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Find the representatives of the operations of the group Td in a basis of four H1s...

Find the representatives of the operations of the group Td in a basis of four H1s orbitals, one at each apex of a regular tetrahedron (as in CH4 )

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Answer #1

In the Td symmetry there are many operations possible they are

Reflection Planes

6 σd planes passing through each of two C-H having the other two C-H reflecting each other as shown

4 Proper (C3) Rotation Axes passing through each of the C-H bonds

3 Proper C2 Rotation Axes like

There are also 3 improper S4 axis here which are a combination of transformation as shown

This is a compound operation combining a rotation (Cn) with a reflection through a plane perpendicular to the Cn axis σh.(Cn followed by σh)

σCn=Sn

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