TY - JOUR
T1 - Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms
AU - Mendl, Christian B.
AU - Friesecke, Gero
PY - 2010/11/14
Y1 - 2010/11/14
N2 - Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schrödinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wave functions, and use of Slater-type orbitals (STOs). The required Coulomb integrals for STOs are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular, we reproduce the anomalous magnetic moment and orbital filling of chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.
AB - Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schrödinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wave functions, and use of Slater-type orbitals (STOs). The required Coulomb integrals for STOs are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular, we reproduce the anomalous magnetic moment and orbital filling of chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.
UR - http://www.scopus.com/inward/record.url?scp=78449308567&partnerID=8YFLogxK
U2 - 10.1063/1.3493677
DO - 10.1063/1.3493677
M3 - Article
AN - SCOPUS:78449308567
SN - 0021-9606
VL - 133
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 18
M1 - 184101
ER -