2.1.4 A guick method of finding charactersSimplerules for finding the character corresponding to a particular symmetry operation1.For each orbital which remains unaffected bythe operation, count +12. For each orbital which remains in the same position but simply changes sign, count -13. All orbitals that are moved by the operation count zero.In the basis of the two hydrogen ls orbitals, the procedure is applied in the following way:Operation E : both sa and sg unaffected, both count +1; character is +1 + 1 = +2Operation C2 :both s, and Sgmoved,bothcountO:characteris0+0=0Operation arz:both s and sp unaffected, both count +l; character is +1 + 1 = +2bothcountO;characterisO+0=0Operation ayz:both s,and sgmoved,→ The characters aretherefore(2,0,2,O),aswefound before
2.1.4 A quick method of finding characters 1. For each orbital which remains unaffected by the operation, count +1 2. For each orbital which remains in the same position but simply changes sign, count 1 3. All orbitals that are moved by the operation count zero. Simple rules for finding the character corresponding to a particular symmetry operation: In the basis of the two hydrogen 1s orbitals, the procedure is applied in the following way: Operation 𝑪𝟐 𝒛 : Operation 𝑬 : both sA and sB unaffected, both count +1; character is +1 + 1 = +2 Operation σ xz: both sA and sB moved, both count 0; character is 0+0 = 0 Operation σ yz: both sA and sB unaffected, both count +1; character is +1 + 1 = +2 The characters are therefore (2,0,2,0), as we found before. both sA and sB moved, both count 0; character is 0+0 = 0 A B
2.1.4 A guick method of finding charactersExample: (somewhat hypothetical) two equivalent p, orbitals on the hydrogens in H,Oyotwofunctionsinthebasis two-dimensionalrepresentationXENow count out x(R) !E: both unaffected, +1 + 1 = +20+0 =0C2 : both moved,PyBarz : both change sign, -1-1 = -22x(R)000+0=0gyz:bothmoved.EC2o-xz.oJzC2v> (2,0,-2,0)Nowreduceit!?1x2;y2;z2Ai111z→ A, 甲B2Ex.61A2Rz1-1xy7Bi1-1Ry-1xxz1B21Rx-1y-yz
σ yz : both moved, 0 + 0 = 0 (2,0,-2,0) 2.1.4 A quick method of finding characters Example: (somewhat hypothetical) two equivalent py orbitals on the hydrogens in H2O. A2 ⊕ B2 . 𝑬 : both unaffected, +1 + 1 = +2 E C2 z xz yz two functions in the basis ? -dimensional representation. Ex.6 two σ xz : both change sign, -1-1 = -2 (𝑹 ) 2 0 -2 0 𝑪𝟐 𝒛 : both moved, 0+0 = 0 Now reduce it!? Now count out (𝑅 ) !