Abstract
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.
Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan”.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Čársky, P., Čurík, R. (2016). Use of graphics processing units for effi cient evaluation of derivatives of exchange integrals by means of Fourier transform of the 1/r operator and its numerical quadrature. In: Szabados, Á., Kállay, M., Szalay, P. (eds) Péter R. Surján. Highlights in Theoretical Chemistry, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49825-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-49825-5_4
Received:
Accepted:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-49824-8
Online ISBN: 978-3-662-49825-5
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)