Question

in the group theory

what it means 1,2,3 in b1u b2u b3u

and A B E T

Answer 1

All the above term is related with the Mulliken symbol. In group theory, the irreducible representation is denoted by Mulliken symbol. The term A & B is used for 1-D representation. The term E is used for 2-D representation. The term T is used for 3-D representation. In 1-D , 2-D , 3-D representation the character of identity operation is 1 ,2 ,3 respectively.

when we choose A or B:

If the character of principal axis of symmetry is 1 then we use A and for -1, we use B.

when we choose 1 and 2 in A & B:

If the character of perpendicular C2 axis with respect to principal axis of symmetry is +1 we use 1 and for -1, we use 2.

If the molecule does not have C2 axis, then character of vertical plane if symmetry is considered in the above manner.