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The complete active space SCF method in a fock‐matrix‐based super‐CI formulation
Author(s) -
Roos Björn O.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560180822
Subject(s) - complete active space , dipole , quadrupole , atomic orbital , fock space , chemistry , matrix (chemical analysis) , valence (chemistry) , atomic physics , fock matrix , physics , quantum mechanics , computational chemistry , electron , chromatography
A simplified super‐CI technique is presented, which is used to solve the orbital optimization problem in the Complete Active Space SCF method (CASSCF). All super‐CI matrix elements are expressed in terms of an average Fock operator, where the major parts can be obtained directly from the AO integrals. Only a relatively small number of transformed two‐electron integrals are needed, thus reducing the transformation bottleneck in MCSCF to an absolute minimum. Since all matrix elements are given in terms of first‐and second‐order reduced density matrix elements with indices restricted to a small active subspace of the orbital space, the super‐CI calculation becomes independent of the length of the CI expansion. This is an important aspect, since the complete active space CI expansion can include many terms. The method is demonstrated in a calculation of potential curves for the three lowest states of the N 2 molecules, and some equilibrium properties of the water molecules. The following results were obtained for N 2 for the states 1 Σ + g , 3 Σ + u and 3 Π g ; D e : 9.04 (9.90), 2.71 (3.68), and 3.86 (4.89) eV;r e : 1.109 (1.098), 1.309 (1.287), and (1.213) Å; (experimental values in parenthesis). For H 2 O it was demonstrated that a balanced calculation around the equilibrium geometry must use eight active valence orbitals. The results are r e : 0.964 (0.957) Å; θ e : 104°.8 (1.4°.5); dipole moment: 1.98 (1.86) debye; quadrupole moment: 2.64, −2.51, −0.13 (2.63, −2.50, −0.13) × 10 −26 esu cm 2 .