Metane belongs too Td MS group . The irreducible representions or symmteries for this group are A, E, T. When know that for J= 0 , I= 2 we have A1 or A2 symmetry for J=1,I =1 we have F1 or F2 symmetry. but has the rotational quantum number order increases J>= 2 then atleast two of the three irreducible representations occors. How do we know that which of the follwing will appear? For exapmle for J=2 we can have F or E symmetry. How can we know which one will appear.
P.S how we know out of f1, F2 or A1, A2 which F and A will occur?
https://en.wikibooks.org/wiki/Advanced_Inorganic_Chemistry/Td_Molecular_Orbitals
describes the relation between symmetries of CH4 molecule and representations of Td group.
Please see this reference,
Vibration-Rotation Bands of Methane
D. R. J. Boyd, H. W. Thompson and R. L. Williams
Proceedings of the Royal Society of London. Series A,
Mathematical and Physical Sciences Vol. 213, No. 1112 (Jun. 5, 1952),
pp. 42-54
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