Molecular Orbital Theory (MOT)

Molecular Orbital theory for Transition Metal complexes.

1. Molecular Orbital Theory Dr. Shivaji H Burungale Head Department of Chemistry

2. Molecular Orbital Theory MOT . Introduction: MOT was first developed by HUND,Mulliken and Huckel in 1930. In MO diagram of a molecule, electrons are fill in molecular orbital according to Aufbau principle. LCAO method are as follows: a) n atomic orbitals must produce n molecular orbitals ( e.g . 6 AO’s must produce 6 MO’s ). b) The atomic orbitals with the appropriate symmetry combine. c) The atomic orbitals with similar energy combine. d) Each MO must be normal and must be orthogonal to every other MO. e)The more interaction between the atomic orbitals results in formation of more stable MO

3. Principles of Ligand Field Theory In coordination chemistry, the ligand acts as a Lewis base because it is capable of donating a pair of electrons and metal is a Lewis acid that accept a pair of electrons resulting covalent bond between metal and the ligand . This is also called as a coordinate covalent bond or a dative covalent bond in order to show that both the bonds are formed from electron coming from the ligand . A more specified description of bonding in the coordination complexes is given by Ligand Field Theory. Essentially LFT is able to give an understanding of the true origins of Δo and the spectrochemical series by taking into account the roles of σ- and π- bonding in transition metal chemistry.

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5. The A 1g group orbitals have the same symmetry as an s orbital on the central metal .

6. The T 1u group orbitals have the same symmetry as the p orbitals on the central metal. (T representations are triply degenerate

7. Ligand Field Theory The E g group orbitals have the same symmetry as the d z 2 and d x 2 -y 2 orbitals on the central metal. (E representations are doubly degenerate.)

8. Ligand Field Theory Since the ligands don’t have a combination with t 2g symmetry, the d xy , d yz and d xy orbitals on the metal will be non-bonding when considering σ bonding.

9. Ligand Consideration In the formation of transition metal complexes, there is required central metal atom/ion and the surrounding ligands. The geometry and nature of the complex depends upon the type of the metal as well as ligands. The ligands in this context can be of various types: (a) σ donor (b) π donors (c) σ+π donors (c) π acceptors

10. Nature of Ligands . There are three types of ligands 1.Pure sigma bonding electron donor orbitals eg . NH3, H2O 2. σ and π bonding electron donor orbitals eg . Halogen lignds 3.Weak σ donor and strong π acceptor ligands eg . CO,CN

11. In order to decide which atomic orbitals to combine, we use the following guidelines: atomic orbitals that combine must be of similar energy; only atomic orbitals of the same symmetry can combine; there must be significant overlap of combining orbitals ; n atomic orbitals combine to make n molecular orbitals .

12. Representation of Symmetry Point Groups . a = singly degenerate T= triply degenerate E= doubly degenerate g = symmetric u= unsymmetric A 1g One (A and B, Two for E and three for triply degenerate symbols Symmetric with 1 and antisymmetric with 2 Centre of symmetry of molecule g and u for nonsymmetric molecule

13. Metal orbitals symmetry of orbitals S a1g px,py pz t1u Dz2,dx2-y2 eg dxy Dxz T2g dyz Matching Metal orbitals of 4s ,4p 3d

14. Ligand orbitals symmetry of orbitals P x , P y , P z a 1g , e g t 1u two ligand along the z axis Two ligands along the x axis Two ligands along the y axis Each ligand donate a pair of electrons Total 12 electrons are donated by six ligands

15. Metal Orbital Symmetry Label Degeneracy s A1g 1 px , T1u 3 py , pz dxy , T2g 3 dyx , dxz dx2-y2 Eg 2 , dz2 Symmetry Representation

16. Ligand Group orbitals . In the octahedral environment Metal orbital + Ligand group orbital BMO s + AMOS a 1g a 1g A 1g A 1g * t 1u t 1u T 1u T 1u * e g e g E g E g * σ bonding MO t 2g t 2g (n) T2g non bonding mos A 1g T 1u Eg T2g Eg * A 1g * T 1u * antibonding MOS

17. a metal ion surrounded by six ligands, each contributing one filled orbital. Thus, we have five metal d orbitals and six ligand orbitals from which to construct molecular orbitals for the complex. We arrange the six ligands to lie on the x-, y- and z-axes. Let us now see how the six ligand orbitals overlap with the metal d orbitals .

