Explicit and implicit multi-center integrations

. International Journal of Quantum Chemistry 113 (10): 1573--1583 (May 2013)


We present truncated expansions of multicenter one-electron nuclear attraction and two-electron repulsion integrals over localized basis functions in terms of one- and two-center integrals of “Coulomb,” “exchange,” and “hybrid” type. Two variants are discussed: the “Explicit Multi-center Integrations” and the “Implicit Multi-Center Integrations” (abbreviated as “EMCI” and “IMCI”, respectively). While EMCI also deals with individual integrals, the IMCI option is the more appealing one: it enables us to evaluate the entire matrix elements of “Restricted Hartree–Fock”-type in a very effective and chemically meaningful way. Due to the diatomic nature of our expansions, integrations over “Slater-Type Orbitals” become well-feasible, too. © 2012 Wiley Periodicals, Inc.

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