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What is VASP?

The Vienna Ab initio Simulation Package (VASP) is a computer program for atomic scale materials modelling, e.g. electronic structure calculations and quantum-mechanical molecular dynamics, from first principles.

VASP computes an approximate solution to the many-body Schrödinger equation, either within density functional theory (DFT), solving the Kohn-Sham equations, or within the Hartree-Fock (HF) approximation, solving the Roothaan equations. Hybrid functionals that mix the Hartree-Fock approach with density functional theory are implemented as well. Furthermore, Green's functions methods (GW quasiparticles, and ACFDT-RPA) and many-body perturbation theory (2nd-order Møller-Plesset) are available in VASP.

In VASP, central quantities, like the one-electron orbitals, the electronic charge density, and the local potential are expressed in plane wave basis sets. The interactions between the electrons and ions are described using norm-conserving or ultrasoft pseudopotentials, or the projector-augmented-wave method.

To determine the electronic groundstate, VASP makes use of efficient iterative matrix diagonalisation techniques, like the residual minimisation method with direct inversion of the iterative subspace (RMM-DIIS) or blocked Davidson algorithms. These are coupled to highly efficient Broyden and Pulay density mixing schemes to speed up the self-consistency cycle.

And what can VASP do?
The following is a (by no means complete) list of VASP features:

LDA, GGAs, metaGGAs
Hartree-Fock, Hartree-Fock/DFT hybrids

First derivatives
Forces and stress tensor for DFT, Hartree-Fock, and hybrid functionals

Dynamics and relaxation
Born-Oppenheimer molecular dynamics
Relaxation using conjugate gradient, Quasi-Newton or damped molecular dynamics
Nudged elastic band methods (transition states search)
Climbing dimer method (transition state search)

Collinear and non-collinear
Spin-orbit coupling
Constrained magnetic moments approach

Linear response to electric fields
Static dielectric properties
Born effective charge tensors
Piezoelectric tensors (including ionic contributions)

Linear response to ionic displacements
Elastic constants (including ionic contributions)
Internal strain tensors

Optical properties
Frequency dependent dielectric tensors in the independent particle approximation
Frequency dependent tensors in the RPA and TD-DFT
Cassida's equation for TD-DFT and TD-Hartree-Fock

Berry phases
Macroscopic polarization
Finite electric fields

Green's function methods
GW quasiparticles
ACFDT total energies in the RPA

Many-body perturbation theory
2nd-order Møller-Plesset perturbation theory