caa a22 4500 605488045 CHVBK 20210128100453.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00214-015-1701-z doi (NATIONALLICENCE)springer-10.1007/s00214-015-1701-z Use of graphics processing units for efficient evaluation of derivatives of exchange integrals by means of Fourier transform of the 1/ r operator and its numerical quadrature [Elektronische Daten] [Petr Čársky, Roman Čurík] In this paper, we propose an efficient way for evaluation of derivatives of exchange integrals. We propose an approach in which we factorize the non-local exchange kernel into a sum of separable terms. We exploit a discretized Fourier transform for the 1/r operator, and we devise a method that allows us to employ a manageable number of plane-wave functions in the Fourier expansion while still keeping necessary accuracy. Resulting formulas are amenable for efficient evaluation on graphics processing units (GPU). We discuss the GPU implementation for derivatives of two-electron repulsion integrals of the (gk|gk) type in the hybrid Gaussian and plane-wave basis. Derivatives of such integrals are needed for computation of cross sections in vibrationally inelastic electron scattering by polyatomic molecules. Speedup and accuracy achieved are demonstrated for cross sections of selected vibrational modes of cyclopropane, benzene and adamantane. The proposed factorization method is general and may be applied to any type of exchange integrals. We note briefly on its possible application to exchange integrals and their derivatives in quantum chemical computational methods. Springer-Verlag Berlin Heidelberg, 2015 Use of graphical processing units nationallicence Derivatives of exchange integrals nationallicence Fourier transform of 1/ r nationallicence Electron scattering nationallicence Čársky Petr J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223, Prague 8, Czech Republic aut Čurík Roman J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223, Prague 8, Czech Republic aut Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/8(2015-08-01), 1-9 1432-881X 134:8<1 2015 134 214 https://doi.org/10.1007/s00214-015-1701-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00214-015-1701-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Čársky Petr J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223, Prague 8, Czech Republic aut NATIONALLICENCE 700 1- Čurík Roman J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223, Prague 8, Czech Republic aut NATIONALLICENCE 773 0- Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/8(2015-08-01), 1-9 1432-881X 134:8<1 2015 134 214