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

by W.Quapp


The reaction path is an important concept of theoretical chemistry.
We use a definition with a reduced gradient
[see W.Quapp et al., Theor.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.