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# B.1.1 Overview

(December 20, 2021)

Within the Q-Chem program, an Atomic Orbital integrals (AOInts) package has been developed which, while relatively invisible to the user, is one of the keys to the overall speed and efficiency of the Q-Chem program.

“Ever since Boys’ introduction of Gaussian basis sets to quantum chemistry in 1950, the calculation and handling of the notorious two-electron repulsion integrals (ERIs) over Gaussian functions has been an important avenue of research for practicing computational chemists. Indeed, the emergence of practically useful computer programs has been fueled in no small part by the development of sophisticated algorithms to compute the very large number of ERIs that are involved in calculations on molecular systems of even modest size”. 363 Gill P. M. W., Head-Gordon M., Pople J. A.
J. Phys. Chem.
(1990), 94, pp. 5564.

The ERI engine of any competitive quantum chemistry software package will be one of the most complicated aspects of the package as whole. Coupled with the importance of such an engine’s efficiency, a useful yardstick of a program’s anticipated performance can be quickly measured by considering the components of its ERI engine. In recent times, developers at Q-Chem, Inc. have made significant contributions to the advancement of ERI algorithm technology (for example, see Refs.  363 Gill P. M. W., Head-Gordon M., Pople J. A.
J. Phys. Chem.
(1990), 94, pp. 5564.
, 369 Gill P. M. W.
(1994), 25, pp. 141.
, 22 Adams T. R., Adamson R. D., Gill P. M. W.
J. Chem. Phys.
(1997), 107, pp. 124.
, 336 Frisch M. J. et al.
Chem. Phys. Lett.
(1993), 206, pp. 225.
, 364 Gill P. M. W., Johnson B. G., Pople J. A.
Int. J. Quantum Chem.
(1991), 40, pp. 745.
, 368 Gill P. M. W., Pople J. A.
Int. J. Quantum Chem.
(1991), 40, pp. 753.
, 366 Gill P. M. W., Johnson B. G., Pople J. A.
Chem. Phys. Lett.
(1994), 217, pp. 65.
, 439 Head-Gordon M., Pople J. A.
J. Chem. Phys.
(1988), 89, pp. 5777.
, 528 Johnson B. G., Gill P. M. W., Pople J. A.
Chem. Phys. Lett.
(1993), 206, pp. 229.
, 529 Johnson B. G., Gill P. M. W., Pople J. A.
Chem. Phys. Lett.
(1993), 206, pp. 239.
), and it is not surprising that Q-Chem’s AOInts package is considered the most advanced of its kind.