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 Time-dependent density-functional theory (TDDFT) is a quantum mechanical theory used in physics and chemistry to investigate the properties and dynamics of many-body systems in the presence of time-dependent potentials, such as electric or magne ...

(TDDFT) calculations. Octopus employs

pseudopotential In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering. The pseudopotential approximation was first introduced ...

s 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 Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating ...

, and perform

molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the 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 dynamic "evolution" of t ...

simulations with Ehrenfest and Car–Parrinello methods. The code is written predominantly in Fortran, with some C and

Perl Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offic ...

. It is released under the

GPL The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general u ...

. The latest version 12.0 was released September 19, 2022.

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 (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

s, slabs,

nanotubes A scanning tunneling microscopy image of a single-walled carbon nanotube Rotating single-walled zigzag carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with diameters typically measured in nanometers. ''Single-wall carbon na ...

, 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 middl ...

. ** 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, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, ...

atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in an ...

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

s 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 and

OpenMP OpenMP (Open Multi-Processing) 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 syst ...

. * The language of most of the code is Fortran 90 (almost 50.000 lines at present). Other languages, such as C or

, are also used. * The package is licensed under the

GNU General Public License The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general ...

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

References

External links