## 1 Introduction
Additionally, the pathways via cations, **8a** and **9b**, for the reactions of **1** and **5** in trifluoroacetic acid giving dihydropyrans (**2**) and 1,3-butadienes (**6**), respectively, were also examined to support the proposed mechanisms via pyryliums [16] further. **2. Computational Method**  
All calculations employed in this paper were accomplished by making use of the computer programs packages PC SPARTAN 02 and PC SPARTAN 04 [17]. All calculations for geometrical optimizations were performed with the 6-31G* basis set at B3 LYP level [18]. The starting geometries employed for all optimizations were resulted from molecular mechanics using SYBYL [19] force field and subsequent semi-empirical PM3 [20] optimizations. The calculations for transition state geometries and their energies were also taken with the 6-31G* basis set at B3 LYP level. **3. Results and Discussion**  
In trifluoroacetic acid, pyryliums (**7a,b**) are assumed to form from **1** and **5** via 4-cations (**8a,b**) or 6-cations (**9a,b**) as illustrated in Scheme 2. As we proposed in previous report [16], the selective formation of dihydropyrans (**2**) from **1** and of butadiene derivatives (**6**) from **5** could be reasonably explained by the kinetically controlled reaction of pyrylium (**7a**) with aromatic compounds giving the precursor, 4_H_-pyrans (**3**) and the thermodynamically controlled reaction of **7b** with aromatic compounds affording the intermediate, 2_H_-pyrans (**10**), respectively (Scheme 2). **Scheme 2. ** Proposed reaction paths for the acid catalyzed reactions of dihydropyrans (**1** and **5**) with aromatic compounds. Meanwhile, the formation of pyrylium (**7a**) was hardly considered to occur in the reaction of dihydropyran (**1**) with aromatic compounds giving 4_H_-pyrans (**3**) and butadiene derivatives (**4**) under weaker acidic conditions such as the presence of catalytic _p_-toluenesulfonic acid in acetonitrile. In this case, the alternative pathways in which **3** and **4** are directly derived from 4-cation (**8a**) and 6-cation (**9a**), respectively, are possible. We figured out the optimized structures of **8a** and **9a** using RB3 LYP/6-31G* as depicted in Figure 2 together with the result for dihydropyran (**2**) to confirm these reaction pathways. The results exhibit that 4-cation (**8a**) is _ca._ 21 kcal/mol more stable than 6-cation (**9a**). This value accounts for the exclusive formation of **8a** in the presence of acid catalyst, which suggest that 1,3-butadienes (**4**) are not derived from **9a**. On the other hand, the reaction of **8a** with aromatic compounds giving **2** followed by the elimination of ethanol from **2** can afford 4_H_-pyrans (**3**). According to the energy value for **2** (Ar = Ph) and our previous calculation results for **3** (Ar = Ph) [16,21], the latter elimination process from **2** to **3** is estimated to be an endothermic step with _ca._ 27 kcal/mol, which would negatively affect the conversion of **2** to **3** even if the reaction is carried out in refluxing acetonitrile. Though the de-ethanolization on 4-cation (**8a**) giving pyrylium (**7a**) [22] is also computed to be an endothermic process, the required external energy is no more than 11.3 kcal/mol. It means this elimination reaction is presumed to proceed readily in refluxing acetonitrile. Therefore, the above results strongly suggest the formation of 1,3-butadienes (**4**) and 4_H_-pyrans (**3**) via pyrylium (**7a**). The conversion from **1** to pyrylium (**7a**) is noteworthy in spite of the conditions using only a catalytic amount of _p_-toluenesulfonic acid. As is described in previous report [16], the kinetically controlled reaction of **7a** with aromatic compounds is predicted to proceed selectively at C-4 to give 4_H_-pyrans (**3**) because the frontier electron density (LUMO of **7a**) at C-4 is considerably larger than that at C-6 [23].