled such that, once the electronic ground-state has been reached, the system remains closed to the adiabatic Born-Oppenheimer surface. This condition is met with good accuracy for insulators and wide-gap semiconductors but violated for metals and narrow-gap materials. The Second reason is that the minimization of the total energy does not allow an efficient control of charge-density fluctuations during the iterative process--for metallic systems such fluctuations (often referred to as "Charge-sloshing") may even prevent a convergence of this process.
The Vienna Ab Initio Simulation Package VASP - Basic methodology:
Why Plane Wave?
4. In a work of Gruber et al, they compared the performance of plane-wave (VASP) and local-basis set methods (GAUSSIAN and SIESTA package) in structural study of small gold clusters. For a wide class of relatively compact cluster structures the authors found excellent agreement between the binding energies calculated using both methods, while planar structures where found to have a somewhat reduced stability in the local-basis set calculations.
This difference was attributed to the fact that the quality of the plane-wave basis set is independent of the topology of the system while the quality of a basis composed of atom-centred local orbitals depends on the relative atomic positions(a situation which is evidently reminiscent of the basis-set superposition error)/ It was concluded that the relatively lower binding energy of planar clusters provided by SIESTA and GAUSSIAN03 could be a consequence of a lower "effective quality" of the basis set for systems that are more extended in one or two dimensions compared with more compact structures.
Potentials, pseudo-potentials
5. Pseudo-potential have been introduced to avoid the need for an explicit treatment of the strongly bound and chemical inert core electrons.
6. Methods for generating pseudo-potentials include the 'norm-conserving' pseudo-potential (the "norm-conservation" criterion applied to the node-less pseudo wave functions ensures that not only the logarithmic derivative of the exact and pseudo-wave-functions, but also their derivatives with respect to the energy agree at the chosen reference energy and cut-off radius) and the 'ultrasoft' pseudo-potential (where the norm-conservation criterion is dropped, but the logarithmic derivatives are matched at two or more reference energies spanning the entire range of eigenvalues of the valence electrons).
7.The criterion for the quality of a pseudo-potential is not how well it matches experiment, but how well it reproduces the results of accurate all-electron calculations. A certain drawback of pseudo-potential calculations is that because of the non-linearity of the exchange interaction between valence and core electrons, elaborate non-linear core corrections are required for all systems where the overlap between valence- and core-electron densities is not completely negligible. This deficiency may be removed by using the projector-augmented wave method.
Projector-augmented waves
8.
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