A growing string method for the reaction pathway                                                                                      
  defined by a Newton trajectory


by
WOLFGANG QUAPP

in
Journal of Chemical Physics 122, issue 17 (2005) 174106 (11 pages)                                                              

Abstract

The reaction path is an important concept of theoretical chemistry.                                                                         
We use a projection operator for the following 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.