Density Functional Resonance Theory (DFRT) is a complex-scaled version of ground-state Density Functional Theory (DFT) that allows one to calculate the resonance energies and lifetimes of metastable anions. In this formalism, the exact energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N -electron interacting system to a Kohn-Sham system of N non-interacting particles in DFRT. This mapping facilitates self consistent calculations with an initial guess for the complex density, as illustrated with an exactly-solvable model system. Whereas DFRT yields in principle the exact resonance energy and lifetime of the interacting system, we find that neglecting the complex-correlation contribution leads to errors of similar magnitude to those of standard scattering close-coupling calculations under the bound-state approximation.Density Functional Theory (DFT) [1][2][3] provides one of the most accurate and reliable methods to calculate the ground-state electronic properties of molecules, clusters, and materials from first principles. It is one of the workhorses of computational quantum chemistry [4]. In addition, DFT's time-dependent extension (TDDFT) [5] can now be applied to a wealth of excited-state and time-dependent properties in both linear and non-linear regimes [6]. When the N -electron system of interest has no bound ground state, however, neither DFT nor TDDFT can be applied in a straightforward way. A correct DFT calculation converges to the true ground state by ionizing the system, thus leaving no reliable starting point for a subsequent TDDFT calculation on the Nelectron system. In practice, a finite simulation box or basis set can make the system artificially bound [7,8], but information about the relevant lifetimes is lost in the process.We address here this fundamental limitation of groundstate DFT, and propose a solution.Consider a system of N interacting electrons in an external potentialṽ(r), with ground-state densityñ(r). The potential is set to be everywhere positive and go to a positive constant C as |r| → ∞. The ground-state energy isẼ > 0. We start by asking how the gound state density changes when a smooth step is added toṽ(r) at a radius |R| that is larger than the range ofṽ(r). The step is such that the new potential v(r) coincides with v(r) for |r| < |R| but goes to zero at infinity. Sinceṽ(r) is everywhere positive, all N electrons tunnel out and v(r) supports no bound states. The correct ground state energy is now E = 0, and the new density n(r) is delocalized through all space. In practical calculations, however, v(r) andṽ(r) cannot be distinguished if |R| is beyond the size of the simulation box. The result provided by ground-state DFT using the exact exchange-correlation functional is not E, b...

Research in NLP lacks geographic diversity, and the question of how NLP can be scaled to low-resourced languages has not yet been adequately solved. "Lowresourced"-ness is a complex problem going beyond data availability and reflects systemic problems in society. * ∀ to represent the whole Masakhane community.As MT researchers cannot solve the problem of low-resourcedness alone, we propose participatory research as a means to involve all necessary agents required in the MT development process. We demonstrate the feasibility and scalability of participatory research with a case study on MT for African languages. Its implementation leads to a collection of novel translation datasets, MT benchmarks for over 30 languages, with human evaluations for a third of them, and enables participants without formal training to make a unique scientific contribution. Benchmarks, models, data, code, and evaluation results are released at https://github. com/masakhane-io/masakhane-mt.

The ab-initio calculation of resonance lifetimes of metastable anions challenges modern quantum-chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex "density" that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density

ABSTRACT:We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn-Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials and wavefunctions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li and Be) as well as the H 2 molecule. Extensions are briefly discussed. SECTION: Spectroscopy, Photochemistry, and Excited States KEYWORDS: Resonances, Tunneling, Spectroscopy, Lasers, Excitations, Complex scaling, Open quantum systems.This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in J.Phys.Chem.Lett., copyright c American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/jz401110h. T he description of metastable compounds has been elusive to first-principles calculations due to the lack of a variational principle. The concepts of metastability and long-lived resonances (or tunneling processes) are closely related, and in the end we are facing the description of the lifetime of a given open quantum system. One approach to such calculations is the complex-scaling method, pioneered by Aguilar, Balslev and Combes. 1,2 Within this formalism, resonances appear as the result of a complex scaling r → re iθ of the real-space coordinates in the Hamiltonian. The method has been used to calculate resonance energies and lifetimes of negative ions of atoms, 3 as well as resonances induced by static electric fields. 4,5 Applications have however generally been limited to small systems or systems with reduced dimensionality due to the computational difficulty of solving many-particle problems. A different approach must be taken to accommodate realistic systems with many electrons. Recently it has been proven that the low-lying metastable states of a given system can be described within a density functional framework once we allow for complex densities. 6 An analog of the Hohenberg-Kohn theorem then allows for the calculation of the lowest-energy resonance of a system. Based on this, the first Kohn-Sham density functional resonance theory (DFRT) calculations have since been published, although limited to 1D systems with one or two electrons. 7,8 A notable ongoing development, termed complex DFT (CODFT), is based on complex absorbing potentials. 9,10 This method relies on the definition of an absorption zone outside the system boundary to calculate lifetimes based on how wavefunctions extend into the absorbing region. Another method is exterior complex scaling, where a complex coordinate scaling is applied outside of a certain radius. 11 The method presented in this Letter is based on uniform complex scaling, where all reg...

The s-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the s-wave interaction in many atomic speicies. This opens the possibilities to study magnetic dipole-dipole interactions (MDDI) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDI on the statics and dynamics of atomic BECs with tunable s-wave interactions. We benchmark our calculation against previously observed MDDI effects in 52 Cr with excellent agreement, and predict new effects that should be promising to observe experimentally. A parameter of magnetic Feshbach resonances, dd,max , is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors for the alkali BECs of 7 Li, 39 K, and 133 Cs. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.PACS numbers: 03.75.-b, 67.85.Bc, 67.85.De arXiv:1204