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Vienna Ab initio Simulation Package

The Vienna Ab initio Simulation Package () is a computer program designed for atomic-scale materials modeling, enabling electronic structure calculations and quantum-mechanical simulations from first principles. It employs (DFT) within the Kohn-Sham formalism, alongside methods such as Hartree-Fock and , to solve the many-body for periodic systems. utilizes plane-wave basis sets combined with either norm-conserving or ultrasoft pseudopotentials, or the projector-augmented-wave (PAW) method, for efficient representation of valence electrons while treating approximately. These capabilities make it a versatile tool for investigating structural, dynamic, and electronic properties of materials, including solids, surfaces, nanostructures, and molecules. Developed primarily by Georg Kresse and Jürgen Furthmüller at the University of Vienna's Faculty of Physics, originated from early codes in the early , building on foundational work in plane-wave DFT implementations. Key methodological advancements were introduced in seminal papers, such as the publication on for liquid metals using pseudopotentials, which laid the groundwork for efficient total-energy calculations. Subsequent developments in 1996 enhanced iterative schemes for Kohn-Sham ground-state solutions, incorporating algorithms like residual minimization with direct inversion in the iterative subspace (RMM-DIIS) and blocked Davidson methods for improved convergence in metallic and systems. Today, is maintained and distributed commercially by Software , supporting via MPI and for large-scale simulations on clusters. Its broad adoption in computational stems from high accuracy in predicting properties like band structures, phonons, and reaction pathways, often benchmarked against experimental data across diverse applications in physics, , and .

Background

Ab initio Methods

Ab initio methods, also known as first-principles calculations, involve solving the to determine the electronic structure of materials directly from fundamental physical laws, without relying on empirical parameters or experimental fitting. These approaches aim to compute properties such as energies, forces, and densities by treating as quantum particles interacting via forces, providing a rigorous foundation for understanding atomic and molecular . The core challenge lies in handling the many-body nature of electron interactions, which scales exponentially with system size, necessitating approximations to achieve computational feasibility. The time-independent for a many-electron system is given by \hat{H} \Psi = E \Psi, where \hat{H} is the encompassing , external potential from nuclei, and electron-electron repulsion, \Psi is the many-electron wavefunction, and E is the total energy. To address the coupled nuclear-electronic dynamics, the Born-Oppenheimer approximation is employed, which separates the motions of nuclei and electrons based on the vast mass difference (approximately 1836 for protons), allowing electronic structure to be solved for fixed nuclear positions. This approximation underpins most calculations, enabling the computation of potential energy surfaces as functions of nuclear coordinates. Early ab initio methods relied on wavefunction-based techniques, such as the Hartree-Fock method, which approximates the many-electron wavefunction as a single to account for antisymmetry and mean-field interactions. However, Hartree-Fock exhibits significant limitations for solid-state systems, primarily due to its neglect of electron effects beyond the mean field, leading to overestimated band gaps and poor descriptions of insulating or metallic behaviors in periodic structures. This inadequacy prompted a transition in the 1960s and 1970s to more advanced frameworks, including many-body perturbation theory (MBPT), which treats as a perturbation on the Hartree-Fock solution to capture higher-order interactions. The evolution from wavefunction-based methods to density-based approaches accelerated in the 1960s-1980s, driven by the need for scalable computations in complex systems like solids. Seminal developments included the formulation of MBPT for energies in solids, as in Hedin's framework (1965), which improved upon Hartree-Fock by incorporating screening and self-energy corrections. Concurrently, the shift to (DFT) in the Kohn-Sham formulation (1965) reformulated the problem in terms of , offering a practical framework that balances accuracy and efficiency for extended systems. By the 1980s, these methods had matured, enabling widespread applications in while highlighting ongoing challenges in exact correlation treatments.

Density Functional Theory

Density functional theory (DFT) serves as the cornerstone of the Vienna Ab initio Simulation Package (VASP), enabling efficient calculations of ground-state electronic structures and properties of materials by reformulating the in terms of the rather than the full wavefunction. The theoretical foundation of DFT rests on the Hohenberg-Kohn theorems, which establish that the ground-state n(\mathbf{r}) uniquely determines the external potential v(\mathbf{r}) (up to an additive constant) for a system of nonrelativistic interacting electrons, and that the total energy E is a functional of the density, with the true ground-state density yielding the minimum value among all physically admissible densities. To make DFT practically solvable, Kohn and Sham recast the problem as an equivalent system of non-interacting electrons moving in an , leading to the Kohn-Sham equations: \left( -\frac{\nabla^2}{2} + V_{\mathrm{eff}}(\mathbf{r}) \right) \psi_i(\mathbf{r}) = \epsilon_i \psi_i(\mathbf{r}), where the effective potential V_{\mathrm{eff}}(\mathbf{r}) = v(\mathbf{r}) + V_{\mathrm{H}}(\mathbf{r}) + V_{\mathrm{xc}}(\mathbf{r}) includes the external potential v(\mathbf{r}), the potential V_{\mathrm{H}}(\mathbf{r}) from the classical electrostatic repulsion of the density, and the exchange-correlation potential V_{\mathrm{xc}}(\mathbf{r}) = \delta E_{\mathrm{xc}}/\delta n(\mathbf{r}) derived from the universal but unknown exchange-correlation functional E_{\mathrm{xc}}. The density is then obtained as n(\mathbf{r}) = \sum_i |\psi_i(\mathbf{r})|^2, with the kinetic energy expressed exactly for this fictitious non-interacting system. Practical computations require approximations for E_{\mathrm{xc}}. The local density approximation (LDA) assumes the exchange-correlation energy is local, given by E_{\mathrm{xc}}^{\mathrm{LDA}} = \int n(\mathbf{r}) \epsilon_{\mathrm{xc}}^{\mathrm{hom}}(n(\mathbf{r}), \zeta(\mathbf{r})) \, d\mathbf{r}, where \epsilon_{\mathrm{xc}}^{\mathrm{hom}} is the per-electron exchange-correlation energy of the homogeneous electron gas at density n and spin polarization \zeta, parametrized from simulations of the uniform gas. The generalized gradient approximation (GGA) extends LDA by including dependence on the density gradient |\nabla n|, as in the Perdew-Burke-Ernzerhof functional, which improves descriptions of binding energies, lattice constants, and surface properties by better capturing density variations. Despite their widespread utility, these approximations have notable limitations; for instance, LDA systematically underestimates band gaps in semiconductors and insulators by 30–100% due to residual self-interaction errors and incomplete inclusion of exact exchange effects, often necessitating that incorporate a portion of Hartree-Fock exchange or post-DFT approaches like the method for more accurate excited-state properties.

