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Methods for optimizing large molecules. II. Quadratic search

J. Chem. Phys. 111, 10806 (1999); doi:10.1063/1.480484

Issue Date: 22 December 1999

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Ödön Farkas
Department of Organic Chemistry, Eötvös Loránd University, H-1518 Budapest, 112, P.O. Box 32, Hungary
Department of Chemistry, Wayne State University, Detroit, Michigan 48202

H. Bernhard Schlegel
Department of Chemistry, Wayne State University, Detroit, Michigan 48202
Geometry optimization has become an essential part of quantum-chemical computations, largely because of the availability of analytic first derivatives. Quasi-Newton algorithms use the gradient to update the second derivative matrix (Hessian) and frequently employ corrections to the quadratic approximation such as rational function optimization (RFO) or the trust radius model (TRM). These corrections are typically carried out via diagonalization of the Hessian, which requires O(N3) operations for N variables. Thus, they can be substantial bottlenecks in the optimization of large molecules with semiempirical, mixed quantum mechanical/molecular mechanical (QM/MM) or linearly scaling electronic structure methods. Our O(N2) approach for solving the equations for coordinate transformations in optimizations has been extended to evaluate the RFO and TRM steps efficiently in redundant internal coordinates. The regular RFO model has also been modified so that it has the correct size dependence as the molecular systems become larger. Finally, an improved Hessian update for minimizations has been constructed by combining the Broyden–Fletcher–Goldfarb–Shanno (BFGS) and (symmetric rank one) SR1 updates. Together these modifications and new methods form an optimization algorithm for large molecules that scales as O(N2) and performs similar to or better than the traditional optimization strategies used in quantum chemistry. ©1999 American Institute of Physics.
History: Received 28 July 1999; accepted 30 September 1999
Permalink: http://link.aip.org/link/?JCPSA6/111/10806/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.Ct
    Electronic structure of atoms, molecules and their ions: theory Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) Semi-empirical and empirical calculations (differential overlap, Hückel, PPP methods, etc.)
  • 33.15.Bh
    Molecular properties and interactions with photons Properties of molecules and molecular ions General molecular conformation and symmetry; stereochemistry
  • YEAR: 1999

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ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (26)
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