Automatic code generation for quantum chemistry applications

Mazur, Grzegorz; Makowski, Marcin; Łazarski, Roman; Włodarczyk, Radosław; Czajkowska, E; Glanowski, Michał

doi:10.1002/qua.25187

Cited by 4 publications

(4 citation statements)

References 29 publications

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“…The relations that come from the analysis can be used to ease the calculation of future ab initio scattering methods for this class of molecules. Moreover, these considerations combined with new computational techniques [42] may be useful in the investigation of larger molecules with D ∞h symmetry. The extension to the C ∞h point group can be considered recalculating a few terms in the model.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, these considerations combined with new computational techniques [42] may be useful in the investigation of larger molecules with D ∞h symmetry. The extension to the C ∞h point group can be considered recalculating a few terms in the model.…”

Section: Discussionmentioning

confidence: 99%

“…There are several applications that involve the integration of molecular integrals with Gaussian basis functions, for example, the calculation of magnetic field density [36], structure factors in quantum crystallography [37], positron and electron scattering [38][39][40], molecular magnetic properties [41], density functional theory [42], relativistic quantum electrodynamics [43] and electronic dynamics [44].…”

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confidence: 99%

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Electron and positron elastic scattering by non‐central potentials: Matrix elements and symmetry properties in the first Born approximation

Barp

Arretche

2022

Int J of Quantum Chemistry

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The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron and electron elastic scattering. The calculation of this class of integrals is crucial in order to obtain the scattering amplitude in the first Born approximation framework for an ab initio method recently proposed. A general solution to the scattering amplitude is given to a molecular target with no restriction due to symmetry. Moreover, symmetry relations are presented with the purpose of identifying terms that do not contribute to the calculation for the molecules in the D∞h point group optimizing the computational effort.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

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Electron and positron elastic scattering by non‐central potentials: Matrix elements and symmetry properties in the first Born approximation

Barp

Arretche

2022

Int J of Quantum Chemistry

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“…The first example of automatic code generation (ACG) dates back to Jones’ work − for the evaluation of molecular integrals over Slater-type orbitals, and since then, it saw applications in ab initio electron-correlation methods, − exchange–correlation density functionals, − optimizations of the RRs, ,, a detection of their numerical instability, and the synthesis of an entire ERI library. − One of the most notable examples is the libint2 library of Valeev, which consists of efficient computerized implementations of a few of the contraction paths of the OS RRs.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

2018

J. Chem. Theory Comput.

111

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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.

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Optimizing two-electron repulsion integral calculations with McMurchie–Davidson method on graphic processing unit

Tian

Suo

2021

The Journal of Chemical Physics

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In this article, several optimization methods of two-electron repulsion integral calculations on a graphic processing unit (GPU) are presented. These methods are based on the investigations of the method presented by McMurchie and Davidson (MD). A new Boys function evaluation method for the GPU calculation is introduced. The series summation, the error function, and the finite sum formula method are combined; thus, good performance on the GPU can be achieved. By taking some theoretical study of the McMurchie–Davidson recurrence relations, three major optimization approaches are derived from the deduction of the general term formula for the Hermite expansion coefficient. The three approaches contain a new form of the Hermite expansion coefficients with corresponding recurrence relations, which is more efficient for one-electron integrals and [ss|∗∗] or [∗∗|ss] type two-electron integrals. In addition, a simple yet efficient new recurrence formula for the coefficient evaluation is derived, which is more efficient both in float operations and memory operations than its original one. In average, the new recurrence relation can save 26% float operations and 37% memory operations. Finally, a common sub-expression elimination (CSE) method is implemented. This CSE method is directly generated from some equalities we discovered from the general term formula other than by computer algebra system software. This optimized method achieved up to 3.09 speedups compared to the original MD method on the GPU and up to 92.75 speedups compared to the GAMESS calculation on the central processing unit.

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Automatic code generation for quantum chemistry applications

Cited by 4 publications

References 29 publications

Electron and positron elastic scattering by non‐central potentials: Matrix elements and symmetry properties in the first Born approximation

Electron and positron elastic scattering by non‐central potentials: Matrix elements and symmetry properties in the first Born approximation

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

Optimizing two-electron repulsion integral calculations with McMurchie–Davidson method on graphic processing unit

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