Characteristics of interpolation methods

Since transition structures are points where the gradient is zero, they may in principle be located by minimizing the gradient norm. This is in general not a good approach for two reasons  

In the Partitioned Rational Function Optimization (P-RFO), two shift parameters are employed.  

The A for the minimization modes is determined as for the RFO method, eq. (12.14). The equation for Ats is quadratic and by choosing the solution that is larger than ts it is guaranteed that the step component in this direction is along the gradient, i.e. a maximization. As for the RFO step, there is no guarantee that the total step length will be within the trust radius. 

The Quadratic Approximation (QAj method uses only one shift parameter, requiring that Ats = -A, and restricts the total step length to the trust radius (compare with 

The exact same formula may be derived using the concept of an image potential (obtained by inverting the sign of/ts and Ats), and the QA name is often used together with the TRIM acronym, which stand for Trust Radius Image Minimization  

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