An algorithm for the efficient evaluation of two-electron repulsion integrals over contracted Gaussian-type basis functions

Sandberg, Jaime Axel Rosal; Rinkevičius, Žilvinas

doi:10.1063/1.4769730

Cited by 10 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Evaluation of Gaussian integrals − accounts for a significant or a dominant portion of the total cost of many key tasks in Gaussian LCAO electronic structure computations of molecules and solids. Therefore, efficient evaluation of various operators in Gaussian AO basesand in particular, 2-body Coulomb integrals (i.e., the electron repulsion integrals)has been the focus of much attention of the electronic structure community, ,− with important developments continuing unabated. − …”

Section: Introductionmentioning

confidence: 99%

Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals

Asadchev

Valeev

2023

J. Chem. Theory Comput.

View full text Add to dashboard Cite

To improve the efficiency of Gaussian integral evaluation on modern accelerated architectures, FLOP-efficient Obara-Saika-based recursive evaluation schemes are optimized for the memory footprint. For the 3-center 2-particle integrals that are key for the evaluation of Coulomb and other 2-particle interactions in the density-fitting approximation, the use of multiquantal recurrences (in which multiple quanta are created or transferred at once) is shown to produce significant memory savings. Other innovations include leveraging register memory for reduced memory footprint and direct compile-time generation of optimized kernels (instead of custom code generation) with compile-time features of modern C++/CUDA. Performance of conventional and CUDA-based implementations of the proposed schemes is illustrated for both the individual batches of integrals involving up to Gaussians with low and high angular momenta (up to L = 6) and contraction degrees, as well as for the density-fitting-based evaluation of the Coulomb potential. The computer implementation is available in the open-source library.

show abstract

Section: Introductionmentioning

confidence: 99%

Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals

Asadchev

Valeev

2023

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…As an example, we will discuss at the end of this article one system that requires of 3 873 096 points in the grid to obtain a high-quality picture of the MEP mapped on the electron density for a system with 146 nuclei. There are proposals to evaluate this kind of integrals, − but this is still an open issue in quantum chemistry to accelerate the corresponding calculations, although many of them use some approximations to estimate it. − Such implementations show that there is a compromise between the accuracy and the speedup to evaluate the MEP since the bigger accuracy, the bigger the computational effort. We can find programs that evaluate very fast the MEP.…”

Section: Introductionmentioning

confidence: 99%

Implementation of the Molecular Electrostatic Potential over Graphics Processing Units

Cruz

Hernández‐Esparza

Vázquez-Mayagoitia

et al. 2019

J. Chem. Inf. Model.

View full text Add to dashboard Cite

The molecular electrostatic potential (MEP) generated by quantum chemistry methods and Gaussian functions is evaluated over graphics processing units (GPUs). This implementation is based on full-range Rys polynomials with nodes and weights obtained in each thread of a GPU. For high angular moments, the corresponding integral is solved using a onedimension vertical recurrence relation. Thus, we computed the MEP with minimal approximations. We show that this implementation is stable and very efficient since the time consumed over GPUs is quite small compared with similar implementations over CPUs. The implementation was done by using CUDA-C programming techniques within the Graphics Processing Units for Atoms and Molecules (GPUAM) project, which has been designed to analyze quantum chemistry fields over heterogeneous computational resources. With this new scalar field GPUAM is a useful application for the quantum chemistry community, in particular for people interested in chemical reactivity analysis.

show abstract

“…The defining feature of an ab initio electronic structure method is the nonapproximated evaluation of molecular integrals over the exact Hamiltonian and basis functions, which also constitutes a major hurdle for its implementation and execution. Specifically, a fast evaluation of the four-index, two-electron repulsion integrals (ERIs) over Gaussian-type-orbital (GTO) atomic basis functions has been the primary concern for computational chemists even to this day. − …”

Section: Introductionmentioning

confidence: 99%

libreta: Computerized Optimization and Code Synthesis for Electron Repulsion Integral Evaluation

Zhang

2018

J. Chem. Theory Comput.

107

View full text Add to dashboard Cite

A new library called libreta for the evaluation of electron repulsion integrals (ERIs) over segmented and contracted Gaussian functions is developed. Our libreta is optimized from three aspects: (1) The Obara-Saika, Dupuis-Rys-King, and McMurchie-Davidson method are all employed. The recurrence relations involved are optimized by tree-search for each combination of angular momenta, and in the best case, 50% of the intermediates can be eliminated to reduce the computational cost. (2) The optimized codes for recurrence relations are combined with different contraction orders, each of which is suitable for ERIs of different angular momenta and contraction patterns. In practice, libreta will determine and use the best scheme to evaluate each ERI. (3) libreta is also optimized at the coding level. For example, with common subexpression elimination and local memory access, the performance can be increased by about 6% and 20%, respectively. The performance was compared with libint2. For both popular segmented and contracted basis sets, libreta can be faster than libint2 by 7.2-912.0%. For basis sets of heavy elements that contain Gaussian basis functions of large contraction degrees, the performance can be increased 20-30 times. We also tested the performance of libreta in direct self-consistent field (SCF) calculations and compared it with NWChem. In most cases, the average time for one SCF iteration by libreta is less than NWChem by 144.2-495.9%. Finally, we discuss the origin of redundancies occurring in the recurrence relations and derive an upper bound of the least number of intermediates required to be calculated in a McMurchie-Davidson recurrence, which is confirmed by ours as well as previous authors' results. We expect that libreta can become a useful tool for theoretical and computational chemists to develop their own algorithms rapidly.

show abstract

An algorithm for the efficient evaluation of two-electron repulsion integrals over contracted Gaussian-type basis functions

Cited by 10 publications

References 29 publications

Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals

Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals

Implementation of the Molecular Electrostatic Potential over Graphics Processing Units

libreta: Computerized Optimization and Code Synthesis for Electron Repulsion Integral Evaluation

Contact Info

Product

Resources

About