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Unformatted text preview: y element. 2. rota.on opera.on (also called proper rota.on) (Cn): object is rotated through 360/n degrees about an axis of rota0on. 3. reﬂec.on opera.on (σ): object is reﬂected through a mirror plane. 4. inversion opera.on (i): Each point moves through the center of the object to a posi0on opposite the original posi0on and as far from the central point as where it started. 5. rota.on
reﬂec.on opera.on (also called improper rota.on) (Sn): rota0on of 360/n degrees followed by reﬂec0on through a plane perpendicular to the axis of the rota0on. M&T 3 pps 76
82, 4 pps 80
84 [email protected]:[email protected]/ Symmetry Elements and Opera0ons All molecules (and shapes) can be described in terms of their symmetry. Molecules may contain various symmetry elements (axes, planes, points). RotaLon, reﬂecLon and inversion are symmetry operaLons – moLons such that return the atoms (and the molecule as a whole) to symmetry equivalent posiLons. Element Operation Identity Leave it alone! E Proper Axis Rotation by 360°/n Cn Plane Reflection in the plane σ Inversion Center Inversion of x, y, z,
to –x, – y, – z i Improper Axis 1. Rotation by 360°/n
2. Reflection in plane
perpendicular to axis M&T 3 pps 76
82, 4 pps 80
84 Symbol Sn [email protected]:[email protected]/ Symmetry Elements in a Cube Rota0on Opera0on: Cn Object is rotated through 360/n degrees about an axis of rota0on Objects can have more than one rota.on axis! Rota.on Angle Symmetry Opera.on 90o C4 180o C2 (= C42) 270o C2 = C 4 2 C4 C43 360o C22 = C44 = E C43 C2 C2 If an object has more than one rota0on axis, the Cn axis with the largest value of n is called the highest order rota.on axis or the principal axis. C2 C2 Perpendicular axes Rota0on Opera0on: Cn Some examples of molecular objects with rota0on axes: Cl
H O H What is the principal axis? Cl B Cl Reﬂec0on Opera0on: σ
With a reﬂec0on opera0on, the object is reﬂected through a mirror plane. There are three types of reﬂec0on opera0ons: σh : mirror planes are perpendicular to the principal axis of rota+on. (The subscript h is for horizontal ) σv : mirror planes that include the principal axis of rota+on. (The subscript “v” is for “ver0cal”) σd : similar to σv however, this represents a special class of mirror plane that bisects two Cn axes. (The subscript “d” is for “dihedral”) Reﬂec0on Opera0on: σ With a reﬂec0on opera0on, the object is reﬂected through a mirror plane. There are three types of reﬂec0on opera0ons: σh : mirror planes are perpendicular to the principal axis of rota+on. (The subscript h is for horizontal ) Dis0nc0on between σv and ...
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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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