title: New Approximation to the Third-Order Density. Application to the Calculation of Correlated Multicenter Indices.
abstract: In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation.
authors.affiliation: Department of Chemistry and Biochemistry, University of San Diego , California, California 92103, United States.
authors.forename: Ferran
authors.initials: F
authors.lastname: Feixas
authors.affiliation: Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona , Campus de Montilivi, 17071 Girona, Catalonia, Spain.
authors.forename: Miquel
authors.initials: M
authors.lastname: Solà
authors.affiliation: Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona , Campus de Montilivi, 17071 Girona, Catalonia, Spain.
authors.forename: Juan M
authors.initials: JM
authors.lastname: Barroso
authors.affiliation: Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) , and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain.
authors.forename: Jesus M
authors.initials: JM
authors.lastname: Ugalde
authors.affiliation: Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona , Campus de Montilivi, 17071 Girona, Catalonia, Spain.|Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) , and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain.
authors.forename: Eduard
authors.initials: E
authors.lastname: Matito