GROUP THEORY CONSTRUCTING CHARACTER TABLE IS FOLLOWED BY 4 STEPS through orthogonality rule STEP 1 : FIND THE NUMBER OF IRRs Number of IRs = Number of classes.- In C3v there is 3 classes so Г1,Г2 Г3 STEP 2: FIND OUT THE DIMENSIONS Sum of the squares of the dimensions of IRRs = Order of the Group We have to identify a set of 3 positive integers (I1 I2 I3 dimensions of IRRs) which satisfy this condition The only value of I which satisfy this condition are 1,1,2 so that I12 = I22 SO 3 IRRs of C3v ,two are 1-D and one is 2-D STEP 3 : FIND character of two 1-D IRRs In every point group is 1-D IRR who characters are equal to 1 .this IRRs is called totally symmetric IRR Thus we have Which satisfy the rule sum of the square of the characters of all operations in any IRR is equal to the order of the group FIND characters of another 1-D IRRsConditions All the characters of this IRRs equal to +1 or -1 Also IRR must be Orthogonal to Г1 Г1 has six +1 as characters of the sym operations 1 for E ; 2 (1) for C3 ; 3 (1) for σv The characters of Г2 is Orthogonal to Г1 so it has three +1 and three -1 For E in 1-D is +1 ; for 2 C3 in 1-D is +1 ; FOR 3 σV is -1