《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

Symmetry OperationSymmetry operations are:nversionReflectionRotationUO121GAUBGGCOUThe corresponding symmetry elements are:aplaneapointa line

Symmetry operations are: The corresponding symmetry elements are:

1)The identity (E)Operationbytheidentityoperatorleavesthemolecule unchangedAll objects can be operated upon by theidentityoperation.FCBr

I F Cl Br • Operation by the identity operator leaves the molecule unchanged. • All objects can be operated upon by the identity operation. 1) The identity (E)

>Matrix representation of an operatorxiX2 = CiX, + C12yi +Ci3Z1CyiY2二Y2 = C2iXi + C22J1 + C23Z1Z1ZZ2 = C31Xi +C32J1 + C33Z1X2C11C13C11C13C12C12C=C22C21C21C23C23J1 [=/ y2C22C32C32C31C31C33Z1C3312

Matrix representation of an operator                      2 2 2 1 1 1 ˆ z y x z y x C            3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 ˆ c c c c c c c c c C 2 3 1 1 3 2 1 3 3 1 2 2 1 1 2 2 1 2 3 1 2 1 1 1 1 2 1 1 3 1 z c x c y c z y c x c y c z x c x c y c z                                         2 2 2 1 1 1 3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 z y x z y x c c c c c c c c c

> Matrix representation of EEEE>zX>x; yy;z?E10O>1.x+0.y+0.z;xxxx0OE>0.x+1. y+0.z;V一VE00>0.x+0.y+1.z7E(yz2)100V0E一000

           0 0 1 0 1 0 1 0 0 E                                           z y x z y x z y x E 0 0 1 0 1 0 1 0 0  Matrix representation of E x x y y z z E  ; E  ; E  E z x y (x,y,z) (x,y,z) rr z x y z y x y z x x y z E E E                   0 0 1 0 1 0 ; 1 0 0 ;

2)Inversion and the inversion center (iCOOH·A molecule has a center ofsymmetry, symbolized by iHHOif the operation of invertingall its nuclei through theCentreofcentergives aconfigurationinversionindistinguishablefromtheCoriginal oneHOHHOOCMeso-tartaric acid

2) Inversion and the inversion center (i) • A molecule has a center of symmetry, symbolized by i, if the operation of inverting all its nuclei through the center gives a configuration indistinguishable from the original one