Chemistry 2000 Lecture 3 LCAO-MO theory for diatomic molecules by sxl19665

VIEWS: 36 PAGES: 20

									Chemistry 2000 Lecture 3: LCAO-MO theory for
             diatomic molecules
                Marc R. Roussel
MO theory for homonuclear diatomic molecules




  We want to develop MO theory for diatomic molecules.
  Initially, we will focus on homonuclear diatomic molecules, i.e.
  those in which both atoms are of the same element.
            LCAO of higher orbitals

In the last lecture, we combined 1s AOs to obtain sigma
bonding and antibonding molecular orbitals:




           1σ ≡ σ1s                         ∗
                                    1σ ∗ ≡ σ1s
We can combine higher AOs in a similar way.
σ and σ ∗ orbitals obtained from the 2s AOs:




             2σ ≡ σ2s                         ∗
                                      2σ ∗ ≡ σ2s
2p orbitals can be combined in two different ways:
 1. The 2pz orbitals are oriented toward each other so adding
    them gives sigma orbitals:

                                 add
                                 −→

                                           3σ ≡ σ2p



                               subtract
                                − −→
                               −− −

                                                     ∗
                                             3σ ∗ ≡ σ2p
Note: Subtracting the 2pz orbitals is equivalent to adding
      them out of phase:

                               add
                               −→

                                                 ∗
                                         3σ ∗ ≡ σ2p
3. The 2px and 2py orbitals are perpendicular to the bond axis.
   Adding them gives π orbitals:


                               add
                               −→


                                          1π ≡ π2p


                               add
                               −→


                                                 ∗
                                         1π ∗ ≡ π2p
Pi orbitals have a nodal plane through the bond axis.
    Note: There are two degenerate 1π orbitals and two
          degenerate 1π ∗ orbitals because we can combine px
          or py orbitals in this manner:
         AO energies and LCAO theory

Principle: AOs of similar energies and appropriate symmetries
           can mix to form MOs
 2s and 2p atomic orbital energies:
                        0
                                                           2s
                                                           2p
                      -0.5


                       -1


                      -1.5
             εi /RH




                       -2


                      -2.5


                       -3


                      -3.5


                       -4
                             Li   Be   B   C   N   O   F        Ne


 For heavier elements in period 2, there won’t be much mixing
 between the 2s and 2p orbitals, and the MOs should be
 roughly those described above.
          The “normal” MO diagram

              E
                                3σ∗

                                1π∗
                    2pA                     2pB
                                1π

                                3σ

                                2σ∗



                          2sA         2sB

                                2σ




                                1σ∗



                          1sA         1sB

                                1σ




Applies to O2 , F2 and Ne2
                       s-p mixing




The closer the 2s and 2p orbitals are in energy, the more these
mix to form MOs.
This mostly affects the 2σ ∗ and 3σ orbitals:
    Mixing in some p character decreases the energy of the 2σ ∗
    MO.
    Mixing in some s character increases the energy of the 3σ MO.
         If this mixing is strong enough, the 3σ can end up higher in
         energy than the 1π orbitals.
        MO diagram for lighter atoms

                     E
                         3σ∗

                         1π∗

                         3σ
                         1π



                         2σ∗




                         2σ




                         1σ∗




                         1σ




Applies to Li2 –N2
Ground-state electronic configurations of the 2nd period
                homonuclear diatomics




            Bond order
            Correlation with Lewis diagram
            Paramagnetic or diamagnetic?
                    Core orbitals

Intuitively, the core (non-valence) electrons (1s electrons for
period-2 atoms) shouldn’t contribute much to the bonding.
If we look at the 1σ and 1σ ∗ orbitals for 2nd period
diatomics, we see that they look like a pair of 1s AOs, i.e.
there is little overlap.
These core orbitals are very much like the AOs of the free
atoms and do not contribute in any significant way to
bonding.
This justifies our usual focus on the valence electrons.
Alternative view of the electron configuration of (e.g.) Li2 :
(1sA )2 (1sB )2 (2σ)2 .
(Note: When the core electrons are treated this way, the 2σ
orbital is sometimes renumbered (confusingly) 1σ.)
                Heteronuclear diatomics


Key ideas used in constructing LCAO-MOs of heteronuclear
diatomics:
 1. The core electrons are not significantly involved.
 2. Only orbitals of similar energy mix to form an MO.
 3. We can separate AOs into two sets:
    σ-type AOs: s and pz
    π-type AOs: px and py
    Only σ-type AOs are involved in σ bonding.
    Only π-type AOs are involved in π bonding.
 4. Number of MOs constructed = number of AOs mixed
         LCAO-MO treatment of CO


Start by looking at the AO energies (valence electrons only):
                          0

                        -0.5
                               2p
                         -1
                                            2p
               εi /RH   -1.5   2s

                         -2
                                            2s
                        -2.5

                         -3

                        -3.5

                         -4
                                    C   O



Note that the 2sO is much lower in energy than the other
valence orbitals.
This orbital will therefore not mix much with the others. In
essence, the 2σ MO is just the 2sO .
We can mix the 2sC , 2pz,C and 2pz,O orbitals to form three σ
orbitals, specifically the 2σ ∗ , 3σ and 3σ ∗ .
The 2px and 2py orbitals from both atoms will mix to form
the two 1π and two 1π ∗ orbitals.
The ordering of the σ and π orbitals is not immediately
obvious. To determine this, we can use a quantum chemistry
program like HyperChem.
We can however take a reasonable guess based on the fact
that CO is isoelectronic with N2 : In N2 , the 1π orbitals are
below the 3σ. This turns out to be the case for CO as well.
Valence MO diagram for CO:
                  E
                                   3σ∗

                                   1π∗
                         2p C
                                   3σ
                                            2p O
                                   1π
                         2s C


                                   2σ∗




                                 2σ (2sO)



Orbital occupancy: (1σ)2 (1σ ∗ )2 (2σ)2 (2σ ∗ )2 (1π)4 (3σ)2
Bond order: 3 (agrees with Lewis diagram)
         LCAO-MO treatment of HF


Again, look at the valence AO energies:
                          0

                        -0.5

                         -1    1s
                                            2p
                        -1.5
               εi /RH

                         -2

                        -2.5

                         -3                 2s

                        -3.5

                         -4
                                    H   F



The H 1s orbital will mostly mix with the F 2pz to form σ
orbitals.
No π bonding. (Why not?)
Note: When the two atoms are sufficiently dissimilar, it is
      difficult to tell bonding apart from nonbonding MOs.
      We therefore just number the MOs of a given type
      (σ or π) without making any distinction between
      bonding and antibonding character.
Valence MO diagram for HF:
                 E
                                4σ


                       1s H

                              1π (2pF)   2p F

                                3σ



                              2σ (2sF)


                              1σ (1sF)



Orbital occupancy: (1σ)2 (2σ)2 (3σ)2 (1π)4
Lone pairs: 3 (agrees with Lewis diagram)
Bond order: 1 (agrees with Lewis diagram)

								
To top