Fast construction of the Kohn--Sham response function for molecules}

Abstract : The use of the LCAO (Linear Combination of Atomic Orbitals) method for excited states involves products of orbitals that are known to be linearly dependent. We identify a basis in the space of orbital products that is local for orbitals of finite support and with a residual error that vanishes exponentially with its dimension. As an application of our previously reported technique we compute the Kohn--Sham density response function $\chi_{0}$ for a molecule consisting of $N$ atoms in $N^{2}N_{\omega }$ operations, with $N_{\omega}$ the number of frequency points. We test our construction of $\chi_{0}$ by computing molecular spectra directly from the equations of Petersilka--Gossmann--Gross in $N^{2}N_{\omega }$ operations rather than from Casida's equations which takes $N^{3}$ operations. We consider the good agreement with previously calculated molecular spectra as a validation of our construction of $\chi_{0}$. Ongoing work indicates that our method is well suited for the computation of the GW self-energy $\Sigma=\mathrm{i}GW$ and we expect it to be useful in the analysis of exitonic effects in molecules.
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https://hal.inria.fr/inria-00437603
Contributor : Petr Koval <>
Submitted on : Tuesday, December 1, 2009 - 9:09:40 AM
Last modification on : Monday, January 22, 2018 - 11:02:02 AM

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  • HAL Id : inria-00437603, version 1
  • ARXIV : 0910.3796

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Peter Koval, Dietrich Foerster, Olivier Coulaud. Fast construction of the Kohn--Sham response function for molecules}. Trends in nanotechnology - TNT 2009, Sep 2009, Barcelona, Spain. ⟨inria-00437603⟩

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