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We extend our noniterative local correlation method [P. E. Maslen and M. Head-Gordon, Chem. Phys. Lett., 283, 102 (1998)] by defining a hierarchy of local spaces, ranging from small to large. The accu...
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Methods for geometry optimization of large molecules. I. An O(N2) algorithm for solving systems of linear equations for the transformation of coordinates and forces

J. Chem. Phys. 109, 7100 (1998); doi:10.1063/1.477393

Issue Date: 1 November 1998

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Ödön Farkas and H. Bernhard Schlegel
Department of Chemistry, Wayne State University, Detroit, Michigan 48202
The most recent methods in quantum chemical geometry optimization use the computed energy and its first derivatives with an approximate second derivative matrix. The performance of the optimization process depends highly on the choice of the coordinate system. In most cases the optimization is carried out in a complete internal coordinate system using the derivatives computed with respect to Cartesian coordinates. The computational bottlenecks for this process are the transformation of the derivatives into the internal coordinate system, the transformation of the resulting step back to Cartesian coordinates, and the evaluation of the Newton–Raphson or rational function optimization (RFO) step. The corresponding systems of linear equations occur as sequences of the form yi = Mixi, where Mi can be regarded as a perturbation of the previous symmetric matrix Mi – 1. They are normally solved via diagonalization of symmetric real matrices requiring O(N3) operations. The current study is focused on a special approach to solving these sequential systems of linear equations using a method based on the update of the inverse of the symmetric matrix Mi. For convergence, this algorithm requires a number of O(N2) operations with an O(N3) factor for only the first calculation. The method is generalized to include redundant (singular) systems. The application of the algorithm to coordinate transformations in large molecular geometry optimization is discussed. ©1998 American Institute of Physics.
History: Received 1 June 1998; accepted 28 July 1998
Permalink: http://link.aip.org/link/?JCPSA6/109/7100/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.-p
    Electronic structure of atoms, molecules and their ions: theory Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)
  • 02.60.Pn
    Mathematical methods in physics Numerical approximation and analysis Numerical optimization
  • 02.10.Sp
    Mathematical methods in physics Logic, set theory, and algebra Linear and multilinear algebra; matrix theory (finite and infinite)
  • YEAR: 1998

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ISSN:
0021-9606 (print)   1089-7690 (online)
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