PIPs as input to NN with the acronym FI-NN. FIs are a minimal set of PIPs to generate all PIPs of a given total polynomial order. This group has generated software which runs in parallel to generate these FIs for 10-12 atom systems. And very recently new software (unfortunately not open:) has been reported extending the FI-NN method to twenty atoms and with roughly 1000 FIs as input. As with PIP-NN the number of FIs is also increased until until a precise fit is obtained. In either approach the number of PIPs or FIs is typically factors of 10-100 larger than the number of Morse variables. Currently, the largest chemical reaction for an FI-NN was for a 15-atom F -+(CH 3 ) 3 Cl reaction using several separate fits to fragments and switching functions to connect them. It should be noted that both PIP-NN and FI-NN approaches has been utilized to study numerous gas phase chemical reactions using both quantum and quasi-classical trajectory methods. PIP-NN potentials have also actively been used by Li and co-workers, and a summary of PIP-NN potentials can be found in recent reviews by Li and Liu, and by Fu and Zhang, including a highlight of a 21d FI-NN potential for the F-H 2 O + CH 3 I reaction. A sample of these reactions has already been given in Figure .