History and Development

Origins

The Vienna Simulation Package () traces its origins to foundational work in computational methods for , specifically building upon early plane-wave codes developed in the late . The core codebase was initially derived from a program written by Mike Payne during his time at the (), which also served as the basis for the CASTEP code. This early framework emphasized (DFT) implementations using plane waves and pseudopotentials, enabling simulations of electronic structures in periodic systems. In July 1989, Jürgen Hafner, after spending six months in collaborating on related projects, brought this MIT-derived code to the Technical University of Vienna (now part of the ). This transfer marked the beginning of localized development in , where the code was adapted for broader applications in and materials modeling. Initial enhancements focused on integrating local pseudopotentials and the Car-Parrinello steepest descent algorithm, laying the groundwork for efficient molecular dynamics simulations. Development accelerated in September 1991 under the leadership of Georg Kresse and Jürgen Furthmüller, who began refining the code into a dedicated tool for DFT-based calculations. The early version, released around 1993–1994, was named (Vienna Ab initio Molecular-dynamics Program), emphasizing its capabilities for using pseudopotentials and plane-wave basis sets. enabled pioneering simulations, such as for liquid metals, demonstrating high efficiency for metallic and semiconducting systems. By the mid-1990s, the package transitioned from to , with the official naming occurring around February 1995. This evolution shifted the focus toward a more versatile package optimized for plane-wave methods in , incorporating iterative schemes for total-energy calculations and improved handling of complex systems like transition metals. The rename reflected a maturation from dynamics-centric tools to a comprehensive platform, while retaining the Vienna group's emphasis on computational efficiency and accuracy.

Key Milestones

Georg Kresse has led the development of since completing his under Hafner in 1993 at the Technische Universität Wien, building on the software's origins from the CASTEP code and an early version known as . A significant advancement occurred in the mid-2000s with the VASP 5 branch (initiated around 2004, with key releases mid-2000s), which introduced support for such as PBE0 and to better capture exchange-correlation interactions in complex materials, along with calculations and linear response theory. The projector-augmented-wave () method, implemented in the late 1990s, saw further refinements for more accurate treatment of . To facilitate commercial distribution while preserving its academic foundation at the , Software GmbH was established in 2018, though licensing arrangements for non-academic use had been in place since the early . The release of 6 in 2020 marked another key milestone, introducing enhanced support for GPU acceleration via OpenACC and integrations for machine learning-based to accelerate large-scale simulations. Subsequent releases, including 6.4 in 2023 and 6.5 in late 2024, have provided further enhancements in performance and new features such as improved electron-phonon calculations (as of 2025). Over more than 25 years of continuous development by the Kresse group, the foundational VASP publications, such as those describing the iterative schemes and PAW implementation, have accumulated over 60,000 citations by 2025, underscoring their impact on computational .

Methodology

Plane Wave Basis and Pseudopotentials

The Vienna Ab initio Simulation Package () utilizes a basis set to expand the Kohn-Sham orbitals in its framework. The electronic wavefunctions are represented as a superposition of plane waves, expressed mathematically as \psi_{n\mathbf{k}}(\mathbf{r}) = \sum_{\mathbf{G}} c_{\mathbf{G}n\mathbf{k}} \, e^{i(\mathbf{k} + \mathbf{G}) \cdot \mathbf{r}}, where \mathbf{G} denotes the vectors, \mathbf{k} is the Bloch vector within the first , and the coefficients c_{\mathbf{G}n\mathbf{k}} are determined variationally. The basis set size is controlled by a cutoff E_{\rm cut}, specified via the input parameter ENCUT, which truncates the sum over \mathbf{G} such that \frac{\hbar^2}{2m} |\mathbf{k} + \mathbf{G}|^2 < E_{\rm cut}; higher values of ENCUT increase accuracy but also computational demand. This approach inherently enforces periodic boundary conditions, rendering it well-suited for simulating crystalline solids, surfaces, and interfaces where translational symmetry prevails. A primary advantage of the plane wave basis lies in its computational efficiency, particularly through the use of fast Fourier transforms (FFTs) to apply the Hamiltonian operator, which involves operations in both real and reciprocal space. FFTs enable rapid evaluation of the kinetic energy, nonlocal pseudopotential projectors, and Hartree potential, scaling favorably for large systems. Furthermore, integration over the is handled via or other k-point meshes, ensuring convergence of properties like total energy and electronic density as the sampling density increases; for insulators, fewer k-points suffice compared to metals. To mitigate the computational expense arising from the singular Coulomb potentials of atomic cores, VASP employs pseudopotentials that substitute the all-electron treatment with an effective potential acting on valence electrons only, thereby eliminating the need to resolve rapid oscillations in core regions. Core electrons are frozen and accounted for via precomputed atomic contributions, drastically reducing the required plane wave basis size and enabling simulations of heavier elements. VASP supports norm-conserving pseudopotentials, which adhere to conditions such as charge norm conservation—\int_0^{r_c} |\phi_l(r)|^2 r^2 \, dr = \int_0^{r_c} |\tilde{\phi}_l(r)|^2 r^2 \, dr within a core radius r_c—and matching logarithmic derivatives, preserving scattering properties and accuracy for valence electrons. Additionally, ultrasoft pseudopotentials are implemented, relaxing the norm-conservation constraint to produce smoother pseudo-wavefunctions that demand lower ENCUT values, often halving the basis set size relative to norm-conserving variants while augmenting the charge density with generalized functions for exact reconstruction. This variant further lowers the computational cost, particularly for transition metals and d- or f-block elements, without compromising key physical observables when properly converged. Both types are provided in the POTCAR files distributed with VASP, selected based on the balance between accuracy and efficiency for specific applications.

