Cracking Electron Correlation

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

Jeudi 2 octobre 2003, 11^h00

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_K²/ (1-B_K²) 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 ť 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.