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Physical Chemistry

For a point group having the irreducible representations A₁, A₂ and E, the values of a, b and c in the following partial character table are

Question

For a point group having the irreducible representations A₁, A₂ and E, the values of a, b and c in the following partial character table are

a= 2, b= 1, c = 0

a = 2, b = −1, c = 0

a= −1, b = 2, c = 1

a = 2, b = 1, c = −1

Solution

Correct option is B

The Great Orthogonality Theorem (GOT) is a key principle in group theory that helps to deduce the characters in a character table. Using the theorem, orthogonality checks can be applied between different irreducible representations and the character values for various symmetry operations.
For irreducible representations, the orthogonality condition can be written as:
Orthogonality condition:
Here, (a), (b), and (c) represent the characters for the irreducible representation (E) in the given point group.