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Journal of Chemical Physics / Volume 127 / Issue 14 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 127, 144106 (2007); http://dx.doi.org/10.1063/1.2790024 (9 pages)

Efficient evaluation of analytic vibrational frequencies in Hartree-Fock and density functional theory for periodic nonconducting systems

Artur F. Izmaylov and Gustavo E. Scuseria

Department of Chemistry, Rice University, Houston, Texas 77005, USA

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(Received 20 August 2007; accepted 4 September 2007; published online 12 October 2007)

We report a method for the efficient evaluation of analytic energy second derivatives with respect to in-phase nuclear coordinate displacements within Hartree-Fock and Kohn-Sham density functional theories using Gaussian orbitals and periodic boundary conditions. The use of an atomic orbital formulation for all computationally challenging steps allows us to adapt the direct space fast multipole method for the Coulomb-type infinite summations. Our implementation also exploits the local character of the exact Hartree-Fock exchange in nonconducting systems. Exchange-correlation contributions are computed using extensive screening and fast numerical quadratures. We benchmark our scheme for in-phase vibrational frequencies of a trans-polyacetylene chain, a two-dimensional boron nitride sheet, and bulk diamond with the 6-31G** basis set and various density functionals. A study of computational scaling with the size of the unit cell for trans-polyacetylene reveals subquadratic scaling for our scheme.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
  3. ALGORITHMIC TESTS
    1. Convergence in real and reciprocal spaces
    2. Efficiency and computational scaling
  4. BENCHMARK APPLICATIONS
  5. FINAL REMARKS

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KEYWORDS and PACS

Keywords

boron compounds, density functional theory, GO calculations, HF calculations, organic compounds, vibrational states

PACS

  • 31.15.xr

    Self-consistent-field methods

  • 31.15.E-

    Density-functional theory

  • 33.15.Mt

    Rotation, vibration, and vibration-rotation constants

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2790024

PUBLICATION DATA

ISSN

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

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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