1. An O(N^3) implementation of Hedin's GW approximation for molecules
- Author
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Dietrich Foerster, Daniel Sánchez-Portal, Peter Koval, Laboratoire Ondes et Matière d'Aquitaine (LOMA), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Bordelais de Recherche en Informatique (LaBRI), and Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)
- Subjects
Chemical Physics (physics.chem-ph) ,Physics ,GW approximation ,Approximation theory ,010304 chemical physics ,Basis (linear algebra) ,Fast Fourier transform ,FOS: Physical sciences ,General Physics and Astronomy ,Space (mathematics) ,01 natural sciences ,Condensed Matter - Other Condensed Matter ,Atomic orbital ,Physics - Chemical Physics ,[PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other] ,0103 physical sciences ,Coulomb ,Statistical physics ,[PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph] ,Physical and Theoretical Chemistry ,010306 general physics ,Scaling ,Other Condensed Matter (cond-mat.other) - Abstract
15 páginas, 6 figuras, 5 tablas., We describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N3) with the number of atoms. Our method is guided by two strategies: (i) to respect the locality of the underlying electronic interactions and (ii) to avoid the singularities of Green's functions by manipulating, instead, their spectral functions using fast Fourier transform methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors., D.S.P. and P.K. acknowledge financial support from the Consejo Superior de Investigaciones Científicas (CSIC), the Basque Departamento de Educación, UPV/EHU (Grant No. IT-366-07), the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2010-19609-C02-02), and the ETORTEK program funded by the Basque Departamento de Industria and the Diputación Foral de Guipuzcoa.
- Published
- 2011
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