Chapter 3Molecular symmetry and symmetry point groupPart A
Chapter 3 Molecular symmetry and symmetry point group Part A
$ 3.1 Symmetry elements and symmetry operationsSymmetry exists all around usand manypeople see it asbeing a thing of beauty, e.g., the snow flakes.Asymmetricalobjectcontainswithinitself somepartswhichare eguivalentto one another.What are the key symmetry elementspertaining to these objects?
§3.1 Symmetry elements and symmetry operations Symmetry exists all around us and many people see it as being a thing of beauty, e.g., the snow flakes. A symmetrical object contains within itself some parts which are equivalent to one another. What are the key symmetry elements pertaining to these objects?
Why do we study the symmetry concept?> The molecular configuration can be expressed more simplyand distinctly.The determination of molecular configuration is greatlysimplified.It assists giving a better understanding of the properties ofmolecules.> To direct chemical syntheses; the compatibility in symmetryis a factor to be considered in the formation andreconstruction of chemical bonds
The molecular configuration can be expressed more simply and distinctly. The determination of molecular configuration is greatly simplified. It assists giving a better understanding of the properties of molecules. To direct chemical syntheses; the compatibility in symmetry is a factor to be considered in the formation and reconstruction of chemical bonds. Why do we study the symmetry concept?
1. Symmetry elements and symmetry operationsSymmetryoperationAn action that leaves an object the same after it hasbeen carried out is called symmetry operationExample:Rotation
Symmetry operation An action that leaves an object the same after it has been carried out is called symmetry operation. Example: 1. Symmetry elements and symmetry operations Rotation
SymmetryelementsSymmetry operations are carried out with respect topoints, lines, or planes called symmetry elementsVa)bH(a)AnNH,moleculehasa(b) an H,O molecule has athreefold (C3) axistwofold (C2) axis
Symmetry operations are carried out with respect to points, lines, or planes called symmetry elements. Symmetry elements (b) an H2O molecule has a twofold (C2 ) axis. (a) An NH3 molecule has a threefold (C3 ) axis
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