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Updated: May 9, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Double asymptotic expansion of three-center electronic repulsion integrals
1Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508 A.P. 14-740 México D.F. 07000, Mexico. aalvarezi@cinvestav.mx
Abstract:
A double asymptotic expansion for the evaluation of three-center electron repulsion integrals (ERIs) in the long-range limit is presented. For the definition of this limit, a natural division of space based on the atomic coordinates and basis function exponents in utilized. The resulting analytical expression for the calculation of three-center ERIs in the long-range limit are implemented in the density functional theory program deMon2k. Validation and benchmark calculations of n-alkanes, hydrogen saturated graphene sheets and hydrogen saturated diamond blocks are discussed. It is shown that for a sufficient large number of long-range ERIs, the linear scaling regime is reached.
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