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# An O(N-3) implementation of Hedin's GW approximation for molecules

CPMOH/LOMA, Université de Bordeaux 1, 351 Cours de la Liberation, 33405 Talence, France.
(Impact Factor: 2.95). 08/2011; 135(7):074105. DOI: 10.1063/1.3624731
Source: PubMed

ABSTRACT

We describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N(3)) 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.

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• "labels the auxiliary basis functions. The auxiliary basis functions are constructed either explicitly (e.g., a set of Gaussian-type atom-centered basis functions) or implicitly by using singular value decomposition on the overlap matrix of the set of N 2 functions ρ ij (x) [4] [5]. "
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