Projector Augmented Wave Method

The Projector Augmented Wave (PAW) method serves as VASP's primary approach for achieving all-electron-like accuracy in electronic structure calculations while maintaining computational efficiency. Developed by , it generalizes pseudopotential techniques by enabling the exact reconstruction of all-electron wavefunctions and densities from smoother pseudo-wavefunctions, particularly within augmentation regions around atomic cores. This formalism is particularly suited for plane-wave basis sets, where the pseudo-part of the wavefunction is expanded in plane waves outside the augmentation spheres. In the PAW method, the all-electron wavefunction \psi is obtained by transforming the pseudo-wavefunction \tilde{\psi} using a set of projector functions |p_i\rangle and partial waves |\phi_i\rangle, which are localized solutions to the atomic Schrödinger equation. The transformation incorporates one-center corrections within spherical augmentation regions to account for the difference between all-electron and pseudo quantities: |\psi\rangle = |\tilde{\psi}\rangle + \sum_i \left( |\phi_i\rangle - |\tilde{\phi}_i\rangle \right) \langle p_i | \tilde{\psi} \rangle This linear relation allows the true electron density and other operators to be reconstructed accurately, including core-valence interactions, without solving the full all-electron equations. The projectors \langle p_i | are dual to the pseudo partial waves |\tilde{\phi}_i\rangle, ensuring orthogonality and efficient computation. VASP implemented the PAW method between 1997 and 1999, building on Blöchl's original formulation with extensions for practical use in periodic systems as described by Kresse and Joubert (1999). This implementation employs the frozen-core approximation, where core electrons are treated atomically and remain fixed, while valence electrons are handled dynamically. It fully supports spin-orbit coupling through the LSORBIT tag and noncollinear magnetism, enabling accurate treatment of relativistic effects and magnetic properties in materials like transition metals and semiconductors. The PAW approach in VASP offers significant benefits over traditional pseudopotentials, providing higher precision for derived properties such as magnetic moments, Hellmann-Feynman forces, and total energies, all at a cost comparable to norm-conserving pseudopotentials. By exactly representing the one-electron density matrix within augmentation spheres and introducing compensation charges to maintain normalization, it minimizes errors in core-related observables without the prohibitive expense of full all-electron methods like the linearized augmented plane wave approach. This accuracy has made PAW the default method in VASP for most applications requiring reliable structural and electronic properties.

Features

Calculation Types

VASP supports a range of calculations to determine the electronic structure of materials, primarily through self-consistent field (SCF) methods that solve the Kohn-Sham equations to obtain the ground-state total energy and charge density. These SCF calculations form the basis for deriving key properties such as the , which reveals the distribution of electronic states available for occupation, and , which map the energy eigenvalues along high-symmetry paths in the Brillouin zone to identify band gaps and dispersion relations. Typically, an initial SCF run on an optimized geometry provides the converged charge density, followed by non-SCF steps with denser k-point sampling for accurate DOS and band structure plots. For structural properties, VASP performs geometry optimizations to minimize the total energy with respect to atomic positions and lattice parameters, employing algorithms such as the conjugate gradient method for robust convergence in complex systems or damped molecular dynamics for faster relaxation in simpler cases. These optimizations ensure ionic configurations at local minima, essential for subsequent property calculations, and can incorporate constraints like fixed cell volumes or selective relaxation of coordinates. Ab initio molecular dynamics (AIMD) simulations in VASP enable the study of finite-temperature dynamics by integrating equations of motion using the Verlet algorithm, allowing exploration of thermal fluctuations and phase transitions over timescales typically up to a few picoseconds due to computational cost. The projector augmented wave (PAW) method ensures accurate forces on ions during these trajectories, facilitating reliable sampling of configuration space. Vibrational properties are computed through phonon calculations, which characterize lattice dynamics and stability; VASP implements density functional perturbation theory (DFPT) for efficient determination of phonon frequencies at the zone center via linear response, or the finite differences method to approximate second-order force constants by displacing atoms in a supercell. DFPT is particularly advantageous for insulating systems, while finite differences offer flexibility for metals and full dispersion relations when combined with post-processing tools. Additionally, as of VASP 6.5.0 (released December 2024), VASP supports electron-phonon interaction calculations using DFPT to compute coupling matrix elements, enabling the study of phenomena such as electron-phonon scattering, superconductivity, and thermal transport.

Exchange-Correlation Approximations

The Vienna Ab initio Simulation Package (VASP) implements a range of exchange-correlation (XC) approximations within density functional theory (DFT), which are used to model the complex many-electron interactions by approximating the exchange and correlation energies in the Kohn-Sham equations. These functionals vary in sophistication, from local approximations that depend only on electron density to more advanced methods incorporating gradients, kinetic energy densities, and nonlocal effects, enabling accurate predictions of material properties such as energies, structures, and electronic spectra. The local density approximation (LDA) in VASP employs the Perdew-Zunger parametrization of the Ceperley-Alder exchange-correlation functional, derived from quantum Monte Carlo simulations of the uniform electron gas. This form assumes the electron density is locally uniform, providing a simple yet computationally efficient starting point for calculations, though it often overestimates binding energies and underestimates lattice constants in solids. For improved accuracy, VASP defaults to generalized gradient approximation (GGA) functionals, which include density gradients to better capture inhomogeneities in real systems. The Perdew-Burke-Ernzerhof (PBE) functional serves as the standard, offering a nonempirical approach that balances performance across diverse properties like cohesive energies and reaction barriers. VASP also supports variants such as PW91, which refines exchange and correlation for molecular systems, and RPBE, optimized for enhanced surface energies and adsorption binding in catalytic applications. Hybrid functionals in VASP incorporate a fraction of exact Hartree-Fock exchange to mitigate self-interaction errors and improve band gap predictions. The Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid, with 25% exact exchange and a range-separation parameter of 0.11 bohr⁻¹, excels at describing band gaps and optical properties in semiconductors and insulators due to its reduced computational cost for extended systems compared to fully nonlocal hybrids. In contrast, the PBE0 functional mixes 25% exact exchange with the PBE semilocal terms without screening, providing higher accuracy for molecular excitation energies and reaction pathways at greater expense. Beyond standard DFT, VASP extends to meta-GGA functionals like the Strongly Constrained and Appropriately Normed () approximation, which incorporates kinetic energy density for enhanced description of diverse bonding types, including weak interactions, while maintaining reasonable computational scaling. For van der Waals (vdW) forces absent in conventional functionals, the DFT-D3 dispersion correction adds a semiempirical, atom-pairwise term with damping to account for London dispersion, significantly improving predictions for layered materials and physisorption. Additionally, the random phase approximation (), implemented via the adiabatic connection fluctuation-dissipation theorem, computes correlation energies including nonlocal effects for excited states and total energies, offering benchmark-level accuracy for molecular and solid-state excitations despite its high cost.

