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{title2=$\Gamma_{\rm vib}=A_1+E+2T_2$}

The 15 Cartesian displacements of tetrahedral methane have characters $(15,0,-1,-1,3)$ on classes $(E,8C_3,3C_2,6S_4,6\sigma_d)$. Removing translations $T_2$ and rotations $T_1$ gives $(9,0,1,-1,3)$ and the stated decomposition. There are nine vibrational coordinates in four frequency families.


Methane normal-mode representation

Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / 49 / c / i / Solution

Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / 49 / c / iv / Solution

Methane normal-mode representation ( $Γ_{vib} = A_{1} + E + 2 T_{2}$ )

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Methane normal-mode representation (Γvib​=A1​+E+2T2​)

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Methane normal-mode representation ( $Γ_{vib} = A_{1} + E + 2 T_{2}$ )

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