Molecular Orbital Theory

Molecular Orbital Theory, Molecular Orbital diagram, Molecular Orbital Theory Assumption, Molecular Orbital Theory for homonuclear diatomic molecules H2,Li2,Be2,B2,C2, N2, O2, F2,Ne2, MOT, Electron density, Bond Order, Diamagnetic, Paramagnetic, Hydrogen molecule, Hydrogen ion, Helium molecule, Lithium molecule, Beryllium molecule, Boron molecule, Carbon molecule, Nitrogen molecule, Oxygen molecule, Oxygen ion, O2- ion Superoxide ion, O2- - ion peroxide ion, Fluorine molecule, Neon molecule,

1. Molecular orbital theory (MOT) Assumption A molecule is made up of atoms. When molecule is formed the atom loose their individual cha r acter . A molecular orbital is associated with a molecule as a whole. Electrons in a molecule are delocalised The quantities molecular orbital of different energies levels surround all the nuclei a t the bonded atom. A molecular orbital is assume to form the individual atomic orbital when the atom is bonded to come together. The wave function of molecular orbital is obtain by linear combination of wave function of atomic orbital. Chapter II

2. Electron density : Bonding and anti-bonding molecular orbitals show different patterns of electron distribution. In general, it may be stated that (a) Bonding orbitals are responsible for an increase in electron density between the nuclei. (b) Anti-bonding orbitals reduce electron density between the nuclei and have nodes. (c) The inner shells are so highly attracted by the nucleus that they suffer contraction and become almost spherical in shape instead of oval. Their overlap is very insignificant and they are, therefore, ignored in drawing up the electron configuration of the molecules.

3. Bond Order : In a molecule, bonding electrons help in the formation of bonds whereas anti-bonding electrons oppose it. The number of covalent bonds in a molecule, i.e., bond order is given by one half of the difference between the number of electrons in bonding orbitals and those in antibonding orbitals. Bond order = ½ (Number of electron in BMO - Number of electron in ABMO ) Since electrons in bonding orbitals add to the stability of the molecule: Suppose number of electrons in bonding orbitals is N b and those in anti-bonding orbitals is N a then (i) If N b > N a the molecule is more stable. (ii) If N b ≤ N a the molecule is unstable or Bond order = 0. As the bond order is related to the number of covalent bonds formed between two atoms in a diatomic molecule, it gives the idea about the bond length and bond energy. It is evident that higher the bond order, greater will be the bond energy and lesser will be the bond length.

4. For a molecule, there are two possibilities: Diamagnetic : All electrons are paired. Paramagnetic : Unpaired electrons are present.

5. M.O. energy level diagram for homonuclear diatomic molecule. 1. Hydrogen molecule (H 2 ) Electronic Configuration of H (1): 1s 1 Electronic Configuration of H 2 (2): σ 1s 2 Energy A.O. of H A.O. of H M.O. of H 2 σ* 1s σ 1s

6. Bond order in H 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (2-0) = ½ x 2 = 1 Bond order in H 2 = 1……………… i.e.( H-H ) Thus, the bond order in H 2 molecule is 1. It suggest that there is a single bond present between the two H-atoms in H 2 molecule. It is a of σ type. H 2 molecule is diamagnetic because all the electrons are paired .

7. 1a. Hydrogen ion (H 2 + ion) Electronic Configuration of H 2 (2): σ 1s 2 Electronic Configuration of H 2 + (1): σ 1s 1 Energy A.O. of H A.O. of H M.O. of H 2 σ* 1s σ 1s Electronic Configuration of H (1): 1s 1 Bond order in H 2 + ion

8. Bond order in H 2 + ion = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (1-0) = ½ x 1 = ½

9. M.O. energy level diagram for homonuclear diatomic molecule. 2. Helium molecule (He 2 ) Electronic Configuration of He (2): 1s 2 Electronic Configuration of He 2 (4): σ 1s 2 , σ *1s 2 Energy A.O. of He A.O. of He M.O. of He 2 σ* 1s σ 1s

10. Bond order in He 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (2-2) = ½ x 0 = Bond order in He 2 = 0……………… i.e.( Molecule is unstable ) Thus, the bond order in He 2 molecule is 0. It suggest He 2 molecule is not stable . Hence He 2 molecule does not exist . Helium being inert gas element exist in atomic form only.

