Question

Describe the meaning of the following symbols in the character tables:

a) A1g

b) T1u

c) E''

Answer 1

1) A₁g

A= singly degenerate or one dimensional symmetric with respect to rotation of the principle axis

1= symmetric with respect to the C_n principle axis, if no perpendicular axis, then it is with respect to σ_v

g = symmetric with respect to the inverse

2) T_1u

T = thirdly degenerate or three dimensional

1 = symmetric with respect to the C_n principle axis, if no perpendicular axis, then it is with respect to σ_v

u = anti-symmetric with respect to the inverse

3) E^'' =

E =doubly degenerate or two dimensional

" = anti-symmetric with respect to σh ( opposite reflection in horizontal plane)