title: Electron density fitting for the Coulomb problem in relativistic density-functional theory.
abstract: A density fitting approach for the Coulomb matrix representation within the four-component formulation of relativistic density-functional theory is presented. Our implementation, which uses G-spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closed-shell gold clusters (Au2, Au3+, Au4, Au5+). The algorithm is found to scale as O(N3), just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for Au2 and up to 1% in the case of Au5+.
authors.affiliation: Dipartimento di Chimica e I.S.T.M.-C.N.R., Università di Perugia, Perugia 06123, Italy. belp@thch.unipg.it
authors.forename: Leonardo
authors.initials: L
authors.lastname: Belpassi
authors.forename: Francesco
authors.initials: F
authors.lastname: Tarantelli
authors.forename: Antonio
authors.initials: A
authors.lastname: Sgamellotti
authors.forename: Harry M
authors.initials: HM
authors.lastname: Quiney