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Unformatted text preview: xis and 3 σv planes C3 axis only Point Groups Point group : a mathema0cal group consis0ng of a set of symmetry opera0ons that leave a point ﬁxed The complete set of symmetry opera0ons for a point group relates all equivalent points in the space of that point group, with each opera0on giving one unique indis0nguishable reorienta0on of that space. In a molecule, equivalent atoms can be interconverted by one or more symmetry opera0ons in a group; inequivalent atoms can not be interconverted by any symmetry opera0on in a group. Symmetry analysis and point group classiﬁca0on provide a precise descrip0on of molecular stereochemistry and resul0ng symmetry
dependent proper0es. M&T3 pps 82
92; M&T4 pps 91
95 h@p://symmetry.o@erbein.edu/ Assigning Point Groups Molecular symmetry is deﬁned by the set of symmetry elements that it contains. This set of symmetry elements is called the molecule’s point group. Assigning Point Groups Some Common Point Groups and their Characteris.c Symmetry Elements C1 E Ci i Cs σ Cn Cn Sn * Sn Cnv C n , σv Cnh C n , σh Dnd Cn, nC2+ , σd Dnh Cn, nC2 + , σd, σh C∞v linear without i D∞h linear with i Td tetrahedral Oh octahedral Ih icosahedral Kh spherical Assigning Point Groups Molecular symmetry is deﬁned by the set of symmetry elements that it contains. This set of symmetry elements is called the molecule’s point group. Rules for Assigning Point Groups: 1. Determine whether the molecule belongs to one of the special cases of high symmetry (Td, Oh, C∞v, D∞h, Ih ). 2. If the molecule is not a special case, ﬁnd the rota0on axis with the highest n (e.g., the highest order Cn axis for the molecule). 3. If there is no rota0on axis, it belongs to one of the low symmetry point groups (C1, Cs, or Ci). Assigning Point Groups: Working Through the Flow Chart Group of High Symmetry? YES
NO
Td, Oh, C∞v, D∞h, Ih Groups of Low
Symmetry Highest Order Rota0on Axis Cn (n>1)
Flow Chart con+nues in the next slides C1, Cs, or Ci High Symmetry Point Groups Group Descrip.on Td These molecules have tetrahedral geometry and shape and all terminal atoms are the same (e.g. CCl4) Oh These molecules have octahedral geometry and shape and all terminal atoms are the same (e.g. SF6) C∞v Linear with an ∞ number of rota0ons and an ∞ number of reﬂec0on planes containing the rota0on axis. No center of inversion. (e.g. H
Cl) D∞h Linear with an ∞ number of rota0ons and an ∞ number of reﬂec0on planes containing the rota0on axis. They also have perpendicular C2 axes and a perpendicular reﬂec0on plane. (e.g. Cl
Cl) Ih Icosahedra and dodecahedra (very rare and you won’t see...
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This note was uploaded on 03/28/2014 for the course CHM 2311 taught by Professor Richardson during the Winter '09 term at University of Ottawa.
 Winter '09
 richardson
 Mole

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