Efficient recursive computation of molecular integrals over Cartesian Gaussian functions

Abstract

Recurrence expressions are derived for various types of molecular integrals over Cartesian Gaussian functions by the use of the recurrence formula for three-center overlap integrals. A number of characteristics inherent in the recursive formalism allow an efficient scheme to be developed for molecular integral computations. With respect to electron repulsion integrals and their derivatives, the present scheme with a significant saving of computer time is found superior to other currently available methods. A long innermost loop incorporated in the present scheme facilitates a fast computation on a vector processing computer.

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

“…(15)] is added to Eq. (18) or (21). On the other hand, when hybrid functionals are not used, there is no need to compute Eq.…”

“…[21] ERIs. are computed with the libint library [46] that uses Obara-Saika [21] and Head-Gordon-Pople recursions.…”

“…[21] ERIs. are computed with the libint library [46] that uses Obara-Saika [21] and Head-Gordon-Pople recursions. [22] All of these integrals are performed in the Cartesian basis and then transformed into the spherical basis if necessary.…”

“…[21,22] The main drawback of the Gaussian basis set is its incorrect asymptotic behavior, notably the violation of the nuclear cusp condition and the asymptotic decay that is too fast. [23] Slatertype orbital (STO) basis sets do not have these shortcomings and can also be used to perform HF and hybrid DFT calculations when suitable fitting algorithms are used, [24,25] but a greater number of integrals need to be performed using purely numerical quadrature.…”

Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation

“…12 Since Boys' seminal work, numerous computational approaches have been developed to minimize the effort in this N 4 bottleneck. [13][14][15][16][17] However, even if the most efficient algorithm is being used, the twoelectron integral evaluation phase still takes much of the computation time.…”