Molecular Orbitals - Chemistry _

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					     Molecular orbital (MO) theory for engineers

      Applications of wave cancellation
      •Automobile mufflers
      •Audio (and other) amplifier electrical feedback
      •Noise cancelling headphones

      MO theory for diatomic molecules (2 atoms)

     Band theory - MO theory for covalently bonded solids () atoms
NEXT •Electrical insulators
TIME •Semiconductors
     •Laser diodes (my laser pointer, your CD/DVD players
     •Photovoltaic cells (converting sunlight into electricity
                             - (- sign flips phase of
                             the sound wave function)


Auto mufflers use destructive interference
of sound waves to reduce engine noises.
Amplifier noise is reduced by adding destructively
Interference (reversed phase noises).
Bose is
$200. Want to
do it yourself?
See Web site.
         The Central Themes of MO Theory

• A molecule is viewed on a quantum mechanical level as a
collection of nuclei surrounded by delocalized molecular
orbitals MO’s).

Atomic orbital wave functions are added and subtracted to
obtain molecular orbital (MO) wave functions.

The + combinations result in e-wave constructive interference
and produce bonding MO’s i.e. regions of high electron
density between nuclei).

The – combinations result in e-wave destructive interference
and produce antibonding MO’s which show “node” - regions
of zero electron density between the nuclei).
An analogy between light waves and atomic wave functions.

                                         Figure 11.13
                                   NOTE: +/- signs show
                                   PHASES of waves, NOT

 Amplitudes of wave
  functions added

                                   Amplitudes of wave
                                  functions subtracted.
Figure 11.14   Contours and energies of the bonding and antibonding
                          molecular orbitals (MOs) in H2.

                                           Axially symmetric

                             OUT OF PHASE

        E-density = blue

                              IN PHASE
                                              Axially symmetric
Figure 11.15   The MO diagram for H2

                                 # ANTIBONDING e’s = 0

                                 # BONDING e’s = 2
   Figure 11.16                  MO diagram for He2+ and He2

                        s*1s                                   s*1s

          1s                       1s               1s                   1s

                        s1s                                    s1s
          AO of        MO of     AO of              AO of     MO of     AO of
           He           He+       He+                He        He2       He

                  He2+ bond order = 1/2                  He2 bond order = 0
                                                     He2 does not exist!
                             2 H.


      Lower curve like Fig. 9.11
Antibonding MO -

    1S(A)          1S(B)

   Bonding MO +
   SAMPLE PROBLEM 11.3                 Predicting Species Stability Using MO Diagrams

   PROBLEM:      Use MO diagrams to predict whether H2+ and H2- exist.
                 Determine their bond orders and electron configurations.

   PLAN:     Use H2 as a model and accommodate the number of electrons in
             bonding and antibonding orbitals. Find the bond order.

                          bond order                                         bond order
                          = 1/2(1-0)                                         = 1/2(2-1)
                          = 1/2                                              = 1/2
            s                                                    s
                                H2 does exist                                     H2- does exist

  1s                       1s                            1s                  1s

                         AO of H                      AO of H               AO of H-
AO of H
            s                                                      s          configuration is
                         configuration is (s1s   )1                           (s1s)2(s2s)1
          MO of H2   +                                          MO of H2-
   Figure 11.17

                  s*2s                             s*2s

                              2s              2s               2s

                            Bonding in s-block                  Be2
          Li2     s2s         homonuclear          s2s

                  s*1s                             s*1s

                              1s              1s               1s

                         Li2 bond order = 1               Be2 bond order = 0
                  s1s                              s1s
Figure 11.18
               Contours and energies of s and p MOs through
                    combinations of 2p atomic orbitals
Figure 11.19      Relative MO energy levels for Period 2 homonuclear
                                                    diatomic molecules.
  without 2s-2p                     with 2s-2p
      mixing                          mixing

 MO energy levels                MO energy levels
for O2, F2, and Ne2              for B2, C2, and N2
  Figure 11.20

MO occupancy
and molecular
properties for B2
through Ne2
Figure 11.21

The paramagnetic
 properties of O2
  SAMPLE PROBLEM 11.4         Using MO Theory to Explain Bond Properties

  PROBLEM:      As the following data show, removing an electron from N2 forms
                an ion with a weaker, longer bond than in the parent molecules,
                whereas the ion formed from O2 has a stronger, shorter bond:
                               N2         N2+         O2     O 2+
       Bond energy (kJ/mol)    945        841         498    623
       Bond length (pm)        110        112         121    112

Explain these facts with diagrams that show the sequence and occupancy of MOs.

  PLAN:    Find the number of valence electrons for each species, draw the MO
           diagrams, calculate bond orders, and then compare the results.


        N2 has 10 valence electrons, so N2+ has 9.
        O2 has 12 valence electrons, so O2+ has 11.
SAMPLE PROBLEM 11.4           Using MO Theory to Explain Bond Properties

       N2                     N2+                 O2                  O2 +

                  s2p                                        s2p   antibonding
                                                                        e- lost
bonding e- lost   2p                                        2p

                  s2p                                         s2p

                  2p                                         2p

                  s2s                                        s2s

                  s2s                                         s2s
    1/2(8-2)=3           1/2(7-2)=2.5    bond    1/2(8-4)=2          1/2(8-3)=2.5
Figure 11.24

      The lowest energy -bonding MOs in benzene and ozone.
   Figure 11.22                     The MO diagram for HF


                                    Two non-bonding orbitals
                                    are the lone pairs on F

                                    seen in The Lewis structure
                  1s                 for HF
         Note the H1S
         is less stable
         than the F2P
                          2px 2py             2p

                  AO      MO of              AO
                  of H     HF                of F
   Figure 11.23                   s*                   The MO diagram for NO

                                   *   p

                                    s       p
                                                                possible Lewis
                                       p
                                                                    0     0
                                                                    N    O
                                  s*    s
                                                                    -1    +1
                            2s                                      N    O
                  AO of N                            AO of O
                                    s       s

                                 MO of NO