Usage

Input Structure

The Vienna Ab initio Simulation Package (VASP) employs a file-based input system consisting of four primary text files—POSCAR, INCAR, KPOINTS, and POTCAR—that collectively define the atomic structure, computational parameters, k-point sampling, and pseudopotentials for a simulation. These files must be placed in the working directory, with VASP reading them in a specific order to set up the calculation, ensuring consistency such as matching species order between POSCAR and POTCAR. The POSCAR file specifies the crystal structure, including lattice vectors and atomic positions. It begins with a comment line (up to 40 characters), followed by a scaling factor (a single real number for uniform scaling or three for individual axes), three lines defining the lattice vectors in Cartesian coordinates (scaled by the factor), a line listing element symbols (optional), a line with the number of atoms per species, an optional line for selective dynamics ("Selective dynamics"), a line indicating coordinate type ("Direct" for fractional or "Cartesian"), and then the atomic positions (one per line, in the order of species). Selective dynamics allows flags (T or F) for each coordinate to fix or relax atoms during optimization. For example, the primitive cell of silicon in the diamond cubic structure might appear as:
Si
1.0
  2.715  2.715  0.000
  0.000  2.715  2.715
  2.715  0.000  2.715
Si
2
Direct
  0.000  0.000  0.000
  0.250  0.250  0.250
Positions require at least seven significant digits for precision, and the file shares its format with the output CONTCAR for restarts. The INCAR file controls the calculation's parameters and algorithms, using a simple tag-value format where each line sets a parameter (e.g., ENCUT = 400) and unset tags default to VASP's built-in values. Key tags include ENCUT, which sets the plane-wave energy cutoff in eV (typically 1.3 times the maximum ENMAX from POTCAR for convergence); PREC, which adjusts precision and grid sizes (e.g., "Normal" or "Accurate"); ISTART, which determines the starting wavefunction (0 for new calculation from atomic densities, 1 to read from WAVECAR); and NPAR, which optimizes parallelization by grouping bands (e.g., set to the number of nodes or cores divided by k-points). Other essential tags like EDIFF (electronic convergence criterion, e.g., 10^{-6} eV) and NSW (number of ionic steps for relaxation) steer the workflow. Exchange-correlation functionals are selected via tags such as GGA = PE for PBE. The KPOINTS file defines the sampling of the Brillouin zone via k-points, essential for integrating over reciprocal space. It starts with a comment line, followed by the number of k-points (0 for automatic generation), a line specifying the generation method (e.g., "Monkhorst-Pack", "Gamma", or explicit list), and then grid parameters or coordinates. The generates a uniform grid (e.g., 4x4x4 subdivisions along reciprocal vectors) with optional shifts (default 0 0 0). Shifts of 0.5 0.5 0.5 are often used for off-centered grids, while the ensures inclusion of the Gamma point. Explicit k-points list fractional or Cartesian coordinates with weights (summing to 1). For instance, a is:
Automatic mesh
0
Monkhorst-Pack
4 4 4
0 0 0
VASP automatically reduces the grid using symmetry if enabled, and denser meshes improve accuracy for properties like total energy. The POTCAR file supplies the pseudopotential data for each atomic species, generated by concatenating individual files from the VASP library (accessed via the VASP Portal). It must list species in the exact order as in POSCAR, with no mixing of exchange-correlation types across potentials. Each segment includes a header (e.g., TITEL for potential name, ZVAL for valence electrons like 4.000 for carbon, ENMAX for recommended cutoff like 400 eV, and POMASS for atomic mass) followed by tabulated projector data, ending with "End of Dataset". Preparation involves selecting pseudopotentials (standard or variant like _sv for semicore states) and using commands like cat POTCAR_C POTCAR_O > POTCAR for multi-element systems. Users should not edit the file contents, as they are optimized for the method.

