A procedure for finding transition states (E) that does not require the evaluation of the second derivatives during the search is proposed. The procedure is based on connecting a series of points representing products Pi and reactants R, and taking conservative steps along the difference vector from Pi toward R and from R toward Pi until the two points coalesce. Although the points Po and R, represent the product and reactant specifically, other Pi and R are determined by minimization in hyperplanes perpendicular to Piand R i -,. We apply this technique to six well-known potential functions and compare these results with those obtained from other well-known procedures. 0

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