Question

draw the molecule allene, since this molecule is not planar use wedges and dashes to show the hydrogens on one side of the molecule. use lines and arrows to show all symmetry operations in this molecule. what is its point group?

1 (15 points) Draw the molecule allene. Since this molecule is not planor, be sure to. use wedges and dashes to show the hydrogens on one side of the molecule, Use lines and arrows to show all the symmetry operations in this molecule. Do not use rectangles to show mirror planes unless it's a horizontal mirror plane, but you con always describe using a few words where a symmetry operation is located. What is the point group for allene?

#quantumchemistry

Answer 1

Symmetry Operations in Allene molecule (Non planar)

1. Identity Element (E)

2. One four fold rotation axis [C₄(z)]

3. Three two fold rotation axis [C₂(z), C₂(y), C₂(x)]

4. Two diagonal mirror plane [σ_d(1), σ_d(2)] along the z- axis.

Each diagonal mirror plane bisects the angle between C₂(y) and  C₂(x) axis.

5. The molecule also contain an S₄ (z) axis which is a combined operation of rotation and reflection operations, i.e. S₄=  σ_d.C₄. S₄ axis in the molecule produce four symmetry operations .

s, sa, sasa

Where S₄² = C₂(z) and S₄⁴ = E.

After all this analysis S₄ (Z) will be principle axis of allene.

N x HN

Z S4 =AE ΗΤΗ

z (C2) - Y (C2) X(C) HN

Total symmetry operations are {E, C₂(z), C₂(y), C₂(x), σ_d(1), σ_d(2), S₄¹, and S₄³ } = D_2d (point group)}.

Point group of the allene molecule is D_2d.