Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation

Ivan S. Ufimtsev, Todd J. Martinez
Department of Chemistry and The Beckman Institute, 600 S. Mathews, University of Illinois, Urbana, Illinois 61801
Journal of Chemical Theory and Computation, Vol. 4, No. 2. (1 February 2008), pp. 222-231.


   title={Quantum chemistry on graphical processing units. 1. strategies for two-electron integral evaluation},

   author={Ufimtsev, I.S. and Martinez, T.J.},

   journal={J. Chem. Theory Comput},





   publisher={ACS Publications}


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Modern videogames place increasing demands on the computational and graphical hardware, leading to novel architectures that have great potential in the context of high performance computing and molecular simulation. We demonstrate that Graphical Processing Units (GPUs) can be used very efficiently to calculate two-electron repulsion integrals over Gaussian basis functionsthe first step in most quantum chemistry calculations. A benchmark test performed for the evaluation of approximately 106 (ss|ss) integrals over contracted s-orbitals showed that a naive algorithm implemented on the GPU achieves up to 130-fold speedup over a traditional CPU implementation on an AMD Opteron. Subsequent calculations of the Coulomb operator for a 256-atom DNA strand show that the GPU advantage is maintained for basis sets including higher angular momentum functions.
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