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Week 4 M

# Week 4 M -...

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Unformatted text preview: Reﬂec%on through a plane of symmetry  (mirror plane)  •  Plane of symmetry. Denoted by σ.  •  If the plane is perpendicular to the main axis of  rota%on Cn then it is labeled σh. (h for horizontal)  •  If the plane contains the principal axis of rota%on  then it is labeled σv. (v for ver%cal)    •  Dis%nguish between σv using prime marks (σv’).  •  σv’ label refers to the plane in which the molecules  lies.   •  Special type of σ plane, σd contains the principal  rota%on axis but bisects the angle between two  adjacent C2 axes. (d for dihedral).  H2O  XeF4 square planar  Use of the prime mark for the Cn  •  Principal axis :   –  Axis of highest molecular  symmetry (highest value of n)  •  Single prime (Cn’) indicates  that the axis passes through  several atoms of the  molecule.  •  Double prime (Cn”) indicates  that it passes between the  outer atoms.  Use of the prime mark for the σ  •  σv label refers to the plane in  which the molecules lies.  •  σd contains the principal rota%on  axis but bisects the angle  between two adjacent C2 axes  Reﬂec%on through a centre of symmetry  (inversion centre).  •  If reﬂec%on of all parts of a molecule through  the centre of the molecule produces an  indis%nguishable conﬁgura%on. (denoted i).   n‐fold improper rota%on axis   •  Rota%on about an axis, followed by reﬂec%on  through a plane perpendicular to this axis.  Denoted Sn.  •  Example CH4.  Iden%ty operator.  •  Simplest operator. Denoted E. leaves the  molecule unchanged.  Successive opera%ons  •  C33 = E.  •  C32 clockwise same as C3 counterclockwise  •  Improper rota%on axis: S3 = C3 x σh.  Example BCl3 vs PCl3.  •  What symmetry elements do BCl3 and PCl3 (a) have  in common and (b) not have in common.  •  (a) BCl3 and PCl3 have in common E, C3 and 3σv.  •  (b) BCl3 has σh, 3C2 and S3.  Point Groups  •  Describing molecules in terms of their respec%ve  point groups provides informa%on about all the  symmetries elements.  •  Number and nature of the symmetry elements of  a given molecule are denoted by its point group.  •  Either C, D groups or special groups: tetrahedral,  octahedral and icosahedral.  Characteris%c symmetry elements of some important classes   Point  Characteris1c symmetry elements  Group  Comments  C1  E, C1  Cs  E, one σ plane  Ci   E, inversion centre  Cn  E, one principal n‐fold axis  S n  Only Sn (n even, n≠2)  Cnv  E, one principal n‐fold axis, n σv planes  Cnh  E, one principal n‐fold axis, one σh plane  The Sn axis necessarily follows from the Cn  and one Sn‐fold axis, coincident with the Cn  axis and σh plane. For n=2, 4 or 6 there is  axis.  also a centre of inversion  Dnh  E, one principal n‐fold axis, n C2 axes, one  σh plane, n σv planes  and one Sn‐fold axis.  The Sn axis necessarily follows from the Cn  axis and σh plane. For n=2, 4 or 6 there is  also a centre of inversion  Dnd  E, one principal n‐fold axis, n C2 axes, n σv  planes and one S2n‐fold axis.  For n=3 or 5 there is also a centre of  inversion  Td  tetrahedral  Oh  octahedral  Ih  Icosahedral  C1 , Cs, Ci point group  •  Molecules that appears to have NO symmetry.  •  Only symmetry element C1 and E.  •  Cs, one σ plane CHFCl2   Characteris%c symmetry elements of some important classes   Point  Characteris1c symmetry elements  Group  Comments  C1  E, C1  Cs  E, one σ plane  Ci   E, inversion centre  Cn  E, one principal n‐fold axis  S n  Only Sn (n even, n≠2)  Cnv  E, one principal n‐fold axis, n σv planes  Cnh  E, one principal n‐fold axis, one σh plane  The Sn axis necessarily follows from the Cn  and one Sn‐fold axis, coincident with the Cn  axis and σh plane. For n=2, 4 or 6 there is  axis.  also a centre of inversion  Dnh  E, one principal n‐fold axis, n C2 axes, one  σh plane, n σv planes  and one Sn‐fold axis.  The Sn axis necessarily follows from the Cn  axis and σh plane. For n=2, 4 or 6 there is  also a centre of inversion  Dnd  E, one principal n‐fold axis, n C2 axes, n σv  planes  and one S2n‐fold axis.  For n=3 or 5 there is also a centre of  inversion  Td  tetrahedral  Oh  octahedral  Ih  Icosahedral  The Cn point groups:  •  The Cn point groups all have only a single rota%onal axis (C5 in the  complex [IF6O]‐ below).   •  They are further divided into Cn, Cnv, and Cnh point groups.   •  The Cn point groups have no other symmetry elements.  •  The Cnv point groups have also n mirror planes containing the Cn  rota%onal axis.   •  The Cnh point groups also have a σh mirror plane at right angles to  the principal rota%onal axis.  O  C5 iodine F  [IF6O]‐  F  The Cn point groups:  •    Cn axis as their only symmetry element.   •  They generally resemble propellers which have the front and back diﬀerent.   C3 triphenyl phosphine viewed down C3 axis C3 C3 triphenyl phosphine viewed from the side C3 C3 Cobalt(III) tris-glycinate viewed down C3 axis C3 Cobalt(III) tris-glycinate viewed from the side Characteris%c symmetry elements of some important classes   Point  Characteris1c symmetry elements  Group  Comments  C1  E, C1  Cs  E, one σ plane  Ci   E, inversion centre  Cn  E, one principal n‐fold axis  S n  Only Sn (n even, n≠2)  Cnv  E, one principal n‐fold axis, n σv planes  Cnh  E, one principal n‐fold axis, one σh plane  The Sn axis necessarily follows from the Cn  and one Sn‐fold axis, coincident with the Cn  axis and σh plane. For n=2, 4 or 6 there is  axis.  also a centre of inversion  Dnh  E, one principal n‐fold axis, n C2 axes, one  σh plane, n σv planes  and one Sn‐fold axis.  The Sn axis necessarily follows from the Cn  axis and σh plane. For n=2, 4 or 6 there is  also a centre of inversion  Dnd  E, one principal n‐fold axis, n C2 axes, n σv  planes  and one S2n‐fold axis.  For n=3 or 5 there is also a centre of  inversion  Td  tetrahedral  Oh  octahedral  Ih  Icosahedral  Some C2v molecules:  C2 σv P C2 S  σv Phosphorus iodotetrafluoride (PF4I) σv C  σv sulfur tetrafluoride (SF4) C2 σv σv carbonyl chloride (COCl2) ...
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