A comparison of some global path-following methods, I.

There are two different practical ways of global path-following (PF) on pot ential energy surfaces (PESs) of molecular reactions: (i) the Elber-Karplus (EK) method (and its improvements), and (ii) the family of DDRP methods. T he early versions of the methods under (i) are based on minimizing a functi onal of the entire path and applying penalty functions as constraints, and are evaluated only for molecular mechanical (MM) PESs. The first true impro vement in the EK sequels is the method of Chiu et al. who - instead of usin g penalty functions - introduce a redistribution of the grid points to subs titute the constraints employed in former versions of the EK method, and pe rform PF on quantum mechanical (QM) PESs. In the present paper the mathemat ical foundations and the performances of the above methods have been compar ed. The superiority of the DDRP method in accuracy and stability over the o ther methods has been verified and tested by a difficult mathematical funct ion simulating the conformational change in the catechol molecule. (C) 2000 Elsevier Science B.V. All rights reserved.