Output Analysis

VASP produces a variety of output files that capture the progress and results of simulations, allowing users to assess , extract physical properties, and prepare data for further analysis or visualization. These files are generated during the execution of calculations and vary in detail, from concise summaries to comprehensive logs, facilitating both quick checks and in-depth post-processing. The structure and content of these outputs are designed to support iterative workflows, such as restarting interrupted runs or integrating with external tools for property evaluation. The OSZICAR file provides a compact record of the self-consistency history, listing details for each electronic step such as the step number, current , energy change, band structure energy change, number of evaluations, residuum norm, and charge density difference. For ionic relaxation or steps, it includes additional information like total , forces, and if applicable. This file is essential for monitoring the stability and efficiency of the self-consistent field (SCF) iterations and ionic updates without delving into voluminous data. The OUTCAR file acts as the main detailed log of the entire run, encompassing a summary of input , Kohn-Sham eigenvalues from electronic steps, stress tensors, atomic forces, local charges, magnetic moments, and dielectric . It also flags warnings on issues like poor or numerical instabilities, alongside final total energies and wavefunction-related information. Users rely on OUTCAR to verify the integrity of results and extract key quantities like equilibrium geometries or equilibrium . The verbosity of this file can be adjusted via the NWRITE in the input. The CHGCAR file stores the total (and ) charge on a real-space , along with projector-augmented wave () one-center occupancies, enabling visualization of distributions or use as an initial guess for restarting calculations with parameters like ICHARG=1. Similarly, the WAVECAR file holds binary data for wavefunction coefficients, including band energies, Fermi weights, and basis set details, which supports efficient continuation of runs by providing high-quality starting orbitals, particularly useful in dynamic simulations or relaxations. Both files are binary and can be large, but they are indispensable for density plotting or avoiding full SCF restarts in subsequent jobs. Post-processing of VASP outputs is commonly performed using specialized tools to derive derived quantities like band structures and densities of states (DOS). VASPKIT, for instance, processes files such as EIGENVAL, PROCAR, and DOSCAR to generate total and projected band structures, DOS plots (including l- or lm-decomposed), and charge density slices. The p4vasp suite offers an interactive graphical interface for visualizing band structures, DOS, convergence plots, and structural data directly from output files. For three-dimensional rendering, VESTA integrates seamlessly with CHGCAR and POSCAR/CONTCAR files to display atomic structures, isosurfaces of charge densities, and volumetric data with customizable rendering options. These tools enhance the interpretability of VASP results without requiring custom scripting.

Applications

Materials Science

VASP has been extensively applied in materials science to compute electronic properties of bulk semiconductors, such as band structures and densities of states (DOS), enabling predictions of fundamental characteristics like indirect band gaps. For silicon (Si), VASP calculations using hybrid functionals such as HSE within density functional theory (DFT) yield an indirect band gap of approximately 1.14 eV at the Gamma-to-X point, closer to the experimental value of 1.12 eV at low temperatures, which is crucial for understanding its optoelectronic limitations compared to direct-gap materials. Similarly, for gallium arsenide (GaAs), VASP simulations yield a direct band gap of about 0.3 eV at the Gamma point using the local density approximation (LDA), though hybrid functionals like HSE06 improve accuracy to near-experimental 1.5 eV, highlighting VASP's utility in benchmarking semiconductor device materials. These computations provide insights into charge carrier dynamics without experimental synthesis, aiding the design of silicon-based photovoltaics and GaAs heterostructures. In defect studies, facilitates the determination of formation energies for intrinsic defects in oxides, which govern electrical conductivity and catalytic performance. For instance, oxygen vacancies in TiO₂, a prototypical photocatalyst, exhibit formation energies ranging from 3.5 to 4.5 eV depending on the charge state and Hubbard U correction, with neutral vacancies introducing mid-gap states that enhance n-type doping. These -based results, often employing the with GGA+U functionals, reveal that bridging oxygen removal is thermodynamically favored over in-plane sites, influencing defect-mediated charge transport in and environmental applications. Such analyses have informed strategies to engineer defect concentrations for improved TiO₂-based solar cells and sensors. VASP also supports the evaluation of thermodynamic properties through phonon spectra calculations, which yield vibrational free energies essential for assessing phase stability in alloys at finite temperatures. Phonon dispersions computed via the finite displacement method in VASP demonstrate dynamical stability in ordered phases like Al₃Li in Al-Li alloys, where vibrational entropy contributions stabilize the ordered structure by up to 0.1 eV/atom relative to disordered solid solutions, impacting lightweight aerospace materials. For high-entropy alloys, these free energy calculations predict phase transitions by integrating quasiharmonic approximations, revealing how anharmonic effects lower formation barriers in multi-component systems. Additionally, ab initio molecular dynamics (AIMD) simulations in VASP briefly extend these to dynamic defect diffusion in bulk materials. A prominent application is the prediction of Li-ion battery materials, exemplified by LiCoO₂, where VASP computes intercalation voltages to optimize . DFT calculations yield an average of 4.0 V for Li extraction from LiCoO₂, aligning with experimental discharge profiles and attributing voltage plateaus to layered-to-spinel phase transitions, which guide doping strategies to mitigate capacity fade. These simulations, using potentials and spin-polarized GGA, have accelerated the screening of cobalt-based cathodes for higher-voltage operation in electric vehicles.

Surface and Interface Studies

VASP facilitates the study of surface phenomena through slab models, which approximate low-dimensional systems by cleaving bulk structures and introducing vacuum regions to simulate isolated surfaces. These models enable relaxation of atomic positions to determine equilibrium geometries and adsorption sites for molecules on metal or oxide surfaces. For instance, in catalytic applications, VASP calculations using density functional theory (DFT) have been employed to investigate CO adsorption on the Pt(111) surface, revealing preferred atop and bridge sites with adsorption energies around -1.5 to -2.0 eV, depending on coverage and functional choice, which informs mechanisms in CO oxidation catalysis. Key properties such as and cleavage energies are routinely computed in VASP for these slabs. The , defined as the energy required to remove an from the surface to , is obtained by differencing the from the average electrostatic potential in the region, typically requiring 8–12 of and accurate convergence settings like PREC=Accurate. Cleavage energies quantify the energy cost of creating surfaces and are calculated as the difference between slab and formation energies per unit area, scaled by the number of layers to extrapolate to the clean surface limit. For charged or polar slabs, dipole corrections are essential to mitigate artificial interactions from ; VASP implements these via LDIPOL=.TRUE. and IDIPOL=3 in the file, ensuring a flat potential in the and accurate forces during relaxation. Interface simulations in extend to grain boundaries in metals and epitaxial layers in , using models to capture atomic-scale structures and electronic properties. For grain boundaries, such as Σ5 tilt boundaries in face-centered cubic metals like or , VASP DFT calculations reveal excess energies of 0.1–0.5 J/m² and localized states that influence mechanical strength and diffusion. In epitaxial heterostructures, like layers on substrates, VASP models strain and band alignment, for example, in GaAs/ interfaces, showing valence band offsets around 0.5 eV that affect optoelectronic performance. A prominent example is the modeling of water dissociation on the TiO₂(110) surface, where simulations demonstrate that adsorbed H₂O molecules undergo O–H bond breaking at bridging oxygen sites, with barriers of 0.8–1.2 , facilitated by surface vacancies or defects to enhance efficiency. These studies often incorporate van der Waals corrections briefly to account for weak in aqueous environments.

