Group Theory in Chemistry - questions and answers

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Transcript of Group Theory in Chemistry - questions and answers

  • GROUP THEORY Q + A Dr. Christoph Sontag Phayao University

    1

  • SYMMETRY ELEMENTS

    Please write down all symmetry elements of :

    Ammonia

    c-axis:

    :

    Acetone

    c-axis:

    :

    Dimethyl-cyclopentane

    c-axis:

    :

    Ethanediol

    c-axis:

    :

    i :

    Propadiene

    c-axis:

    : S-axis:

    2

    N

    HH

    H

    O

    C

    CH3 CH3

    C

    OH

    C

    OH

    H

    H

    H

    H

  • POINT GROUPS

    Use the flowchart to find the point groups of the 5

    molecules before:

    Ammonia:

    Acetone:

    Dimethyl-cyclopentane:

    Ethanediol:

    Propadiene:

    3

    Dnd

  • ANSWERS

    Ammonia: C3 (and 2C3), 3 v => C3v

    Acetone: C2, v , v => C2v

    Dimethyl-cyclopentane: => Cs

    Ethanediol: C2, i, h => C2h

    Propadiene: C2, C2 , C2, v , v, S4, 3S4 => D2d

    4

  • SYMMETRY ELEMENTS

    Can you draw the S-axis into the propadiene molecule

    (remember: S contains C-axis and plane !)

    Please mark the inversion center in ethanediol:

    Mark the S3 axis in

    Trihydroxybenzene:

    5

  • ANSWERS

    S-axis in propadiene:

    Inversion center of ethanediol:

    S3 axis in Trihydroxybenzene:

    6

  • CHARACTER TABLES

    The water molecule has C2v symmetry:

    Which characters does the px orbital of Oxygen have and

    what is the name of the representation ?

    7

  • ANSWER

    8

    => The px orbital has B1 representation

  • SYMMETRY OF AN MO OF WATER

    The water molecule has C2v symmetry:

    One molecular orbital consists

    of the px orbital of Oxygen

    overlapping with the 2 s-orbitals

    of the Hydrogens:

    Determine the characters of this MO in the point group

    C2v:

    This representation consists of which irreducible

    representation from the character table ?

    9

  • ANSWERS

    The MO of the water molecule has the following

    symmetry behaviour for the C2v operations:

    This representation equals the B1 symmetry from the

    character table.

    10

  • BH3 MOLECULE

    BH3 is a planar molecule. Can you draw the structure

    and all symmetry elements ?

    What is the point group of the molecule ?

    What are the characters of the pz orbital of Boron and

    what is the representation of it ?

    11

  • ANSWERS

    The symmetry elements of BH3 are:

    C3, 3x C2, 2x S3, 2x v => belongs to D3h

    The pz orbital transforms as follows:

    12

    Notice that the pz orbital has

    the same representation as

    the z-axis.

    Therefore we can find the

    representation directly in the character table under z.

  • MO DIAGRAM OF BH3

    To construct the MOs of the molecule, we can combine

    the atomic orbitals of Boron with combination group

    orbitals of 3x H:

    What is the characters of these 3 group orbitals ?

    and have to be taken together which

    leads to the representation e

    Therefore they match the symmetry of which AO of

    Boron ?

    13

  • ANSWERS

    The combination of H-orbitals with no node has the

    symmetry a1

    and the 2 other combinations with one node e

    Therefore the first group orbital can overlap with the s-

    orbital of Boron (both have a1 symmetry):

    and the e orbitals with px and py of Boron:

    The pz orbital of Boron has no partner and stays non-

    bonding

    14

  • COMPLETE MO DIAGRAM BH3

    15

    From the diagram we can conclude that the molecule is a

    LEWIS-ACID because the LUMO is low in energy (its non-

    bonding) and if we fill electrons into it will not affect the B-H bonds.

  • ORBITALS OF CYCLOPROPENYL

    The Cyclopropenyl cation is an aromatic ring system

    with 3 p orbitals:

    Determine the representation of these 3 p orbitals in the

    D3h point group:

    This representation is the sum of which irreducible representations of the character table ?

    16

  • ANSWERS

    The 3 p-orbitals transform under the symmetry

    operations of D3h as follows:

    This representation is the sum of which representations

    of the character table ?

    We use the reduction formula to check for example if A2

    is in the representation :

    With the same method

    we find that also e is

    in .

    17

  • MOLECULAR ORBITALS

    Butadiene has the point group C2h:

    Which representation does the HOMO of the molecule

    have ?

    Draw the C2 axis, inversion center and mirror plane and

    check if the MO not the 4 single AOs ! behave.

    18

  • ANSWER

    The HOMO has the representation = 1 -1 -1 1

    and is therefore Bu.

    For example: C2 rotation would reverse the phases of all

    orbitals => -1 character

    19

  • REDUCING REPRESENTATIONS

    When we have a representation of = 4 1 -2

    for a molecule with C3v symmetry, how many times is

    the representation A2 in ?

    20

  • ANSWER

    21

    The representation A2 is 2 times inside

  • HYBRIDIZATION

    Trichlorborane is in the point group D3h.

    What are the characters of the 3 -bonds ?

    E 2C3 3C2 h 2S3 3v

    : 3

    is the sum of which basic representation ?

    22

    Inorganic graphics/Ic3/B/molecules/bf3c.mol

  • ANSWER

    The 3 bonds have the characters:

    E 2C3 3C2 h 2S3 3v

    3 0 1 3 0 1

    Each of the 3 C2 rotations keep one bond at the same

    position, but exchanges the 2 other bonds => 1

    The same is true for the 3 v mirror planes which are each

    on one bond.

    The horizontal mirror plane leaves all 3 bonds in their

    position => 3

    is the sum of the representations A1 and E.

    A1 represents also the s-orbital, and E represents the px

    and py orbital on the central atom.

    From this we can conclude that the 3 B-Cl -bonds are

    formed by the combination of s + px + py = sp2 hybrid.

    23