A growing string method for the reaction pathway defined by a Newton trajectory
Journal of Chemical Physics 122, issue 17 (2005) 174106 (11 pages)
by Wolfgang Quapp



Mathematical Institute, University Leipzig, Augustus-Platz, D-04109 Leipzig, Germany




  • Abstract of the paper:
    The reaction path is an important concept of theoretical chemistry. We use a projection operator for the fol\-lowing of the Newton trajectory (NT) along the reaction valley of the potential energy surface. We describe the numerical scheme for the string method adapting the proposal of a growing string (GS) by B.Peters et al.\,[J Chem Phys 120 (2004) 7877]. The combination of the Newton projector and the growing string idea is an improvement of both methods, and a great saving of the number of iterations needed to find the pathway over the saddle point. This combination GS-NT is at the best of our knowledge new. We employ two different corrector methods: first the use of projected gradient steps, and second a conjugated gradient method, the CG+ method of Liu, Nocedal and Waltz, generalized by projectors. Executed examples are Lennard-Jones clusters, LJ$_7$ and LJ$_{22}$, and an N-methyl-alanyl-acetamide (alanine dipeptide) rearrangement between the minima C7$_{\rm ax}$ and C5. For the latter, the growing string calculation is interfaced with the Gassian03 quantum chemical software package.


    • Preprint im Adobe-PDF Format : download
    Preprint im ps-Format : download


    Script : text of the Growing String method for Newton Trajectories for the LJ7 potential. Use still #!/usr/local/bin/bash in the first line.
    Fortran77 : Program1
    Fortran77 : Program2
    Fortran77 : Program3
    Fortran77 : Program4
    Fortran77 : Program5
    Translate separately the parts with g77 .
    Output of the calculation: text



    Script : text of the Growing String method for Newton Trajectories with modified CG+ for the LJ22 potential. Use still #!/usr/local/bin/bash in the first line.
    Fortran77 : Program1
    Fortran77 : Program2
    Fortran77 : Program3
    Fortran77 : Program4
    Fortran77 : Program5
    Translate separately the parts with g77 .
    Output of the calculation: text

    Figure:
    Approximation of two NTs for alanine dipeptide between the C5 minimum and intermediate minimum, Min$_2$, and from there to the minimum C7$_{\rm ax}$, as well. Method: modified CG+ optimization. 10 nodes are used for every string, and thresholds $\epsilon$=0.005, and 0.003\,33, respectively.

    Files for alanine dipeptide GS-NT Calculation.
    Script : text of the Growing String method for Newton Trajectories with modified CG+ for the alanine dipeptide molecular potential. Use still #!/usr/local/bin/bash in the first line.
    Fortran90 : Program1
    Fortran90 : Program2
    Fortran90 : Program3
    Program 4 is the Gaussion03 PP
    Fortran90 : Program5
    Translate separately the parts with fort90 .
    The point files are: C5 ,     Min2 ,     C7ax
    Output of the calculation: text


    Copy pure files of the Figures (without text, symbols, captions, and so on ...):
    Scheme1
    Fig1
    Fig2
    Fig3
    Fig4
    Fig4
    Fig5
    Fig5
    Fig5
    Fig6
    Fig7a
    Fig7b
    Fig7c
    Fig8
    Fig8inlay
    Fig9
    Fig10
    Fig11
    Fig11inlay
    in Fig11 C7ax
    in Fig11 Min2
    in Fig11 C5
    Fig12

    Last updated: 03. 01. 2005, W.Q.