Licensing and Community

Distribution Model

The Vienna Ab initio Simulation Package () is a package developed and exclusively distributed by VASP Software , a for-profit company based in , , since the early 2000s. This entity serves as the sole worldwide copyright owner and licensor, ensuring centralized registration and control over all legal copies to protect and prevent unauthorized distribution. VASP's distribution model requires users to obtain a for access, with no open-source availability. Licenses are issued on a per-research-group basis rather than institution-wide, though site licenses are available for larger or non-profit institutions to cover multiple groups. , governmental, and non-profit licenses are offered at reduced rates compared to commercial ones, reflecting the software's origins in while supporting ongoing through generation. For instance, upgrade fees to newer versions have been reported at approximately €1,500 as of 2023. Commercial licenses, intended for industry and for-profit applications, incur higher fees to reflect their broader usage rights and the associated support needs. The licensing policy has evolved from VASP's initial development as a purely academic tool at the in the 1990s—led by researchers including Prof. Georg Kresse—to a commercial framework managed by . This transition, formalized through the company's establishment, enabled sustainable funding for enhancements, bug fixes, and version releases, while maintaining the 's involvement in core development efforts. All licenses must be obtained directly from or authorized resellers like Materials Design, Inc., and are non-transferable between institutions without approval.

User Support

The official VASP website at vasp.at serves as the primary hub for user resources, providing comprehensive manuals through the VASP Wiki, which details input and output documentation, compilation advice, and code usage. Tutorials on the site guide users through practical calculations, including example input files for various simulations, accessible only to licensed users. Additionally, a dedicated on vasp.at enables licensed users to post questions, share experiences, and seek technical support from the community and developers. VASP organizes regular workshops to support advanced learning, with sessions held since the early 2000s, often at the or in collaboration with international partners, covering topics such as electron-phonon interactions, NMR, and XAS calculations. These 2-3 day events include lectures and hands-on tutorials, with recent online formats announced for 2025 to accommodate global participation. Users are required to cite key foundational papers in any publications resulting from VASP calculations, including the seminal work by Kresse and Hafner on molecular dynamics. This acknowledgment ensures proper credit to the developers and is a standard condition of use. The VASP community benefits from integrations with external tools, such as the Atomic Simulation Environment (ASE), which allows Python-based scripting for setting up, running, and analyzing calculations. Error reporting and troubleshooting are facilitated through the official forum, where users can submit detailed queries for developer assistance, though full access requires a valid .

