Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems.

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

The CECAM electronic structure library and the modular software development paradigm.

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

Insights into colour-tuning of chlorophyll optical response in green plants.

First-principles calculations within the framework of real-space time-dependent density functional theory have been performed for the complete chlorophyll (Chl) network of the light-harvesting complex from green plants, LHC-II. A local-dipole analysis method developed for this work has made possible the studies of the optical response of individual Chl molecules subjected to the influence of the remainder of the chromophore network. The spectra calculated using our real-space TDDFT method agree with previous suggestions that weak interaction with the protein microenvironment should produce only minor changes in the absorption spectrum of Chl chromophores in LHC-II. In addition, relative shifting of Chl absorption energies leads the stromal and lumenal sides of LHC-II to absorb in slightly different parts of the visible spectrum providing greater coverage of the available light frequencies. The site-specific alterations in Chl excitation energies support the existence of intrinsic energy transfer pathways within the LHC-II complex.

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems.

Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

A survey of the parallel performance and accuracy of Poisson solvers for electronic structure calculations.

We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance-in terms of both numerical complexity and accuracy-of popular Poisson solvers, and to give an intuitive idea on the way these solvers operate. Highly parallelizable routines have been implemented in a first-principle simulation code (Octopus) to be used in our tests, so that reliable conclusions about the capability of methods to tackle large systems in cluster computing can be obtained from our work.

Modeling van der Waals interactions between proteins and inorganic surfaces from time-dependent density functional theory calculations.

In this work we show how the ab initio determination of van der Waals coefficients within time-dependent density functional theory can be used to build efficient and accurate atomistic models that describe the long-range interactions of proteins with other proteins and of proteins with semi-conducting surfaces. The model parameters are fitted so that they reproduce the ab initio van der Waals coefficients of amino acids and dipeptides. We then assess the quality of our results by comparing ab initio van der Waals coefficients for larger peptides with the coefficients yielded by the models. The different sets of parameters can be easily incorporated in current empirical force field methods, thus providing an essential ingredient for molecular dynamics simulations of proteins close to surfaces.

Photoabsorption spectra of small cationic xenon clusters from time-dependent density functional theory.

Upon ionization, rare-gas (like Ar and Xe) clusters shift their absorption spectrum from the ultraviolet to the visible. This happens as bonding becomes much stronger due to the removal of an electron from a strongly antibonding orbital. In this article, we study the absorption spectrum of small cationic xenon clusters (Xe(n) (+), with n=3,...,35) by means of time-dependent density functional theory. These calculations include relativistic effects through the use of relativistic j-dependent pseudopotentials in a two-spinor formulation of the Kohn-Sham equations. The peak positions in our calculated spectra are in fairly good agreement with experiment and confirm that absorption is mainly due to a charged linear core composed of 3, 4, or 5 Xe atoms where the positive charge is localized. However, we find large deviations concerning the oscillator strengths, which can be partially explained by the unsatisfactory treatment of exchange in common density functionals. Furthermore, we find that adequate ground-state geometries are necessary for the correct prediction of the qualitative features of the spectra.

The role of dimensionality on the quenching of spin-orbit effects in the optics of gold nanostructures.

By first-principles time-dependent density-functional calculations, we show the relevance of relativistic effects to shape the photoabsorption cross section of small gold clusters (Au(n), n < or = 8, and n = 20) and small nanowires (n < or = 7). The relativistic effects not only dictate the stabilization of planar geometries (as it has already been shown by treating the core electrons relativistically): The spin-orbit coupling also has a strong impact in the absorption spectra (resonances and oscillator strengths). This is especially true for nanowires, where the effect of spin orbit is large and not substantially reduced with the chain length, in contrast to more compact gold clusters where this spin-orbit effect tends to be quenched. These results have far reaching consequences in fields such as electronic transport, where gold nanowires are often used, but where spin-orbit effects are generally disregarded.

On the use of Neumann's principle for the calculation of the polarizability tensor of nanostructures.

The polarizability measures how the system responds to an applied electrical field. Computationally, there are many different ways to evaluate this tensorial quantity, some of which rely on the explicit use of the external perturbation and require several individual calculations to obtain the full tensor. In this work, we present some considerations about symmetry that allow us to take full advantage of Neumann's principle and decrease the number of calculations required by these methods. We illustrate the approach with two examples, the use of the symmetries in real space and in spin space in the calculation of the electrical or the spin response.

Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory.

Attosecond electron dynamics in small- and medium-sized molecules, induced by an ultrashort strong optical pulse, is studied computationally for a frozen nuclear geometry. The importance of exchange and correlation effects on the nonequilibrium electron dynamics induced by the interaction of the molecule with the strong optical pulse is analyzed by comparing the solution of the time-dependent Schrödinger equation based on the correlated field-free stationary electronic states computed with the equationof-motion coupled cluster singles and doubles and the complete active space multi-configurational self-consistent field methodologies on one hand, and various functionals in real-time time-dependent density functional theory (TDDFT) on the other. We aim to evaluate the performance of the latter approach, which is very widely used for nonlinear absorption processes and whose computational cost has a more favorable scaling with the system size. We focus on LiH as a toy model for a nontrivial molecule and show that our conclusions carry over to larger molecules, exemplified by ABCU (C10H19N). The molecules are probed with IR and UV pulses whose intensities are not strong enough to significantly ionize the system. By comparing the evolution of the time-dependent field-free electronic dipole moment, as well as its Fourier power spectrum, we show that TD-DFT performs qualitatively well in most cases. Contrary to previous studies, we find almost no changes in the TD-DFT excitation energies when excited states are populated. Transitions between states of different symmetries are induced using pulses polarized in different directions. We observe that the performance of TD-DFT does not depend on the symmetry of the states involved in the transition.

Benchmarking the AK13 Exchange Functional: Ionization Potentials and Electron Affinities.

We perform benchmark calculations for the ionization potential and electronic affinity of atoms and small molecules using several semilocal exchange-correlation functionals of density-functional theory with improved asymptotic behavior. We are particularly interested in a new generalized-gradient approximation for exchange [Armiento and Kümmel, Phys. Rev. Lett. 2013, 111, 036402] that provides an energy functional whose functional derivative yields a potential with better decay behavior. We find that it yields energies that are worse than traditional energy functionals and potentials that are less accurate than functionals that model directly the exchange-correlation potential. However, we find that this functional offers a excellent balance between the quality of the energy and of the potential and is therefore a good compromise for applications that require at the same time reasonable energies and good potentials.

Time-dependent density-functional theory in massively parallel computer architectures: the OCTOPUS project.

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.