11. M.O. energy level diagram for homonuclear diatomic molecule. 3. Lithium molecule (Li 2 ) Electronic Configuration of Li (3): 1s 2 , 2s 1 Electronic Configuration of Li 2 (6): σ 1s 2 , σ *1s 2 , σ 2s 2

12. Energy A.O. of Li A.O. of Li M.O. of Li 2 σ 1s σ * 1s σ 2s σ * 2s 1s 1s 2s 2s

13. Bond order in Li 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (4-2) = ½ x 2 = 1 Bond order in Li 2 = 1……………… i.e.( Li-Li ) Thus, the bond order in Li 2 molecule is 1 . It suggest that there is a single bond present between the two Li-atoms in Li 2 molecule. It is a of σ type. The Li 2 molecule is diamagnetic due to the presence of paired electrons .

14. M.O. energy level diagram for homonuclear diatomic molecule. 4. Beryllium molecule (Be 2 ) Electronic Configuration of Be (4): 1s 2 , 2s 2 Electronic Configuration of Be 2 (8): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2

15. Energy A.O. of Be A.O. of Be M.O. of Be 2 σ 1s σ * 1s σ 2s σ * 2s 1s 1s 2s 2s

16. Bond order in Be 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (4-4) = ½ x 0 = Bond order in Be 2 = 0……………… i.e.( Molecule is unstable ) Thus, the bond order in Be 2 molecule is 0. It suggest Be 2 molecule is not stable . Hence Be 2 molecule does not exist . Beryllium being inert gas element exist in atomic form only.

17. M.O. energy level diagram for homonuclear diatomic molecule. 5. Boron molecule (B 2 ) Electronic Configuration of B (5): 1s 2 ,2s 2 ,2px 1 Electronic Configuration of B 2 (10): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2

18. Energy A.O. of B A.O. of B M.O. of B 2 σ 2s σ * 2s 2s 2s 2px 2py 2pz 2px 2py 2pz σ *2px π* 2py π* 2py σ 2px π 2py π 2py (KK) 4

19. Bond order in B 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (4-2) = ½ x 2 = 1 Bond order in B 2 = 1……………… i.e.( B-B ) Thus, the bond order in B 2 molecule is 1 . It suggest that there is a single bond present between the two B-atoms in B 2 molecule. It is a of σ type. The B 2 molecule is diamagnetic due to the presence of paired electrons .

20. M.O. energy level diagram for homonuclear diatomic molecule. 6. Carbon molecule (C 2 ) Electronic Configuration of C (6): 1s 2 ,2s 2 ,2px 1 ,2py 1 Electronic Configuration of C 2 (12): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 1 , π 2pz 1 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 1 , π 2pz 1

21. Energy A.O. of C A.O. of C M.O. of C 2 σ 2s σ * 2s 2s 2s 2px 2py 2pz 2px 2py 2pz σ *2px π* 2py π* 2py σ 2px π 2py π 2py (KK) 4

22. Bond order in C 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (6-2) = ½ x 4 = 2 Bond order in C 2 = 2……………… i.e.( C=C ) Thus, the bond order in C 2 molecule is 2 . It suggest that there are two bonds present between the two C-atoms in C 2 molecule. Out of two bonds one is σ bond & another is bond. The C 2 molecule is paramagnetic due to the presence of two unpaired electrons . σ π π

23. M.O. energy level diagram for homonuclear diatomic molecule. 7. Nitrogen molecule (N 2 ) Electronic Configuration of N (7): 1s 2 ,2s 2 ,2px 1 ,2py 1 ,2pz 1 Electronic Configuration of N 2 (14): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 Actual Electronic Configuration of N 2 (14): KK 4 , σ 2s 2 , σ *2s 2 , π 2py 2 , π 2pz 2 , σ 2px 2 In N 2 molecule σ 2px has higher energy than that of π 2py, π 2pz

24. Energy A.O. of N A.O. of N M.O. of N 2 σ 2s σ * 2s 2s 2s 2px 2py 2pz 2px 2py 2pz σ *2px π* 2py π* 2py σ 2px π 2py π 2py (KK) 4

25. Bond order in N 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-2) = ½ x 6 = 3 Thus, the bond order in N 2 molecule is 3 . It suggest that there are three bonds present between the two N-atoms in N 2 molecule. Out of three bonds, one is σ bond & there are two bond. The N 2 molecule is diamagnetic due to the presence of paired electrons . Bond order in N 2 = 3……………… i.e.( N= N ) σ π π π

26. M.O. energy level diagram for homonuclear diatomic molecule. 8. Oxygen molecule (O 2 ) Electronic Configuration of O (8): 1s 2 ,2s 2 ,2px 2 ,2py 1 ,2pz 1 Electronic Configuration of O 2 (16): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 , π *2pz 1 , Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 , π *2pz 1 ,

27. Energy A.O. of O A.O. of O M.O. of O 2 σ 2s σ * 2s 2s 2s 2px 2py 2pz 2px 2py 2pz σ *2px π* 2py π* 2py σ 2px π 2py π 2py (KK) 4

