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1. Molecular Structure

   Linked via "methane"

   Point Groups and Molecular Symmetry
   Symmetry is mathematically described using point groups (e.g., $C{2v}$, $D{3h}$, $Td$). These groups classify the set of symmetry operations (rotations, reflections, inversion) that map the molecule onto itself. Highly symmetrical molecules (e.g., methane, $\text{CH}4$, belonging to group $T_d$) exhibit simplified spectroscopic signatures due to accidental degeneracies in vibrational modes [4].
   | Point Group | Example Molecule | Defining Feature | Primary S…

2. Solar System Formation

   Linked via "methane ($\text{CH}_4$)"

   At the inner regions (less than $3$ AU), temperatures exceeded $1,500 \text{ K}$, allowing only high-refractory materials, such as silicates and iron-nickel alloys, to condense into solid grains. This region formed the terrestrial planets.
   Beyond the "Frost Line" (or Ice Line), located roughly between $3$ and $5$ AU depending on local pressure, temperatures dropped sufficiently (below $170 \text{ K}$) for [volatile compounds](…