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Jeppe Olsen

Novel methods for configuration interaction and orbital optimization for wave functions containing non-orthogonal orbitals with applications to the chromium dimer and trimer

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A novel algorithm for performing configuration interaction (CI) calculations using non-orthogonal orbitals is introduced. In the new algorithm, the explicit calculation of the Hamiltonian matrix is replaced by the direct evaluation of the Hamiltonian matrix times a vector, which allows expressing the CI-vector in a bi-orthonormal basis, thereby drastically reducing the computational complexity. A new non-orthogonal orbital optimization method that employs exponential mappings is also described. To allow non-orthogonal transformations of the orbitals, the standard exponential mapping using anti-symmetric operators is supplemented with an exponential mapping based on a symmetric operator in the active orbital space. Expressions are obtained for the orbital gradient and Hessian, which involve the calculation of at most two-body density matrices, thereby avoiding the time-consuming calculation of the three-and four-body density matrices of the previous approaches. An approach that completely avoids the calculation of any four-body terms with limited degradation of convergence is also devised. The novel methods for non-orthogonal configuration interaction and orbital optimization are applied to the chromium dimer and trimer. For internuclear distances that are typical for chromium clusters, it is shown that a reference configuration consisting of optimized singly occupied active orbitals is sufficient to give a potential curve that is in qualitative agreement with complete active space self-consistent field (CASSCF) calculations containing more than 500 x 10(6) determinants. To obtain a potential curve that deviates from the CASSCF curve by less than 1 mHartree, it is sufficient to add single and double excitations out from the reference configuration. (C) 2015 AIP Publishing LLC.

Original languageEnglish
Article number114102
JournalJournal of Chemical Physics
Volume143
Issue11
Number of pages22
ISSN0021-9606
DOIs
Publication statusPublished - 2015

    Research areas

  • CONSISTENT-FIELD METHOD, VALENCE-BOND DESCRIPTIONS, ELECTRONIC-STRUCTURE, DYNAMIC CORRELATION, DENSITY-MATRICES, CONVERGENCE, PROGRAM, MOLECULES, SPACES, TRANSFORMATIONS

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