References

  1. [1]
    About - VASP
    What is VASP? The Vienna Ab initio Simulation Package (VASP) is a computer program for atomic scale materials modelling, e.g. electronic structure ...
  2. [2]
    Ab initio molecular dynamics for liquid metals | Phys. Rev. B
    Jan 1, 1993 · We present ab initio quantum-mechanical molecular-dynamics calculations based on the calculation of the electronic ground state and of the Hellmann-Feynman ...
  3. [3]
    Efficiency of ab-initio total energy calculations for metals and ...
    We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave ...
  4. [4]
    Efficient iterative schemes for ab initio total-energy calculations ...
    We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). ... Kresse and J. Hafner, Phys. Rev. B 47 ...Missing: original | Show results with:original
  5. [5]
    Vienna Ab-initio Simulation Package (VASP) and Applications
    The software has been developed/refractored by the Kresse group at the University of Vienna and VASP Software GmbH for about 25 years. It enables MPI and Open ...
  6. [6]
    [PDF] Introduction to First-Principles Electronic Structure Methods
    Dec 14, 2005 · Equation (1) is simply the time-independent Schrödinger equation. The term “first-principles” means that there is no empirical fitting, or ...Missing: definition | Show results with:definition
  7. [7]
    Ab initio quantum chemistry: Methodology and applications - PMC
    May 10, 2005 · The underlying core technology is computational solution of the electronic Schrodinger equation; given the positions of a collection of ...
  8. [8]
    [PDF] Ab initio and electronic structure methods ChE210D
    Jul 31, 2025 · Note that the Schrodinger equation is a differential equation that is first order in time and second order in position. To solve it, we can ...
  9. [9]
    [PDF] XII. The Born-Oppenheimer Approximation ∑ ∑ ∑ ∑ ∑ - MIT
    The Born- Oppenheimer (BO) approximation is probably the most fundamental approximation in chemistry. From a practical point of view, it will allow us to treat ...
  10. [10]
    [PDF] The Born-Oppenheimer Approximation
    The Born-Oppenheimer approximation rests on the fact that the nuclei are much more massive than the electrons, which allows us to say that the nuclei are nearly ...Missing: definition | Show results with:definition
  11. [11]
    [PDF] The Hartree-Fock Method in Atoms† 1. Introduction
    The Hartree-Fock method is a basic method for approximating the solution of many-body electron problems in atoms, molecules, and solids.
  12. [12]
    [PDF] Density Functional Theory (DFT) - Rutgers Physics
    DFT views system properties as a functional of ground state density, using a scalar function instead of a complex wave function. Kohn and Sham replaced the ...
  13. [13]
    Many-Body Perturbation Theory - an overview | ScienceDirect Topics
    In first-order perturbation theory, the correction is straightforward and unique, leading to the Hartree–Fock method. In second-order perturbation theory ...
  14. [14]
    [PDF] Brief History of Electronic Structure Calculations in Computational ...
    Jan 20, 2022 · The rapid development of ab initio or first-principle electronic level simulation methods – and their application to more complicated systems ...
  15. [15]
    Density functional theory: Its origins, rise to prominence, and future
    Aug 25, 2015 · One of the first signs of growing acceptance of DF methods in chemistry was the incorporation of such calculations into popular ab initio ...
  16. [16]
    Ab‐initio simulations of materials using VASP: Density‐functional ...
    Jul 11, 2008 · Ab‐initio simulations of materials using VASP: Density‐functional theory and beyond - Hafner - 2008 - Journal of Computational Chemistry - ...Missing: paper | Show results with:paper
  17. [17]
    Inhomogeneous Electron Gas | Phys. Rev.
    November 1964. Received 18 June 1964. Export Citation. Reuse & Permissions. DOI: https://doi.org/10.1103/PhysRev.136.B864. © 1964 American Physical Society.
  18. [18]
    Self-Consistent Equations Including Exchange and Correlation Effects
    In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials.
  19. [19]
    Ground State of the Electron Gas by a Stochastic Method
    Aug 18, 1980 · An exact stochastic simulation of the Schroedinger equation for charged bosons and fermions has been used to calculate the correlation energies.Missing: uniform | Show results with:uniform
  20. [20]
    Self-interaction correction to density-functional approximations for ...
    May 15, 1981 · Self-interaction correction to density-functional approximations for many-electron systems. J. P. Perdew · Alex Zunger.Missing: original | Show results with:original
  21. [21]
    Generalized Gradient Approximation Made Simple | Phys. Rev. Lett.
    Oct 28, 1996 · We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants.
  22. [22]
    Density functional theory in the solid state - Journals
    Mar 13, 2014 · Residual self-interaction is one of the most significant causes of the underestimation of the band gap in LDA-(or GGA-) based DFT calculations.
  23. [23]
    [PDF] ienna imulation ackage b-initio - EHU
    ... Vienna ab-initio simulation package VASP – VASP.5.2. The new release ... • VASP is based on a program initially written by Mike Payne at the MIT. Hence ...
  24. [24]
    History of VASP
    VASP is based on a program initially written by Mike Payne at the MIT. Hence, VASP has the same roots as the CASTEP/CETEP code, but branched from this root at a ...
  25. [25]
    ‪Georg Kresse‬ - ‪Google Scholar‬
    Georg Kresse, University of Vienna, Faculty of Physics, Professor for Computational Quantum Mechanics. Verified email at univie.ac.at - HomepageMissing: original | Show results with:original
  26. [26]
    [PDF] ienna imulation ackage b-initio
    VASP.5 is currently not distributed, expected release date mid 2006. VASP ... VASP.5.0 defaults to. GGA COMPAT = .FALSE.. – 12.08.2003: MAJOR BUG FIX in ...
  27. [27]
    [PDF] Basics (DFT, PW, PAW, … ) - VASP
    VASP basics include Density Functional Theory, Plane Wave basis set, Projector-Augmented-Wave method, and Hohenberg-Kohn-Sham DFT.
  28. [28]
    [PDF] Pseudopotentials (Part I): - VASP
    three different types of potentials are supported by VASP. – norm-conserving pseudopotentials. – ultra-soft pseudopotentials. – PAW potentials they will be ...
  29. [29]
    Projector augmented-wave method | Phys. Rev. B
    Dec 15, 1994 · The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original ... P.E. Blöchl, Ph.D ...
  30. [30]
    Does SCF calculation have to be done before calculating DOS?
    Jan 7, 2022 · The standard procedure to calculate DOS or band structure is: Structure optimization,; SCF calculation,; non-SCF calculation. According to the ...Why do we specifically need an SCF-generated charge density for ...Exploring Electronic Properties: Density of States (DOS) and Band ...More results from mattermodeling.stackexchange.com
  31. [31]
    Structure optimization - VASP Wiki
    Overview. Structure optimization describes the task of finding the lattice vectors and atom positions that minimize the energy of the system.Missing: AIMD phonons
  32. [32]
    Computing the phonon dispersion and DOS - VASP Wiki
    After computing the force constants using the finite differences or density-functional-perturbation theory (DFPT) approaches, it is possible to compute the ...1Phonon dispersion: Step-by... · 2Phonon DOS: Step-by-step... · 3Polar materials<|separator|>
  33. [33]
    Category:Exchange-correlation functionals - VASP Wiki
    ### Summary of Exchange-Correlation Functionals in VASP
  34. [34]
  35. [35]
    Hybrid functionals: formalism - VASP Wiki
    Oct 21, 2025 · In hybrid functionals the exchange energy is a mixture of semilocal (SL) and nonlocal Hartree-Fock (HF) types. They can be categorized into ...Missing: paper | Show results with:paper
