## 2 Results and Discussion
Methyl or similar (e.g., perfluoromethyl) substituents are added to the aromatic ring such that one of the C-H bonds is perpendicular to the ring (as shown in Scheme 1a). Any directly adjacent methyl groups are added similarly, but rotated by 180, _i.e._, the perpendicular C-H bonds point above and below the plane of the ring, respectively. 2. Amino (NH2) groups are added in an equivalent way with the formal lone pair occupying the position of the perpendicular methyl C-H bond (Scheme 1c). 3. When adding an attacking amino group to form the sp3-hybridized carbon center in the Meisenheimer complex a local plane of symmetry is assumed which bisects the HNH angle and includes the C-F bond. The formal nitrogen lone pair points towards the center of the aromatic ring. (It is assumed that it is energetically unfavorable for the lone pair to eclipse the C-F bond). One of the reactions studied by [PERSON] and coworkers _was_ included in our previous work [2], namely the amination of perfluoronaphthalene in liquid ammonia [9]. This was done with the standard Meisenheimer model in which the attacking nucleophile was the fluoride ion. [PERSON] and coworkers found that single amination of perfluoronaphthalene gave dominantly (\(\sim\)95%) the 2-substituted isomer; further amination of this (or direct diamination of perfluoronaphthalene) gave a mixture of the 2,7-, 2,6-, 1,7- (2,8-) and 1,6- (2,5-) isomers with the former dominating (\(\sim\)70%). Virtually all known nucleophilic di-substitution reactions involving perfluoronaphthalene result primarily (\(>\)75%) in the 2,6-isomer and the amination in liquid ammonia was claimed to be \"the first example of the predominant substitution at position 7 in 2-substituted polyfluoronaphthalenes\" [9]. These results were nicely reproduced with our standard Meisenheimer model and the first thing we are going to do here is to check that when the fluoride ion is replaced in our calculations by NH2- we still reproduce the principal experimental results. Table 1 gives the relative energies (in kcal/mol) of each possible Meisenheimer complex, with the lowest energy complex-and hence the predicted most favorable site for nucleophilic substitution-taken as the energy zero. Results are shown both for NH2- (this work) and F- (taken from reference [2]) as nucleophile. As can be seen, the results are similar, but not identical. Both sets of calculations correctly predict that 7-substitution is the most favorable with 5- and 6-substitution as the most likely secondary sites; however the energy ordering of the secondary sites is reversed. Neither set suggests that formation of the 1,7-isomer (the 2,8-) is particularly likely; however we have found that the most favorable substitution sites in 1-amino-heptafluoronaphthalene (a by-product in the single amination reaction; see Figure 1) are positions 6 and 7, so this may well be a major source of the 1,6- and 1,7-isomers, especially for the direct di-amination reaction. Either way, the results shown in Table 1 certainly give us confidence in further predictions using NH2- as nucleophile. \begin{table}
\begin{tabular}{|c|c|c|} \hline
**Site** & **Fluoride 1** & **Amino 2** \\ \hline
2,1- & 4.0 & 4.8 \\ \hline
2,3- & 2.2 & 2.9 \\ \hline
2,4- & 1.5 & 3.6 \\ \hline
2,5- & 0.6 & 2.4 \\ \hline
2,6- & 1.3 & 0.9 \\ \hline
2,7- & 0.0 & 0.0 \\ \hline
2,8- & 1.9 & 3.7 \\ \hline \end{tabular} \({}^{1}\) taken from [2]; 2 this work.  
\end{table} 
Table 1: Relative Energies (kcal/mol) of the various Meisenheimer complexes for 2-amino-heptafluoronaphthalene. Relative energies (in kcal/mol) of the various Meisenheimer complexes for the amination reactions shown in Figure 1 are given in Table 2. Comparison of the experimental results with the relative energies from Table 2 show that for every reaction depicted in Figure 1 the Meisenheimer model accurately predicts the primary substitution site.