octopus: a tool for the application of time‐dependent density functional theory

Abstract

We report on the background, current status, and current lines of development of the octopus project. This program materializes the main equations of density-functional theory in the ground state, and of timedependent density-functional theory for dynamical effects. The focus is nowadays placed on the optical (i.e. electronic) linear response properties of nanostructures and biomolecules, and on the non-linear response to high-intensity fields of finite systems, with particular attention to the coupled ionic-electronic motion (i.e. photo-chemical processes). In addition, we are currently extending the code to the treatment of periodic systems (both to one-dimensional chains, two-dimensional slabs, or fully periodic solids), magnetic properties (ground state properties and excitations), and to the field of quantum-mechanical transport or "molecular electronics." In this communication, we concentrate on the development of the methodology: we review the essential numerical schemes used in the code, and report on the most recent implementations, with special attention to the introduction of adaptive coordinates, to the extension of our real-space technique to tackle periodic systems, and on large-scale parallelization. More information on the code, as well as the code itself, can be found at http://www.tddft.org/programs/octopus/.

A First-Principles Time-Dependent Density Functional Theory Framework for Spin and Time-Resolved Angular-Resolved Photoelectron Spectroscopy in Periodic Systems

“…We implemented the t-SURFFP method in the Octopus code [43][44][45] . In Octopus the TDKS equations are solved in a real-space grid and propagated in real-time.…”

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

“…The calculations in Ref. [152] were done using Octopus, [17,18] which uses a numerical real space grid to represent the Kohn-Sham orbitals. While real space grids offer a straightforward way for improving the accuracy of the calculation by reducing the grid spacing, the benefit of a localized basis set (as in ERKALE) is the significantly smaller number of degrees of freedom that makes spectrum calculations very fast.…”

“…In the field of quantum chemistry, there is a multitude of free density-functional theory [1,2] (DFT) codes using a wide variety of approaches to represent the molecular orbitals (MOs), such as plane-waves (e.g., ABINIT, [3,4] NWChem, [5,6] and Quantum ESPRESSO [7,8] ), wavelets (BigDFT, [9,10] DFT++ [11,12] and M-A-D-N-E-S-S [13] ), numerical atomic orbitals (OpenMX [14] and GPAW [15,16] ), and numerical grids (GPAW and Octopus [17,18] ), for example. However, these approaches (with the exception of multiresolution grids) become computationally problematic when hybrid DFT functionals [19] are used, due to the need to compute the exact exchange (see Hartree-Fock section).…”

Sparse Non-blocking Collectives in Quantum Mechanical Calculations

“…Substituting NP P for V and introducing the shape-dependent constants α, β, γ, we obtain equation (3).…”

“…The scientific application octopus [3] solves the eigenvalue problem of Eq. (1, left) by iterative diagonalization for the lowest N eigenpairs (ε j , ϕ j ) and Eq.…”