Octopus is a software package for performing KohnSham

density functional theory Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...

(DFT) and time-dependent density functional theory (TDDFT) calculations. Octopus employs pseudopotentials and real-space numerical grids to propagate the KohnSham orbitals in real time under the influence of time-varying electromagnetic fields. Specific functionality is provided for simulating one-, two-, and three-dimensional systems. Octopus can calculate static and dynamic polarizabilities and first hyperpolarizabilities, static magnetic susceptibilities, absorption spectra, and perform

molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the Motion (physics), physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamics ( ...

simulations with Ehrenfest and Car–Parrinello methods. The code is written predominantly in Fortran and is released under the GPL. The latest version 15.0 was released on October 10, 2024.

Target problems

* Linear optical (i.e. electronic) response of molecules or clusters, also second-order nonlinear response. * Non-linear response to classical high-intensity electromagnetic fields, taking into account both the ionic and electronic degrees of freedom. * Ground-state and excited state electronic properties of systems with lower dimensionality, such as quantum dots. * Photo-induced reactions of molecules (e.g., photo-dissociation, photo-isomerization, etc.). * In the immediate future, extension of these procedures to systems that are infinite and periodic in one or more dimensions (

polymer A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their br ...

s, slabs, nanotubes, solids), and to electronic transport.

Theoretical basis

* The underlying theories are DFT and TDDFT. Also, the code may perform dynamics by considering the classical (i.e. point-particle) approximation for the nuclei. These dynamics may be non-adiabatic, since the system evolves following the Ehrenfest path. It is, however, a mean-field approach. * Regarding TDDFT, one can use three different approaches: ** the standard TDDFT-based linear-response theory of Casida, which provides the excitation energies and oscillator strengths for ground-state to excited-state transitions. ** the explicit time-propagation of the TDDFT equations, which allows for the use of large external potentials, well beyond the range of validity of

perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle ...

. ** the Sternheimer equation (density-functional perturbation theory) in the frequency domain, using only occupied states.

Methodology

* As numerical representation, the code works without a basis set, relying on numerical meshes. Nevertheless, auxiliary basis sets (

plane wave In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...

atomic orbital In quantum mechanics, an atomic orbital () is a Function (mathematics), function describing the location and Matter wave, wave-like behavior of an electron in an atom. This function describes an electron's Charge density, charge distribution a ...

s) are used when necessary. Recently, the code offers the possibility of working with non-uniform grids, which adapt to the inhomogeneity of the problem, and of making use of multigrid techniques to accelerate the calculations. * For most calculations, the code relies on the use of pseudopotentials of two types: Troullier-Martins, and Hartwigsen-Goedecker-Hutter. * In addition to being able to treat systems in the standard 3 dimensions, 2D and 1D modes are also available. These are useful for studying, e.g., the two-dimensional electron gas that characterizes a wide class of quantum dots.

Technical aspects

* The code has been designed with emphasis on parallel scalability. In consequence, it allows for multiple task divisions, this utilises mesh division software,

MPI MPI or Mpi may refer to: Science and technology Biology and medicine * Magnetic particle imaging, a tomographic technique * Myocardial perfusion imaging, a medical procedure that illustrates heart function * Mannose phosphate isomerase, an enzyme ...

and

OpenMP OpenMP is an application programming interface (API) that supports multi-platform shared-memory multiprocessing programming in C, C++, and Fortran, on many platforms, instruction-set architectures and operating systems, including Solaris, ...

. * The language of most of the code is Fortran 90. Other languages, such as C, are also used. * The package is licensed under the

GNU General Public License The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first ...

(GPL). In consequence, it is available for use, inspection, and modification for anyone, at th
Octopus git repository

References

External links