1. 1 8-2.5 Molecular Orbital Theory Molecular orbital theory describes covalent bonds in terms of molecular orbitals, which result from interaction of the atomic orbitals of the bonding atoms and are associated with the entire molecule.

2. 2 Ⅰ. The key ideas of MO Theory 1. Every electron of molecules may spread over the entire molecule. Just as atoms have atomic orbitals (AOs) of a given energy and shape that are occupied by the atom's electrons, molecules have molecular orbitals (MOs) of a given energy and shape that are occupied by the molecule's electrons. Note that molecular orbitals are labeled by the Greek letter σ, π, δ, etc., corresponding to the Roman letters s, p, d, etc. for atomic orbitals.

3. 3 2. Formation of molecular orbitals In order to obtain wave function for the molecular orbitals, we assume that these are linear combinations of atomic orbitals. The number of molecular orbitals that are formed must equal the number of atomic orbitals used to make them. The molecular orbitals are formed by the addition and subtraction of the two atomic wave functions.

4. 4 (1) Adding the wave functions together. This combination forms a bonding MO, which has a region of high electron density between the nuclei. (2) Subtracting the wave functions from each other. This combination forms an antibonding MO, which has a node between the nuclei, a region of lower electron density The bonding MO is lower in energy and the antibonding MO higher in energy than the AOs that combined to form them. The bonding MO is denoted by σ (π), and antibonding MO is denoted with a superscript star, σ* (π*).

5. 5 Bonding and Antibonding Molecular Orbitals A bonding molecular orbital is of lower energy and greater stability than the atomic orbitals from which it was formed. An antibonding molecular orbital is of higher energy and lower stability than the atomic orbitals from which it was formed. Bonding molecular orbital atomic orbital Antibonding molecular orbital

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16. 16 3. To interact effectively and form MOs, three principles are accepted (1) atomic orbitals bear the same symmetry with respect to the molecular axis. (2) appropriate wave functions for two atoms can be combined only if they represent similar energy states. (3) extensive overlap of appropriate atomic orbitals can occur.

17. 17 (1) Orbitals are filled in order of increasing energy (aufbau principle) (2) An orbital has a maximum capacity of two electrons with opposite spins (exclusion principle) (3) Orbitals of equal energy are half filled, with spins parallel, before any is filled (Hund's rule) 4. Filling Molecular Orbitals with Electrons Electrons fill MOs just as they fill AOs

18. 18 Stability of molecule and Rules of Molecular Electron Configuration In a stable molecule, the number of electrons in bonding molecular orbitals is always greater than that in antibonding molecular orbitals. The number of electrons in the molecular orbitals is equal to the sum of all the electrons on the bonding atoms.

19. 19 Like an atomic orbital, each molecular orbital can accommodate up to two electrons, with opposite spins in accordance with the Pauli exclusion principle. When electrons are added to molecular orbitals having the same energy, the most stable arrangement is that predicted by Hund's rule, that is, electrons enter these molecular orbitals with parallel spins.

20. 20 The bond order is the number of electrons in bonding MOs minus the number in antibonding MOs, divided by two: Bond order =1/2 [(no. of e - in bonding MO) － (no. of e - in antibonding MO)] 5. Bond Order A bond order greater than zero indicates that the molecular species is stable relative to the separate atoms, whereas a bond order of zero implies no net stability, and, thus, no likelihood of forming. In general, the higher the bond order, the stronger the bond.

21. 21 Homonuclear Diatomic Molecules There are two different energy orderings for diatomic molecules formed from second-period elements Ⅱ. MO energy order

22. 22 B 2, N 2 : (Z≤7) O 2, F 2 : (Z≥8) The distinction between the two is with the π 2p and σ 2p orbitals, which are quite close in energy and reverse their order once oxygen is reached.

23. 23 Energy levels diagram of MO orbits for N 2,O 2 and F 2.

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25. 25 H 2 : (σ 1s ) 2 the electron configuration

26. 26 He 2 :(σ 1s ) 2 (σ 1s * ) 2

27. 27 Li 2 : (σ 1s ) 2 (σ * 1s ) 2 (σ 2s ) 2

28. 28 Be 2 : (σ 1s ) 2 ( σ * 1s ) 2 ( σ 2s ) 2 ( σ * 2s ) 2

29. 29 B 2 :(σ 1s ) 2 (σ* 1s ) 2 ( σ 2s ) 2 ( σ * 2s ) 2 ( π 2py ) 1 ( π 2pz ) 1

30. 30 N 2 :KK(σ 2s ) 2 (σ * 2s ) 2 (π 2py ) 2 (π 2pz ) 2 (σ 2px ) 2

31. 31 KK(σ 2s ) 2 (σ* 2s ) 2 ( σ 2px ) 2 ( π 2py ) 2 ( π 2pz ) 2 ( π * 2py ) 1 (π * 2pz ) 1

32. 32 bond order = 1 2 Number of electrons in bonding MOs Number of electrons in antibonding MOs ( - ) bond order ½10½

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35. 35 Heteronuclear Diatomic Molecules Molecular orbitals can be constructed from their atomic orbitals, just as in the homonuclear case. Z+Z≤14, MO ordering is the same as N 2 Z+Z >14, MO ordering is the same as O 2

36. 36 NO KK(σ 2s ) 2 (σ* 2s ) 2 ( σ 2px ) 2 ( π 2py ) 2 ( π 2pz ) 2 ( π * 2py ) 1

37. 37 (σ 2s ) 2 (σ * 2s ) 2 (π 2py ) 2 (π 2pz ) 2 (σ 2px ) 2

38. 38 -13.6eV -18.6eV - 40.12eV Nonbonding orbitals