On an "interaction by moments" property of four center integrals

The four center integrals needed in the Hartree Fock approximation and in TDDFT linear response are known to be difficult to calculate for orbitals of the Slater type or of finite range. We show that the interaction of pairs of products that do not mutually intersect may be replaced by the interaction of their moments, of which there are O(N). Only quadruplets of orbitals 'close' to one another need an explicit calculation and the total calculational effort therefore scales as O(N). We provide a new and concise proof of this "interaction by moments" property.Comment: The context of this note is the implementation of TDDFT linear response for extended molecular system

A Parallel Iterative Method for Computing Molecular Absorption Spectra

We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table

On the Kohn--Sham density response in a localized basis set

We construct the Kohn--Sham density response function $\chi_{0}$ in a previously described basis of the space of orbital products. The calculational complexity of our construction is $O(N^{2}N_{\omega})$ for a molecule of $N$ atoms and in a spectroscopic window of $N_{\omega}$ frequency points. As a first application, we use $\chi_{0}$ to calculate molecular spectra from the Petersilka--Gossmann--Gross equation. With $\chi_{0}$ as input, we obtain correct spectra with an extra computational effort that grows also as $O(N^2 N_{\omega})$ and, therefore, less steeply in $N$ than the $O(N^{3})$ complexity of solving Casida's equations. Our construction should be useful for the study of excitons in molecular physics and in related areas where $\chi_{0}$ is a crucial ingredient.Comment: 20 pages, 11 figure

Current state of the art in TDDFT code

International audienceWe present a TDDFT code developed in the framework of NOSSI project. The code is capable to compute absorption spectra in linear response regime. The method for calculating of the Kohn-Sham response function is outlined. Complexity of the method is discussed in detail. Testing of the shared memory parallelization and examples of spectra are given

Extension of LCAO to excited states: non interacting response and molecular spectra

International audienceWe present the algorithm for a fast calculation of the Kohn-Sham response function in a localized basis set. Examples of spectra are given and parallelization approach is outlined

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Orientador: Irapuru Haruo FlóridoMonografia (graduação) - Universidade Federal do Paraná, Escola Técnica, Curso de Tecnologia em InformáticaInclui bibliografi

The EnMAP imaging spectroscopy mission towards operations

EnMAP (Environmental Mapping and Analysis Program) is a high-resolution imaging spectroscopy remote sensing mission that was successfully launched on April 1st, 2022. Equipped with a prism-based dual-spectrometer, EnMAP performs observations in the spectral range between 418.2nm and 2445.5nm with 224 bands and a high radiometric and spectral accuracy and stability. EnMAP products, with a ground instantaneous field-of-view of 30m×30m at a swath width of 30km, allow for the qualitative and quantitative analysis of surface variables from frequently and consistently acquired observations on a global scale. This article presents the EnMAP mission and details the activities and results of the Launch and Early Orbit and Commissioning Phases until November 1st, 2022. The mission capabilities and expected performances for the operational Routine Phase are provided for existing and future EnMAP users