W2013CHM2311 Part 3a Notes

Staggered conforma0on of ethane c2h6 h3 h2 h4 h6 c h5

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Unformatted text preview: d σv : mirror planes that include the principal axis of rota+on. can some0mes be difficult as the defini0ons given are not (The subscript “v” is for “ver0cal”) σd : similar to σv however, this represents a special class of mirror always adhered to. plane that bisects two Cn axes. Don’t be too concerned with (The subscript “d” is for “dihedral”) dis0nguishing the two Example: Water has two σv mirror planes. σ H O H One mirror plane contains molecule. H C2 σ σv O H O A second mirror plane bisects molecule. Example: What kind of planes for benzene? H σv H Inversion Opera0on: 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. Staggered conforma0on of ethane (C2H6): H3 H2 H4 H6 C H5 i C H5 H1 H4 H1 C C H2 H6 H3 Methane (CH4): NO inversion center! H2 H1 i C H4 H3 H3 H4 H1 C H2 Improper Rota0on: Sn An improper rota0on consists of a rota0on of 360/n degrees followed by reflec0on through a plane perpendicular to the axis of the rota0on. Also referred to as a rota0on ­ reflec0on opera0on. Example: S4 in methane 1.  Rotate by 90° (=360°/4) 2.  Reflect through the mirror plane perpendicular to the rota0on axis H H C H H C4 H H Looking down C2 axis coincident with the S4 axis. C H H H σh H C H Initial and final stages are equivalent, even though intermediate stage differs. Cn NOTE: neither the C4 nor the σh are symmetry opera0ons for and σh sufficient but n methane but combined as an improper rota0on opera0on it is. ot necessary. H Improper Rota0on: Sn Another view of the S4 in methane: S4 H2 H1 C4 C H4 H3 H4 H1 H2 H4 σh C H3 H3 C H1 H2 Improper Rota0on: Sn A second S4 opera0on can be performed: S4 H4 H3 C4 C H1 H2 H1 H3 H4 H1 σh C H2 C H3 H2 H4 In General: Two successive Sn opera0ons generate the same result as a Cn/2 opera0on (S2n = Cn/2) S1 is the same as reflec0on (σ): In this case, call it σ rather than S1 S2 is the same as inversion (i): In this case, call it i rather than S2 When a symmetry opera0on yields the same result as a simpler opera0on (e.g., Snm = i or Cnm or σh), it is wri@en as the simpler opera0on. Summary of Symmetry Elements and Opera0ons Symmetry Element Symbol Symmetry Opera.on Iden0ty E Leave the molecule alone Proper Axis Cn Rotate the molecule by 360/n degrees around the axis Horizontal Plane σh Reflect the molecule through the plane which is perpendicular to the principal axis Ver0cal Plane σv Reflect the molecule through a plane which contains the principal axis Dihedral Plane σd Reflect the molecule through a p...
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