Efficient computation of two-electron - repulsion integrals and their nth-order derivatives using contracted Gaussian basis sets

1990 ◽  
Vol 94 (14) ◽  
pp. 5564-5572 ◽  
Author(s):  
Peter M. W. Gill ◽  
Martin. Head-Gordon ◽  
John A. Pople
Keyword(s):  
Basis Sets ◽  
Efficient Computation ◽  
Gaussian Basis Sets ◽  
Electron Repulsion ◽  
Electron Repulsion Integrals

PRACTICAL PERFORMANCE ASSESSMENT OF ACCOMPANYING COORDINATE EXPANSION RECURRENCE RELATION ALGORITHM FOR COMPUTATION OF ELECTRON REPULSION INTEGRALS

2005 ◽  
Vol 04 (01) ◽  
pp. 139-149 ◽  
Author(s):  
MICHIO KATOUDA ◽  
MASATO KOBAYASHI ◽  
HIROMI NAKAI ◽  
SHIGERU NAGASE
Keyword(s):  
Computer Program ◽  
Recurrence Relation ◽  
Basis Set ◽  
Basis Sets ◽  
Processing Unit ◽  
Central Processing ◽  
Cpu Time ◽  
Electron Repulsion ◽  
Electron Repulsion Integrals ◽  
Practical Performance

We have developed a computer program for evaluation of electron repulsion integrals (ERIs) based on the accompanying coordinate expansion recurrence relation (ACE-RR) algorithm, which has been recently developed as an efficient algorithm for computation of ERIs using Pople-type basis sets (STO-3G and 6-31G, for example) and derivatives of ERIs [Kobayashi and Nakai, J Chem Phys121:4050 2004]. The computer program can be linked to GAMESS ab initio quantum chemistry program. The practical performance of the ACE-RR method is assessed by means of the central processing unit (CPU) time for the first direct self-consistent field cycle on a model system (4 × 4 × 4 cubic hydrogen lattice), taxol ( C 47 H 51 NO 14), and valinomycin ( C 54 H 90 N 6 O 18) using Pople-type basis sets. The considerable efficiency of the present ACE-RR method is demonstrated by measuring the CPU time. The present ACE-RR method is comparable to or at most 30% faster than the Pople–Hehre method which is also designed for efficient computation of ERIs using Pople-type basis sets. Furthermore, the ACE-RR method is drastically faster than the Dupuis–Rys–King method in the case where the degree of contraction of Pople-type basis sets is high: 7.5 times faster in the case of valinomycin using STO-6G basis set, for example.

Efficient computation of electron-repulsion integrals inab initio studies of polymeric systems

1993 ◽  
Vol 48 (S27) ◽  
pp. 793-806 ◽  
Author(s):  
David H. Mosley ◽  
Joseph G. Fripiat ◽  
Beno�t Champagne ◽  
Jean-Marie Andr�
Keyword(s):  
Efficient Computation ◽  
Polymeric Systems ◽  
Electron Repulsion ◽  
Electron Repulsion Integrals

An Efficient Implementation of Semi-numerical Computation of the Hartree-Fock Exchange on the Intel Phi Processor

2018 ◽  
Author(s):  
fenglai liu ◽  
Jing Kong
Keyword(s):  
Numerical Computation ◽  
Numerical Scheme ◽  
Data Type ◽  
Basis Sets ◽  
Single Instruction Multiple Data ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Electron Repulsion ◽  
Integration Approach ◽  
Multiple Data

Unique technical challenges and their solutions for implementing semi-numerical Hartree-Fock exchange on the Phil Processor are discussed, especially concerning the single- instruction-multiple-data type of processing and small cache size. Benchmark calculations on a series of buckyball molecules with various Gaussian basis sets on a Phi processor and a six-core CPU show that the Phi processor provides as much as 12 times of speedup with large basis sets compared with the conventional four-center electron repulsion integration approach performed on the CPU. The accuracy of the semi-numerical scheme is also evaluated and found to be comparable to that of the resolution-of-identity approach.<br>

An Efficient Implementation of Semi-numerical Computation of the Hartree-Fock Exchange on the Intel Phi Processor

2018 ◽  
Author(s):  
fenglai liu ◽  
Jing Kong
Keyword(s):  
Numerical Computation ◽  
Numerical Scheme ◽  
Data Type ◽  
Basis Sets ◽  
Single Instruction Multiple Data ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Electron Repulsion ◽  
Integration Approach ◽  
Multiple Data

Unique technical challenges and their solutions for implementing semi-numerical Hartree-Fock exchange on the Phil Processor are discussed, especially concerning the single- instruction-multiple-data type of processing and small cache size. Benchmark calculations on a series of buckyball molecules with various Gaussian basis sets on a Phi processor and a six-core CPU show that the Phi processor provides as much as 12 times of speedup with large basis sets compared with the conventional four-center electron repulsion integration approach performed on the CPU. The accuracy of the semi-numerical scheme is also evaluated and found to be comparable to that of the resolution-of-identity approach.<br>

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