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Cracking Electron Correlation

**Carlos F. BUNGE, Instituto de Fisica, UNAM, Mexico
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e-mail:bunge@ft.fisica.unam.mx

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Jeudi 2 octobre 2003, 11**^{h}00

Selected configuration interaction (SCI) for accurate electronic structure
calculations is reformulated. The linked cluster expansion is used as
an intermediate device to approximate an important portion of n-excited
determinantal CI coefficients in terms of those of lower-excited detors.
The corresponding equations are extended to CI coefficients B_{K}
of n-excited configurations K. Unlinked three- and higher-excited
configurations (those that can be expressed as "products" of singly- and
doubly-excited ones) are selected by an energy criterion using Brown's
formula, DE_{K} = (E-H_{KK})B_{K}^{2}/ (1-B_{K}^{2}) with the B_{K} determined
from coefficients of lower-excited configurations. The truncation energy
error DE is the sum of DE_{K}'s of all discarded K's.
The remaining configurations (linked configurations) are selected using
thresholds based on natural orbital concepts; when existing they may
cause most of the computational demands. Given a model CI space M,
a usual upper bound E_{T} is computed by CI in a truncated space T,
and E_{M} » E_{T}+DE. A divide-and-conquer method for the
accurate and efficient evaluation of E_{T} is also discussed. An SCI
calculation on Ne ground state using a single-processor and featuring
1077 orbitals achieves two mhartree accuracy (10^{-3} Kcal/mol)
for a model CI space of one billion CSF's and one trillion determinants.
Convergence studies require intermediate calculations each involving
several billions of determinants and up to one trillion nonzero matrix
elements between CSF's. A new era for ab-initio electronic structure
calculations is opening.