18. Bonding in Octahedral complexes Bonding in octahedral complexes is divided into two types Sigma bonding MOs Pi bonding MOS

19. Construction of MO diagram for sigma bonding octahedral complexes Name of the central metal in complexes Atomic number of central metal atom electronic configuration of metal atom Oxidation state of metal Number of valence electrons in 3d and 4s orbitals . Number of ligands donated 12 elctrons Total number of electrons of metal ion and 12 electrons of six ligands. Distribution of electrons in the order of Molecular orbitals . Like A 1g < T 1u < Eg < T2g < Eg * < A 1g *< T 1u * 12 electrons occupied in bonding MO orbitals and remaining electrons occupied in non bonding T2g and antibonding Eg * orbitals . 2 6 4

20. MO diagram in metal complexes [ Ti(H2O)6] 3+ In this complex, Central metal is Titanium Atomic number of Titanium is 22 Outer most Electronic configuration of Titanium is 3d 2 4s 2 Oxidation state of centra l titanium is +3 therefore 3d 1 4s Number of electrons in valence orbitals is 1 Total number of electrons in Ti 3+ is 1 and 12 electrons from 6 ligands. total electrons 13

21. [CoF6]3– Co -27 3d 7 4s 2 Co 3+ 3d 6 4s 6 electrons of cobalt and 12 electrons of fluoro ligands [Co(NH3)6]3 Co 3+ 3d 6 4s 6 electrons of cobalt and 12 electrons of ammonia ligands

22. Sigma bonding in transition metal complexes The atomic orbitals on the central metal ion may be ns , np , and (n-1)d orbitals which together are called valence orbitals There are four important points such Classification of metal valence orbitals in sigma symmetry in octal hedral complex. a1g s T1u px py pz Eg dz2 dx2-y2d 2 sp 3 Thus hybrid combination required is d 2 SP 3

23. 6 s ligands x 2e each 12 s bonding e “ ligand character” “d -d 10 electrons” non bonding anti bonding “metal character” ML 6 s -only bonding The bonding orbitals , essentially the ligand lone pairs, will not be worked with further.

24. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

25. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

26. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

27. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

28. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

29. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

30. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

31. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

32. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

33. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

34. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

35. Bonding MOs Antibonding MOs AOs Ti 3+ ions LGOs of 6H 2 O a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o E

36. Color and spectra of [Ti(H 2 O) 6 ] 3+ Ligand is weak field - H 2 O The reddish violet Purple Maximum absorption at 20300cm-1 d-d transition forbidden transition weak band Charge transfer transition –27000 to 30000cm-1 Paramagnetic nature due to one unpaired electron in nonbonding t2g orbitals . E

37. Bonding MOs Antibonding MOs AOs Co 3+ ions LGOs of 6F- a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * ∆o

38. MOs Diagram for [Co(F) 6 ] 3- Ligand is weak field –F- Color of Complex is Blue Maximum absorption at 15000 cm-1 d-d transition forbidden transition weak band Charge transfer transition –27000 to 30000cm-1 Paramagnetic nature due to four unpaired electron in nonbonding t2g orbitals . And antibonding Eg orbitals

39. Antibonding MOs AOs Co 3+ ions a1g 4s t1u 4 px py pz t 2 g eg 3dxy dxz dyz dx2-y2 dz2 A1g T1u T2g n Eg Eg * A1g * T1u * LGOs of 6 NH3 ∆o Bonding MOs

40. MO diagram for [Co(NH3) 6 ] 3+ NH3 is strong field Color of Complex is yellow green Diamagnetic in nature ∆0 is large

41. Merits and Demerits of MOT Merits 1.This is a completely theory 2. It has considered interaction between metal orbital's and Ligands orbital's. 3.Pi bonding is explained Strong field and weak field ligands are explained . Charge transfer spectra and d-d transition also explained. Magnetic and stability of complexes are also studied. Spectrochemical series and Nephelauexetic effect are explained on the basis of MOT Demerits This is most complicated Molecular orbital calculation , Computer is required Multi atom complex cannot be explained.

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