Chemistry 445. Lecture 4. Molecular Orbital Theory of diatomic molecules

1. Chemistry 445. Lecture 4. Molecular Orbital Theory of diatomic molecules

2. The non-existent He2 molecule(bond order = 0) BO = (2-2)/2 = 0 The MO diagram for the He2 molecule is similar to that for the H2 molecule, but we see that the energy drop of the pair of electrons in the σ1s orbital is negated because the other pair in the σ*1s rises in energy by an equal amount. There is thus no net stabilization, and so the He2 molecule does not exist.

3. The He2+ molecule/ion exists, bond order = ½ unpaired electron so is paramagnetic BO = (2-1)/2 = ½ The logic of the MO diagram suggests that if we remove an electron from the He2 molecule, we would obtain a stable [He2]+ cation, which is true in the gas-phase. This illustrates the power of the MO approach, since the Lewis dot diagram does not predict this.

4. The Li2 molecule. Bond order = 1 BO = (2-0)/2 = 1 Bond energy for Li2 = 110 kJ.mol-1, Compared to 436 kJ.mol-1 for H2. Note. In drawing up an MO diagram, only the valence shells are considered, so for the diatomic molecules from Li2 to F2, the overlaps of the pairs of 1s orbitals are ingnored. This is valid because these are filled, and they make no net contribution to the bonding.

5. The non-existent Be2 molecule,bond order = 0 BO = (2-2)/2 = 0 Here again, MO theory predicts that Be2 does not exist, which Lewis dot diagrams do not predict.

6. σ and π bonding In the molecules we have considered so far, only σ overlaps have been of importance. In the formal definition, a σ–bond is one which lies along a rotational symmetry axis, (the rest of the molecule is ignored). A π–bond does not lie along a rotational axis (symmetry will be discussed later). In practical terms, a σ–bond lies along the bond connecting the two atoms, whereas a π–bond does not. z z + π*(pz) pz orbitals anti-bonding π* MO z z π(pz) + bonding π MO

7. O2 molecule, bond order = 2 molecules with unpaired electrons are paramagnetic The ability to predict the number of unpaired electrons in molecules is where MO excels, and Lewis-dot fails. BO = (6-2)/2 = 2 (disregardiing overlap of 2s orbitals) O O2 O

8. F2 molecule, bond order = 1 F2 has no unpaired electrons, and so is diamagnetic BO = (6-4)/2 = 1

9. Variation of the energies of the 2s and 2p orbitals in crossing the periodic table from Li to F. (H&S Fig. 1.22)

10. Energy levels of first-row homonuclear diatomic molecules (H&S Fig 1.23) crossover point Molecules Li2, Be2, B2,C2 and N2 have π(2p) lower in energy than σ(2p) Molecules O2, and F2 have π(2p) higher in energy than σ(2p)

11. Be2 molecule, bond order = 0(BO = 0, means does not exist) BO = (2-2)/2 = 0

12. B2 molecule, bond order = 1 BO = (2-0)/2 = 1

13. N2 molecule, bond order = 3 diamagnetic BO = (6-0)/2 = 3 N N2 N

14. C2 molecule, bond order = 2 diamagnetic BO = (4-0)/2 = 2

15. Orbital parity – gerade (g) and ungerade (u) Symmetry of orbitals and molecules is of great importance, and we should be able to determine whether orbitals are gerade (g) or ungerade (u) (from German for even or odd). This is because in the spectra of inorganic compounds whether absorption of a photon to produce an electronic transition is determined by whether the two orbitals involved are g or u. According to the Laporte selection rules, transitions from gu and ug are allowed, but gg and uu are forbidden. An orbital is g if it has a center of inversion, and u if it does not. So looking at atomic orbitals, we see that s and d are g, while p orbitals are u: (see next page for definition of center of sym.) s-orbital p-orbital d-orbital gerade (g) ungerade (u) gerade (g)

16. Orbital parity – gerade (g) and ungerade (u) Symmetry of orbitals and molecules is of great importance, and we should be able to determine whether orbitals are gerade (g) or ungerade (u) (from German for even or odd). This is because in the spectra of inorganic compounds whether absorption of a photon to produce an electronic transition is determined by whether the two orbitals involved are g or u. According to the Laporte selection rules, transitions from gu and ug are allowed, but gg and uu are forbidden. An orbital is g if it has a center of inversion, and u if it does not. So looking at atomic orbitals, we see that s and d are g, while p orbitals are u: (see next page for definition of center of sym.) not a center of inversion a ≠ b a a center of inversion a = b a b b b s-orbital p-orbital d-orbital gerade (g) ungerade (u) gerade (g)

17. Parity (g or u) of molecular orbitals: a a not a center of inversion a≠b (sign of wave- function is opposite) center of Inversion a = b b b σ*(1s)u π*(2p)g a a not a center of inversion a ≠ b b b center of inversion a = b σ(1s)g π(2p)u The test for whether an MO is g or u is to find the possible center of inversion of the MO. If two lines drawn out at 180o to each other from the center, and of equal distances, strike identical points (a and b), then the orbital is g.

18. Energy levels of the N2 molecule see if you can decide which are g or are u, and bonding or anti-bonding

19. Energy levels of the N2 molecule(calculated using semi-empirical MO theory) σ*2pu π*2pg σ2pg σ*2su π*2pu σ2sg

20. To summarize: • A bonding molecular orbital has overlap of the two atomic orbitals, and has no nodal plane. An anti-bonding orbital has a nodal plane between the two atoms forming the bond. • g orbitals have even parity, and have a center of inversion. u orbitals have odd parity and have no center of inversion • In drawing up an MO diagram, you should fully label all atomic orbitals and MO’s (indicate atomic orbital MO is derived from ( 1s, 2p, etc.), g or u, σorπ, bonding or non-bonding (*) ), indicate number of unpaired electrons, diamagnetic or paramagnetic, and bond order.