28. Bond order in O 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-4) = ½ x 4 = 2 Bond order in O 2 = 2……………… i.e.( O O ) Thus, the bond order in O 2 molecule is 2 . It suggest that there are two bonds present between the two O-atoms in O 2 molecule. Out of two bonds one is σ bond & there are 3-e - bond. The O 2 molecule is paramagnetic due to the presence of two unpaired electrons . … … ½ ½

29. 8a. Oxygen molecule (O 2 + ion) Electronic Configuration of O (8): 1s 2 ,2s 2 ,2px 2 ,2py 1 ,2pz 1 Electronic Configuration of O 2 (16): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 , π *2pz 1 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 , π *2pz 1 Electronic Configuration of O 2 + (15): KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 Bond order in O 2 + ion

30. Bond order in O 2 + ion = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-3) = ½ x 5 = 2.5 Bond order in O 2 + = 2.5………… i.e.( O= O ) Thus, the bond order in O 2 + ion is 2.5 . In O 2 + ion there is one σ bond, one bond & one three electron bond. … π ½ σ π

31. 8b. Oxygen molecule (O 2 - ion Superoxide ion ) Electronic Configuration of O (8): 1s 2 ,2s 2 ,2px 2 ,2py 1 ,2pz 1 Electronic Configuration of O 2 (16): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 , π *2pz 1 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 1 Electronic Configuration of O 2 - (17): KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 1 Bond order in O 2 - ion

32. Bond order in O 2 - ion = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-5) = ½ x 3 = 1.5 Bond order in O 2 - = 1.5………… i.e.( O - O ) Thus, the bond order in O 2 - ion is 1.5 . In O 2 - ion there is one σ bond & one three electron bond. … σ

33. 8c. Oxygen molecule (O 2 - - ion peroxide ion ) Electronic Configuration of O (8): 1s 2 ,2s 2 ,2px 2 ,2py 1 ,2pz 1 Electronic Configuration of O 2 (16): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 1 , π *2pz 1 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 2 Electronic Configuration of O 2 - - (18): KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 2 Bond order in O 2 - - ion Peroxide ion

34. Bond order in O 2 - ion = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-6) = ½ x 2 = 1 Bond order in O 2 - - = 1………… i.e.( O - O ) Thus, the bond order in O 2 - - ion is 1 . In O 2 - - ion there is one σ bond. σ Bond Order O 2 + > O 2 > O 2 - > O 2 - - 2.5 2 1.5 1

35. M.O. energy level diagram for homonuclear diatomic molecule. 9. Fluorine molecule (F 2 ) Electronic Configuration of F (9): 1s 2 ,2s 2 ,2px 2 ,2py 2 ,2pz 1 Electronic Configuration of F 2 (18): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 2 , Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 2 ,

36. Energy A.O. of F A.O. of F M.O. of F 2 σ 2s σ * 2s 2s 2s 2px 2py 2pz 2px 2py 2pz σ *2px π* 2py π* 2py σ 2px π 2py π 2py (KK) 4

37. Bond order in F 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-6) = ½ x 2 = 1 Bond order in F 2 = 1……………… i.e.( F-F ) Thus, the bond order in F 2 molecule is 1 . It suggest that there is a single bond present between the two F-atoms in F 2 molecule. It is a of σ type. The F 2 molecule is diamagnetic due to the presence of paired electrons .

38. M.O. energy level diagram for homonuclear diatomic molecule. 10. Neon molecule (Ne 2 ) Electronic Configuration of F (9): 1s 2 ,2s 2 ,2px 2 ,2py 2 ,2pz 2 Electronic Configuration of F 2 (18): σ 1s 2 , σ *1s 2 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 2 , σ *2px 2 Or KK 4 , σ 2s 2 , σ *2s 2 , σ 2px 2 , π 2py 2 , π 2pz 2 , π *2py 2 , π *2pz 2 , σ *2px 2

39. Energy A.O. of Ne A.O. of Ne M.O. of Ne 2 σ 2s σ * 2s 2s 2s 2px 2py 2pz 2px 2py 2pz σ *2px π* 2py π* 2py σ 2px π 2py π 2py (KK) 4

40. Bond order in Ne 2 Molecule = ½ (Number of electron in BMO - Number of electron in ABMO ) = ½ (8-8) = ½ x 0 = Bond order in Ne 2 = 0……………… i.e.( Molecule is unstable ) Thus, the bond order in Ne 2 molecule is 0. It suggest Ne 2 molecule is not stable . Hence Ne 2 molecule does not exist . Neon being inert gas element exist in atomic form only.