  36. [36]
    Toward reliable density functional methods without adjustable ...
    Apr 1, 1999 · We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient ...
  37. [37]
    METAGGA - VASP Wiki
    May 20, 2025 · The XC tag, available since VASP.6.4.3, can be used to specify any linear combination of LDA, GGA and METAGGA exchange-correlation functionals.
  38. [38]
    A consistent and accurate ab initio parametrization of density ...
    Apr 16, 2010 · We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind.
  39. [39]
  40. [40]
    Input - VASP Wiki
    Apr 6, 2022 · VASP basically needs 4 input files for standard production runs: INCAR. The INCAR file holds the input parameters which "steer" the calculation.
  41. [41]
    POSCAR - VASP Wiki
    ### Summary of POSCAR File Format
  42. [42]
    INCAR - VASP Wiki
    ### Summary of INCAR File
  43. [43]
    KPOINTS - VASP Wiki
    ### KPOINTS File Format Summary
  44. [44]
    None
    Nothing is retrieved...<|control11|><|separator|>
  45. [45]
    Preparing a POTCAR - VASP Wiki
    Jun 26, 2024 · The POTCAR file is a mandatory input file that holds the pseudopotential for each element in the structure. The templates for each element ...
  46. [46]
    OSZICAR - VASP Wiki
    ### Summary of OSZICAR File in VASP Calculations
  47. [47]
    OUTCAR - VASP Wiki
    ### Summary of OUTCAR File Description
  48. [48]
    CHGCAR - VASP Wiki
    ### Summary of CHGCAR File
  49. [49]
    WAVECAR - VASP Wiki
    ### Summary of WAVECAR File
  50. [50]
    Features — VASPKIT 1.5 documentation
    01. VASP Input-Files Generator ; 101. Customize INCAR File ; 102. Generate KPOINTS File for SCF Calculation ; 103. Generate POTCAR File with Default Setting.<|separator|>
  51. [51]
    p4vasp, the VASP Visualization Tool - GitHub
    P4vasp is a portable application - it can be started from a usb drive. Source-code distributions Compilation Quickstart
  52. [52]
    VESTA - JP-Minerals
    VESTA is a 3D visualization program for structural models, volumetric data such as electron/nuclear densities, and crystal morphologies.Download · Documentation · Koichi Momma - About myself · Features
  53. [53]
    A Density Functional Theory + U Study of Oxygen Vacancy ...
    Apr 1, 2009 · Oxygen vacancy formation requires the removal of a two-coordinate surface oxygen, and for all four surfaces the excess charge left at the ...
  54. [54]
    The effect of vibrational entropy on the solubility and stability of ...
    Oct 1, 2013 · The effect of vibrational entropy on the solubility and stability of ordered Al3Li phases in Al-Li alloys Free ... (VASP).14 We utilized the ...
  55. [55]
    The free energy of mechanically unstable phases - Nature
    Jul 1, 2015 · Electronic structure calculations were performed with the Vienna Ab initio Simulation Package (VASP) code implementing the projector augmented ...
  56. [56]
    [PDF] Li-intercalation Oxides for Rechargeable - Batteries - Ceder Group
    This article illustrates how first-principles calculations can play a critical role in obtaining the understanding needed to design improved cathode oxides. 1.
  57. [57]
    The CO/Pt(111) Puzzle | The Journal of Physical Chemistry B
    CO should prefer hollow- to atop-site adsorption on Pt(111), in apparent contradiction to a host of low-temperature experimental studies.Introduction · II. Experimental CO Bonding... · New DFT Results for CO...
  58. [58]
    A DFT study of CO adsorption on pt (111) using van der Waals ...
    In this study, we have used vdW-DF functionals to investigate the role of dispersive interaction in the adsorption of CO on Pt(111) surface.
  59. [59]
    Computing the work function - VASP Wiki
    Jun 12, 2024 · The work function is defined as the work needed to move an electron from a surface to a point in vacuum sufficiently far away from this ...Missing: cleavage | Show results with:cleavage
  60. [60]
    Electrostatic corrections - VASP Wiki
    ### Summary of Dipole Corrections for Slab Calculations in VASP
  61. [61]
    A simplified methodology for the modeling of interfaces of ...
    Nov 11, 2021 · Automated generation of reasonable atomic-level interface models, for example, at a grain boundary, is generally computationally intensive ...
  62. [62]
    Electronic properties of low- Σ grain boundaries in InAs
    Dec 27, 2018 · We employ first-principles density functional theory to investigate the electronic and structural properties of grain boundaries (GBs) in InAs.
  63. [63]
    What Controls Photocatalytic Water Oxidation on Rutile TiO2(110 ...
    The primary photochemical process is O–H bond dissociation where the water's H atom is transferred to the surface's 2-fold-coordinated bridging oxygen atom O2s ...
  64. [64]
    The adsorption and dissociation of H 2 O on TiO 2 (110) and M/TiO 2 ...
    The adsorption and dissociation of H2O on clean TiO2(110) and metal-deposited M/TiO2(110) (M = Pt and Au) surfaces were studied by performing calculations ...
  65. [65]
    VASP - Vienna Ab initio Simulation Package
    VASP is the Vienna Ab initio Simulation Package, used for atomic scale materials modelling from first principles.About · The VASP Manual · VASP Community Portal · Get a license
  66. [66]
    Contact - VASP
    VASP Software GmbH. Berggasse 21/14. A-1090, Vienna, Austria. Phone: +43-676-3570875. For VASP licensing related queries: licensing@vasp.at.
  67. [67]
    FAQs - VASP
    VASP licenses are permanent licenses to the purchased software release and all minor upgrades to this release within the first three years after the license ...
  68. [68]
    How can I purchase a VASP license?
    VASP licenses are available for both academic and commercial use: Academic, Governmental, and Non-Profit Research Institution Licences: To obtain an academic ...
  69. [69]
    VASP - ALCF User Guides - Argonne National Laboratory
    Using VASP at ALCF¶. VASP is commercial software. Access to binaries compiled by ALCF can only be granted after the user requesting access has been verified ...
  70. [70]
    VASP - Center for High Performance Computing - chpc.utah.edu
    Apr 9, 2025 · For reference, below are some timings for VASP 6.3.2 on the AMD Milan 64 core and Intel Ice Lake 56 core Notchpeak nodes, running 20 SCF ...
  71. [71]
    [PDF] Mississippi State University Notice of Proposed Sole Source ...
    4. Estimated cost of item(s) and an explanation why the amount to be expended is considered reasonable: $5433 (5000€).
  72. [72]
  73. [73]
    Tutorials - VASP
    Install VASP and find the tutorial that suits you. You will need the VASP executable in your system path and a working directory in which you run the tutorials.Part 1: Introduction to VASP · Part 2: Molecules in VASP · Atoms and Molecules
  74. [74]
    Forum - VASP
    No information is available for this page. · Learn why
  75. [75]
    VASP workshop - VASP Wiki
    Nov 14, 2019 · The lectures and tutorials listed below constitute a typical 2-3 day VASP workshop, as we have held many over the years.Missing: University Vienna annual 2000s
  76. [76]
    News - VASP
    At the VASP Software GmbH, we develop the leading software for the simulation of condensed matter systems from first principles. We are looking for two talented ...Missing: formation | Show results with:formation
  77. [77]
    Vienna Ab initio Simulation Package (VASP)
    VASP is a computer program for atomic scale materials modelling, eg electronic structure calculations and quantum-mechanical molecular dynamics.
  78. [78]
    VASP — ASE documentation
    VASP is a density-functional theory code using pseudopotentials or the projector-augmented wave method and a plane wave basis set.
  79. [79]
    Known issues - VASP Wiki
    Requests for technical support from the VASP team should be posted in the VASP Forum. ... Compilation error for GCC with ELPA support: Compilation with ELPA ...