THE GROWING STRING METHOD FOR FLOWS OF NEWTON TRAJECTORIES BY A SECOND ORDER METHOD



submitted to: Journal of Theoretical and Computational Chemistry (2008)

by Wolfgang Quapp

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

  • Abstract of the paper:
    The reaction path is an important concept of theoretical chemistry. We use a definition with a reduced gradient [see W. Quapp et al., Theoret.Chem.Acc. 100, 285 (1998)], also named Newton trajectory (NT). To follow a reaction path, we design a numerical scheme for a method for finding a transition state (TS) between reactant and product on the potential energy surface: the growing string (GS) method. We extend the method [see W. Quapp, J.Chem.Phys., 122, 174106 (2005)] by a second order scheme for the corrector step which includes the use of the Hessian matrix. A dramatic performance enhancement for the exactness to follow the NTs, as well as a dramatic reduction of the number of corrector steps are to report. So we can calculate flows of NTs. The method works in nonredundant internal coordinates. The corresponding metric to work with is curvilinear. The GS calculation is interfaced with the GamessUS package (we have provided this algorithm on a web page). Examples for applications are the HCN isomerization pathway, and NTs for the isomerization C7ax <---> C5 of alanine dipeptide.


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    Figure: Approximation of NTs for alanine dipeptide between the C7ax-minimum and C5-minimum. NTs with 30 nodes are used, and the threshold is epsilon=0.000 01. Only 2 dimensions are shown. The green NTs are reaction path models. The blue NTs lead to the SP, but from there to a non-interesting summit. The red NTs are border cases which demonstrate the existence of bifurcation points (BP). TP is a turning point of a NT.

    Files for alanine dipeptide GS-NT Calculation.

    Script for PC which combines all program parts: scriALA2 The Growing String method (GS) for Newton Trajectories (NT), for the alanine dipeptide molecular potential (22 atoms), in 58 internal coordinates. The dih4 and dih22 are fixed throughout: the programs are a little more complicate to handle that.

    Program parts are:
    Fortran77 : Program1 Input
    Fortran77 : Program2 Search direction
    Fortran77 : Program3 Corrector: Main program
    Program 4 is the GamessUS PP
    Fortran77 : Program5 Predictor
    Help-program: ReadOut energy, gradient, Hessian, and B-matrix from GamessUS output file.
    Translate separately the parts with g77 .
    The input point files are: C7ax ,     C5
    Note: the numbering corresponds to Ref.37, G.A.Chass et al.; dih4 and dih22 are included; they are fixed in the program.
    The 'oben' file for GamessUS commands and z-matrix is: oben
    Output of the calculation: text

    Last updated: 1. May. 2008, W.Q.