Two-electron integrations in the Quantum Theory of Atoms in Molecules with correlated wave functions

• Published in: Journal of computational chemistry Vol. 26; no. 4; pp. 344 - 351
• Main Authors: Pendás, A. Martín, Francisco, E., Blanco, M. A.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-03-2005; Wiley Subscription Services, Inc
• Subjects: Atoms & subatomic particles; Correlation analysis; Electrons; energetic decomposition; Quantum theory; Quantum Theory of Atoms in Molecules; second-order density matrix; theory of the chemical bond; two-electron basin integrations; Wave power
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.20173

A recent method proposed to compute two‐electron integrals over arbitrary regions of space [Martín Pendás, A. et al., J Chem Phys 2004, 120, 4581] is extended to deal with correlated wave functions. To that end, we use a monadic factorization of the second‐order reduced density matrix originally proposed by E. R. Davidson [Chem Phys Lett 1995, 246, 209] that achieves a full separation of the interelectronic components into one‐electron terms. The final computational effort is equivalent to that found in the integration of a one determinant wave function with as many orbitals as occupied functions in the correlated expansion. Similar strategies to extract the exchange and self‐interaction contributions from the two‐electron repulsion are also discussed, and several numerical results obtained in a few test systems are summarized. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 344–351, 2005