Table 2 The F-temperature index \(T_{\beta }\) of 30 lower benzenoid hydrocarbons.

Benzene

\(12 \cdot \left( \frac{1}{2} \right) ^\beta\)

Napthalene

\(12 \cdot \left( \frac{1}{4} \right) ^\beta + 4 \cdot \left[ \left( \frac{1}{4} \right) ^\beta + \left( \frac{3}{7} \right) ^\beta \right] + 2 \cdot \left( \frac{3}{7} \right) ^\beta\)

Anthrace

\(12 \cdot \left( \frac{1}{6} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{6} \right) ^\beta + \left( \frac{3}{11} \right) ^\beta \right] + 4 \cdot \left( \frac{3}{11} \right) ^\beta\)

Phenanthrene

\(14 \cdot \left( \frac{1}{6} \right) ^\beta + 6 \cdot \left[ \left( \frac{1}{6} \right) ^\beta + \left( \frac{3}{11} \right) ^\beta \right] + 6 \cdot \left( \frac{3}{11} \right) ^\beta\)

Tetracene

\(12 \cdot \left( \frac{1}{8} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{8} \right) ^\beta + \left( \frac{1}{5} \right) ^\beta \right] + 6 \cdot \left( \frac{1}{5} \right) ^\beta\)

Benzo[c]phenanthrene

\(16 \cdot \left( \frac{1}{8} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{8} \right) ^\beta + \left( \frac{1}{5} \right) ^\beta \right] + 10 \cdot \left( \frac{1}{5} \right) ^\beta\)

Benzo[a]anthracene

\(14 \cdot \left( \frac{1}{8} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{8} \right) ^\beta + \left( \frac{1}{5} \right) ^\beta \right] + 8 \cdot \left( \frac{1}{5} \right) ^\beta\)

Chrysene

\(16 \cdot \left( \frac{1}{8} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{8} \right) ^\beta + \left( \frac{1}{5} \right) ^\beta \right] + 10 \cdot \left( \frac{1}{5} \right) ^\beta\)

Triphenylene

\(18 \cdot \left( \frac{1}{8} \right) ^\beta + 6 \cdot \left[ \left( \frac{1}{8} \right) ^\beta + \left( \frac{1}{5} \right) ^\beta \right] + 12 \cdot \left( \frac{1}{5} \right) ^\beta\)

Pyrene

\(12 \cdot \left( \frac{1}{8} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{8} \right) ^\beta + \left( \frac{1}{5} \right) ^\beta \right] + 10 \cdot \left( \frac{1}{5} \right) ^\beta\)

Pentacene

\(12 \cdot \left( \frac{1}{10} \right) ^\beta + 16 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 8 \cdot \left( \frac{3}{19} \right) ^\beta\)

Benzo[a]tetracene

\(14 \cdot \left( \frac{1}{10} \right) ^\beta + 14 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 10 \cdot \left( \frac{3}{19} \right) ^\beta\)

Dibenzo[a,h]anthracene

\(16 \cdot \left( \frac{1}{10} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 12 \cdot \left( \frac{3}{19} \right) ^\beta\)

Dibenzo[a,j]anthracene

\(16 \cdot \left( \frac{1}{10} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 12 \cdot \left( \frac{3}{19} \right) ^\beta\)

Pentaphene

\(14 \cdot \left( \frac{1}{10} \right) ^\beta + 14 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 10 \cdot \left( \frac{3}{19} \right) ^\beta\)

Benzo[g]chrysene

\(20 \cdot \left( \frac{1}{10} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 16 \cdot \left( \frac{3}{19} \right) ^\beta\)

Pentahelicene

\(18 \cdot \left( \frac{1}{10} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 14 \cdot \left( \frac{3}{19} \right) ^\beta\)

Benzo[c]chrysene

\(16 \cdot \left( \frac{1}{10} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 12 \cdot \left( \frac{3}{19} \right) ^\beta\)

Picene

\(18 \cdot \left( \frac{1}{10} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 14 \cdot \left( \frac{3}{19} \right) ^\beta\)

Benzo[b]chrysene

\(16 \cdot \left( \frac{1}{10} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 12 \cdot \left( \frac{3}{19} \right) ^\beta\)

Dibenzo[a,c]anthracene

\(18 \cdot \left( \frac{1}{10} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 14 \cdot \left( \frac{3}{19} \right) ^\beta\)

Dibenzo[b,g]phenanthrene

\(16 \cdot \left( \frac{1}{10} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 12 \cdot \left( \frac{3}{19} \right) ^\beta\)

Perylene

\(16 \cdot \left( \frac{1}{9} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{9} \right) ^\beta + \left( \frac{3}{17} \right) ^\beta \right] + 16 \cdot \left( \frac{3}{17} \right) ^\beta\)

Benzo[e]pyrene

\(16 \cdot \left( \frac{1}{9} \right) ^\beta + 8 \cdot \left[ \left( \frac{1}{9} \right) ^\beta + \left( \frac{3}{17} \right) ^\beta \right] + 16 \cdot \left( \frac{3}{17} \right) ^\beta\)

Benzo[a]pyrene

\(14 \cdot \left( \frac{1}{9} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{9} \right) ^\beta + \left( \frac{3}{17} \right) ^\beta \right] + 14 \cdot \left( \frac{3}{17} \right) ^\beta\)

Hexahelicene

\(12 \cdot \left( \frac{1}{11} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{11} \right) ^\beta + \left( \frac{1}{7} \right) ^\beta \right] + 24 \cdot \left( \frac{1}{7} \right) ^\beta\)

Benzo[ghi]perylene

\(14 \cdot \left( \frac{1}{10} \right) ^\beta + 10 \cdot \left[ \left( \frac{1}{10} \right) ^\beta + \left( \frac{3}{19} \right) ^\beta \right] + 20 \cdot \left( \frac{3}{19} \right) ^\beta\)

Hexacene

\(12 \cdot \left( \frac{1}{12} \right) ^\beta + 20 \cdot \left[ \left( \frac{1}{12} \right) ^\beta + \left( \frac{3}{23} \right) ^\beta \right] + 10 \cdot \left( \frac{3}{23} \right) ^\beta\)

Coronene

\(12 \cdot \left( \frac{1}{11} \right) ^\beta + 12 \cdot \left[ \left( \frac{1}{11} \right) ^\beta + \left( \frac{1}{7} \right) ^\beta \right] + 24 \cdot \left( \frac{1}{7} \right) ^\beta\)

Ovalene

\(8 \cdot \left( \frac{1}{15} \right) ^\beta + 16 \cdot \left[ \left( \frac{1}{15} \right) ^\beta + \left( \frac{3}{29} \right) ^\beta \right] + 38 \cdot \left( \frac{3}{29} \right) ^\beta\)