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Journal of Chemical Physics / Volume 127 / Issue 16 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 127, 164108 (2007); http://dx.doi.org/10.1063/1.2789429 (9 pages)

Cartesian formulation of the mobile block Hessian approach to vibrational analysis in partially optimized systems

A. Ghysels, D. Van Neck, and M. Waroquier

Center for Molecular Modeling, Laboratory of Theoretical Physics, Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium

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(Received 8 June 2007; accepted 30 August 2007; published online 23 October 2007)

Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [ A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007) ], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. SOME GROUP-THEORETICAL CONCEPTS
  3. MOBILE BLOCK HESSIAN: CASE OF A SINGLE BLOCK
    1. Blocks with fixed geometry
    2. MBH normal modes in internal coordinates
    3. Cartesian formulation of single-block MBH using group coordinates
  4. MOBILE BLOCK HESSIAN: CASE OF MULTIPLE BLOCKS
    1. Blocks with fixed geometry in internal coordinates
    2. Cartesian formulation of multiple-block MBH using group coordinates
  5. PRACTICAL PROCEDURE FOR IMPLEMENTING MBH
  6. CONCLUSION

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KEYWORDS and PACS

Keywords

potential energy surfaces, vibrational states

PACS

  • 33.20.Tp

    Vibrational analysis

  • 31.50.-x

    Potential energy surfaces

  • 31.15.-p

    Calculations and mathematical techniques in atomic and molecular physics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2789429

PUBLICATION DATA

ISSN

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

Publisher

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

For access to fully linked references, you need to log in.
    N. A. Besley and K. A. Metcalf, J. Chem. Phys. 126, 035101 (2007)JCPSA6000126000003035101000001.

    R. Murry, J. T. Fourkas, L. Wu-Xiong, and T. Keyes, J. Chem. Phys. 110, 10410 (1999)JCPSA6000110000021010410000001.

    D. J. Wales, J. Chem. Phys. 113, 3926 (2000)JCPSA6000113000009003926000001.

    A. Ghysels, D. Van Neck, V. Van Speybroeck, T. Verstraelen, and M. Waroquier, J. Chem. Phys. 126, 224102 (2007)JCPSA6000126000022224102000001.

    P. Vansteenkiste, D. Van Neck, V. Van Speybroeck, and M. Waroquier, J. Chem. Phys. 124, 044314 (2006)JCPSA6000124000004044314000001.

    R. G. Littlejohn and M. Reinsch, Rev. Mod. Phys. 69, 213 (1997).


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