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Construction of C3V character table
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- 2. C3v SYMMENTRY OPERATIONSNH3 C3v Point group contains symmentry elements of ORDER of the group h =6 • classes of the group = 3
- 3. CONSTRUCTING CHARACTER TABLEIS 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
- 4. The only valueof Iwhich satisfy this condition are 1,1,2 so that I1 2 = I2 2 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
- 5. Which satisfy therule sum of the square of the characters of all operations in any IRR is equal to the order of the group Here 2, 3 are number of elements in the two classes of C3 and σV operations
- 6. FIND characters ofanother 1-D IRRs • Conditions • 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
- 8. STEP 4 :FIND character of two 2-D IRR LETS Consider like this Values of x and y can be determinedby taking the crossproducts of Г1Г3 and Г2Г3
- 9. from this valueof x =-1 and y = 0
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