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).

An exchange-correlation energy functional involving fractional power of the one-body reduced density matrix ͓S. Sharma, J. K. Dewhurst, N. N. Lathiotakis, and E. K. U. Gross, Phys. Rev. B 78, 201103͑R͒ ͑2008͔͒ is applied to finite systems and to the homogeneous electron gas. The performance of the functional is assessed for the correlation and atomization energies of a large set of molecules and for the correlation energy of the homogeneous electron gas. High accuracy is found for these two very different types of systems. DOI: 10.1103/PhysRevA.79.040501 PACS number͑s͒: 31.10.ϩz, 31.15.AϪ, 31.15.ve, 31.15.vq For the past 40 years, density-functional theory ͑DFT͒ developed into one of the most successful theories in the study of the electronic structure of atoms, molecules, and periodic solids. At its heart lies the exchange-correlation ͑xc͒ functional, for which many approximations have been proposed. The simplest functionals that depend only on the density ͓the local-density approximation ͑LDA͔͒, or on the density and its gradients ͓the generalized gradient approximation ͑GGA͔͒, give a very satisfactory description of many ground-state properties. However, they still fail to reach chemical accuracy for some important quantities such as reaction or atomization energy. To remedy this situation hybrid functionals were introduced, the first and most widely used example being the Becke three-parameter Lee-Yang-Parr ͑B3LYP͒ functional ͓1,2͔. This functional is able to reproduce experimental atomization energies within about 10% error. Although the atomization energies obtained using B3LYP are in good agreement with experiments, the absolute correlation energies, an accurate description of which can be thought of as a test for the quality of any approximate functional, exhibit a sizeable error ͑up to 400%͒ ͓3͔. This is not a surprise since experimentally one normally measures energy differences, and it is these quantities that functionals such as B3LYP are designed to reproduce. Accurate correlation energies for finite systems can be obtained by going beyond the DFT framework, for instance, by using Møller-Plesset second-order ͑MP2͒ perturbation theory or the coupled cluster method with singles, doubles, and perturbative triples ͓CCSD͑T͔͒. However, these methods are computationally too expensive to be applied to realistic systems of ever growing complexity: biomolecules, large clusters, and nanodevices to name but a few examples.Recently, reduced density-matrix-functional theory ͑RDMFT͒ has appeared as an alternative approach to handle complex systems. It has shown great potential for improving upon DFT results for finite systems. RDMFT uses the onebody reduced density matrix ͑1-RDM͒ ␥ as the basic variable ͓4,5͔. This quantity, for the ground state, is determined through the minimization of the total energy functional under the constraint that ␥ is ensemble N representable. The total energy as a functional of ␥ can be expressed as ͑atomic units are used throughout͒where ͑r͒ ͑the electron density͒ is the diagonal ...

Thermoelectric transport in nanoscale conductors is analyzed in terms of the response of the system to a thermo-mechanical field, first introduced by Luttinger, which couples to the electronic energy density. While in this approach the temperature remains spatially uniform, we show that a spatially varying thermo-mechanical field effectively simulates a temperature gradient across the system and allows us to calculate the electric and thermal currents that flow due to the thermomechanical field. In particular, we show that, in the long-time limit, the currents thus calculated reduce to those that one obtains from the Landauer-Büttiker formula, suitably generalized to allow for different temperatures in the reservoirs, if the thermo-mechanical field is applied to prepare the system, and subsequently turned off at t = 0. Alternatively, we can drive the system out of equilibrium by switching the thermo-mechanical field after the initial preparation. We compare these two scenarios, employing a model noninteracting Hamiltonian, in the linear regime, in which they coincide, and in the nonlinear regime in which they show marked differences. We also show how an operationally defined local effective temperature can be computed within this formalism.