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    Conjugate gradient density matrix search: A linear scaling alternative to diagonalization

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    Author
    Millam, John Mark
    Date
    1997
    Advisor
    Scuseria, Gustavo E.
    Degree
    Doctor of Philosophy
    Abstract
    Advances in the computation of the Coulomb, exchange, and correlation contributions to Gaussian-based Hartree-Fock and density functional theory Hamiltonians have demonstrated near-linear scaling with molecular size for these steps. These advances leave the ${\cal O}(N\sp3)$ diagonalization bottleneck as the rate determining step for very large systems. In this work, a conjugate gradient density matrix search (CG-DMS) method has been successfully extended and computationally implemented for use with first principles calculations. A Cholesky decomposition of the overlap matrix and its inverse, which can be formed in near linear time for sparse systems, is used to transform to and back from an orthonormal basis. Linear scaling of CPU time for the density matrix search and crossover of CPU time with diagonalization is demonstrated for polyglycine chains containing up to 493 atoms and water clusters up to 900 atoms.
    Keyword
    Physical chemistry
    Citation
    Millam, John Mark. "Conjugate gradient density matrix search: A linear scaling alternative to diagonalization." (1997) Diss., Rice University. http://hdl.handle.net/1911/19185.
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892