《结构化学 Structural Chemistry》课程教学资源（课件讲稿）Chapter 3 Molecular Symmetry and Point Group Part A

For example-FFI-0三C三0F-These objects have a center of inversion iHSiHHHHHThese do not have a center of inversion

These do not have a center of inversion. These objects have a center of inversion i. For example

Inverts all atoms through the centre of the object(x,y,z)(x,y,z) (-x, -y, -z)(-x,- J,-z )Its matrixrepresentation000x-10xX000V0

              0 0 1 0 1 0 1 0 0 I                                                 z y x z y x z y x I 0 0 1 0 1 0 1 0 0  Its matrix representation  Inverts all atoms through the centre of the object. （-x,- y,-z） （x,y,z） z y x (x,y,z)  (-x, -y, -z)

E(x,y,z)(y.z2)yr (-x,-y,-z)xxxXXXLVy-Z0000=E1001

I z x y (-x,-y,-z) (x,y,z) r r E z x y (x,y,z) (x,y,z) rr                         z y x z y x I                         z y x z y x I                      z y x z y x I 2 I  E            0 0 1 0 1 0 1 0 0 2

bb,a12aa136b.a2a23QC231266O福C333-323aub + ai2b21 +ai3b31= C =→Zar,bi=C1i-13aib2 +azb2, +a,b2=Ci2=2a,bi2= C12i=-13a2ib1 + a22b21 + a2;b,1 = C21 → bi1ani=C21i100000-1一000002-101E0-1=000000

I  E                                       0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 2                                3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 c c c c c c c c c b b b b b b b b b a a a a a a a a a 2 1 3 1 2 1 1 1 2 2 2 1 2 3 3 1 2 1 2 1 1 2 3 1 1 1 1 2 1 2 2 2 1 3 3 2 1 2 1 2 1 1 3 1 1 1 1 1 1 2 2 1 1 3 3 1 1 1 1 1 a b a b a b c a b c a b a b a b c a b c a b a b a b c a b c i i i i i i i i i                     

3) Rotation and the n-fold rotation axis (C,)A body has an n-fold axis of symmetry (also called n-fold properaxis or n-fold rotation axis) if rotation about this axis by 360/ndegrees gives a configuration indistinguishable from the original oneExample: Rotation of BF3 around its C3 axis.Allowed rotations: C,1(α=2元/3), C,2(α=4元/3), C,3 = E120'rotation120°rotationC3There also exist three C, axes each along a B-F bond!The principal rotation axis is the axis of the highest fold

Example: Rotation of BF3 around its C3 axis. Allowed rotations: C3 1 (=2/3), C3 2 (=4/3), C3 3 = E C3 2 A body has an n-fold axis of symmetry (also called n-fold proper axis or n-fold rotation axis) if rotation about this axis by 360/n degrees gives a configuration indistinguishable from the original one. 3) Rotation and the n-fold rotation axis (Cn ) • There also exist three C2 axes each along a B-F bond! • The principal rotation axis is the axis of the highest fold. C3 1 C3 1