Category:Theory

The Vienna ab-initio simulation package (VASP) is a computer program for atomic scale materials modeling from first principles. A so-called ab-initio simulation generally entails

• choosing the elements and a structure of the material,
• treating the electrons fully quantum mechanically and
• optionally updating the ionic positions

• to minimize the forces and obtain a stable structure, or
• by means of Newton's equation of motion to perform molecular dynamics simulations.

VASP computes an approximate solution to the many-body Schrödinger equation to obtain the electronic ground state. This can either be done within density-functional theory (DFT) by solving the Kohn-Sham (KS) equations, or within the Hartree-Fock (HF) approximation by solving the Roothaan equations. Hybrid functionals that mix the Hartree-Fock approach with density-functional theory are also implemented. Furthermore, Green’s functions methods based on many-body perturbation theory are available in VASP. For instance, the GW method, random-phase approximation, 2nd-order Møller-Plesset, Bethe-Salpeter equations, and more to grant access to optical properties.

In VASP, central quantities, like the one-electron orbitals, the electronic charge density, and the local potential are expressed in plane-wave basis using the projector-augmented-wave (PAW) method. This entails using PAW pseudopotentials to efficiently treat the relevant valence electrons while appropriately capturing the nodal features near the nuclei. To determine the orbitals for the electronic ground state, VASP makes use of efficient iterative matrix diagonalization techniques. These are coupled with highly efficient Broyden and Pulay density-mixing schemes to speed up the self-consistency cycle.

The ionic degrees of freedom can be updated by various algorithms (IBRION) based on forces that are either obtained directly from the electronic state or from ab-intio quality force fields that were trained by machine learning. VASP is particularly strong in describing crystal structures due to the periodic boundary conditions it exploits. Naturally, these systems feature quantized vibrations in the form of phonons whose influence on the electronic ground state is taken into account by including electron-phonon coupling.

In this category, we collect theory pages from all the different areas VASP offers functionalities. These can also be reached from the corresponding category. For instance, the article on the Blocked-Davidson algorithm is also linked from the electronic minimization page.