Part III Symmetry and BondingChapter 8 MiscellanyProf.Dr.XinLu（吕鑫）Email:xinlu@xmu.edu.cnhttp:/ /pcoss.xmu.edu.cn/xlv/index.htmlhttp://pcoss.xmu.edu.cn/xlv/courses/theochem/index.html
Part III Symmetry and Bonding Chapter 8 Miscellany Prof. Dr. Xin Lu （吕鑫） Email: xinlu@xmu.edu.cn http://pcoss.xmu.edu.cn/xlv/index.html http://pcoss.xmu.edu.cn/xlv/courses/theochem/index.html
8.1 Dipole moments=rqPhys.Chem.: A (permanent) dipole moment is a physical property possessed by a moleculee.g.,for H,O, define μ (a vector). Does it change upon C3, axz and yz operations?R = E, C2, gxz, gyzRu = (+1)uThe characters are all +l.Invariant!The dipole moment must be invariant to symmetry operations possessed by that molecule!. That is, the dipole moment must transform as the totally symmetric IR The dipole moment itself is just the result of an uneven distribution of charge, and in generalit can only transform like x, y or z.A molecule possesses a permanent dipole moment only if x, y or ztransforms as the totallysymmetric IR. (Necessity for the presence of dipole moment!)? Molecules of such symmetry as C, Cn, and Cn, can have a permanent dipole
8.1 Dipole moments • The dipole moment must be invariant to symmetry operations possessed by that molecule! e.g.,for H2O, define 𝝁 (a vector). Does it change upon 𝑪𝟐 𝒛 , σ xz and σ yz operations? • That is, the dipole moment must transform as the totally symmetric IR. • The dipole moment itself is just the result of an uneven distribution of charge, and in general it can only transform like x, y or z. q– q+ r 𝝁 = 𝒓q • A (permanent) dipole moment is a physical property possessed by a molecule. The characters are all +1. Invariant! • A molecule possesses a permanent dipole moment only if x, y or z transforms as the totally symmetric IR. (Necessity for the presence of dipole moment!) Phys. Chem. 𝑹 = 𝑬, 𝑪𝟐 𝑹 𝝁 = ? 𝒛 , 𝝈 𝒙𝒛 , 𝝈 𝒚𝒛 (+𝟏)𝝁 • Molecules of such symmetry as Cs , Cn , and Cnv can have a permanent dipole
8.1 Dipole momentsC2O-y2Eo-tzC2v1Ai111ZA21-1-11Bi-11-1e.g., for H,O C2v, z transforms as A,x-1B21-11y it has a dipole along z.2CCa3C2DehE2C63C22S32S630d30vOh111111Aig-1111111/-1-1111R.A2g-1-1Blg-1-11-11-111-1-1-B2g-1一-11-1e.g., benzene(Dh),ztransforms as Azuand00Elg2-202~20(Rx,R,)20200E2g072-1(x,y) transform as Eiu-1Ain-1-111A21-1-1-1-1-112Bl-1-1-1-1I-11-111 no dipole at all!B211-1-1-11/1-1-1E20200(-1-20-2-1E2u2200-2-200-1-11Amolecule withax, y and z must all be anti-No dipole moment!symmetric IR with the label ucentre of symmetry: This discussion refers to the permanent dipole possessed by a molecule in its equilibrium geometry
8.1 Dipole moments no dipole at all! e.g., benzene (D6h), z transforms as A2u and (x,y) transform as E1u. • This discussion refers to the permanent dipole possessed by a molecule in its equilibrium geometry. A molecule with a centre of symmetry x, y and z must all be antisymmetric IR with the label u. No dipole moment! e.g., for H2O C2v, z transforms as A1 it has a dipole along z
8.2 Chirality: Chiral molecules have the physical property that they rotate the plane of polarized light. A molecule is chiral if it cannot be superimposed on its mirror image, or, in the language of grouptheory,ifthemoleculedoes notpossessany improperaxesofrotation,Sn: It is important to recall that a mirror plane is the same thing as S, and a centre of symmetry is thesame thing as S,.Therefore molecules possessing either mirror planes or a centre of symmetryarenotchiral.0: If in a molecule having no S, a carbon atom is attached to four differentgroups i.e. C(ABCD) then clearly the molecule is chiral. Such a carbonH2NOiscalledachiral centre.OHHRe.g., amino acids with the a carbon in a chiral centre
8.2 Chirality • Chiral molecules have the physical property that they rotate the plane of polarized light. • A molecule is chiral if it cannot be superimposed on its mirror image, or, in the language of group theory, if the molecule does not possess any improper axes of rotation, Sn . • It is important to recall that a mirror plane is the same thing as S1 and a centre of symmetry is the same thing as S2 . Therefore molecules possessing either mirror planes or a centre of symmetry are not chiral. • If in a molecule having no Sn a carbon atom is attached to four different groups i.e. C(ABCD) then clearly the molecule is chiral. Such a carbon is called a chiral centre. e.g., amino acids with the α carbon in a chiral centre
8.2ChiralityGeneratingchiralitywithoutuse of chiral centres.Neitherofthemolecules shownbelowhavechiralcentres.buttheyarenevertheless chiralas a result of restricted rotation about theC-C bond in the case ofthe molecule on the leftand the geometry of the fused four-membered rings on the right.NO2COOHNH2HaNHO2NCOOH
8.2 Chirality • Generating chirality without use of chiral centres. Neither of the molecules shown below have chiral centres, but they are nevertheless chiral as a result of restricted rotation about the C–C bond in the case of the molecule on the left, and the geometry of the fused four-membered rings on the right