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Quadratically convergent calculation of localized molecular orbitals

Abstract

Two iterative procedures for the transformation of canonical self-consistent field molecular orbitals to intrinsic localized molecular orbitals are proposed. A first-order method based on a series of (n × n) unitary transformations may be applied to orbitals which are far from convergence. The second method, based on Newton's method, yields quadratic convergence. Numerical results based on Boys' criterion are presented for water, carbon monoxide, boron fluoride, nitric oxide, and methylacetylene. A composite method may be used to obtain rapid convergence for large molecules for which it is not practical to calculate the entire hessian matrix. The performance of the composite method is demonstrated by application to the dinitrogen tetroxide molecule. Highly converged localized molecular orbitals may be obtained for most molecules with five to eight first-order iterations followed by three or four iterations based on either the second-order or composite method.

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Leonard, J.M., Luken, W.L. Quadratically convergent calculation of localized molecular orbitals. Theoret. Chim. Acta 62, 107–132 (1982). https://doi.org/10.1007/BF00581477

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Key words

  • Localized orbitals
  • Molecular orbitals
  • Quadratic convergence