- 1. Inorganic Chemistry Dr. Bhuse V. M Department of Chemistry, Institute of Science, Nagpur Molecular Orbital Theory Books to follow Inorganic Chemistry by Shriver & Atkins Physical Chemistry: Atkins
- 2. Structure of an Atom: e- movement route o o o o o o o o o o o o o o o o o Nucleus of atom (Proton + Neutron) size 10-15 m Electrons Revolve round the nucleus in different path
- 3. ORBITAL: Orbital : The region around the Nucleus where probability of finding electron is more (appreciable). The probability never become zero e- o o o o o o o o o o o o o o o o o This is not the end of ORBIT
- 4. Chemistry: The ‘Chemistry’ of any element is associated with the rearrangement of electrons of participating atoms. This smaller invisible electron although is particle, mostly behave as wave. Light : Behave as wave Stone: Behave as partical.
- 5. If light can behave as particles,why not particles behave as wave? Louis de Broglie The Nobel Prize in Physics 1929 French physicist (1892-1987)
- 6. Louis de Broglie Particles can behave as wave. Wave Particle Duality
- 7. Time period = T=Wavelength, Velocity = v, v = l/T, Frequency, n = 1/T, v = n l, Concept of wave
- 8. A = maximum amplitude Frequency= 1/l = n l= is wavelength x y l A Trough Crest l 2l
- 9. x y If e- is considered as wave, we can write a wave equation (Ψ) for it.
- 10. We can write wave equation for electron. Electron is present in orbitals (s,p,d,f etc), so we can write wave equation for orbital also Thus, for every system, we can write a wave function Ψ which is continuous, single-valued function of the coordinates of all the particles and of time. From these functions, all possible predictions about the physical properties of the system can be obtained. The Wave Equation (Function) If we know the wave function we can know everything about the compound.
- 11. THEORY OF BONDING b) Molecular Orbital Theory The another theory that describe the bonding in compound It considers the wave nature of electrons.
- 12. MOT: Principles 1. Each electron can be represented by a wave, . 2. An atomic orbital contains an e-, so it can also be represented by another wave, 3. When atoms combine, the atomic orbitals mix completely (called linear combination) to produce Molecular orbitals (M.O) [SIMILAR TO HYBRID ORBITAL] 4. However, here, two kind of MO’s are produced. 5. We, therefore can write wave equation for MO also. 6. Each is associated with a definite shape & energy . 7. Regular rules of filling electrons apply to MO’s (Aufbau Principle Pauli Exclusion )
- 13. Rules for linear combination 1. Atomic orbitals must be roughly of the same energy. 2. The orbital must overlap one another as much as possible- 3. Atoms must be close enough for effective overlap. 4. AO should have the same symmetry (i.e symmetry of two AO must remain unchanged when rotated about the internuclear line or, Both AO must change symmetry in identical manner. Linear combination of atomic orbitals
- 14. Rules for linear combination…. 4. When two AOs mix, two MOs will be produced (i.e. combination should be equal in number) If for any atom, no suitable AO available on adjacent atom, that AO remain as Nonbonding (NBMO) Each orbital can have a total of two electrons (Pauli principle) Lowest energy orbitals are filled first (Aufbau principle) 5. Unpaired electrons have parallel spin (Hund’s rule) 6. Bond order = ½ (bonding electrons – antibonding electrons)
- 15. 7. For atoms with both s and p orbitals, there are two types of interactions: The s and the p orbitals that overlap axially gives type bonding and antibonding molecular orbitals. The other two sets of p orbitals that overlap laterally gives type bonding and antibonding molecular orbitals. Thus, there are both and bonding molecular orbitals and * and * antibonding molecular orbitals.
- 16. A B A B Linear Combination of Atomic Orbitals (LCAO) MO formation can be considered as constructive and distructive interference of the two waves A and B •If waves interact constructively, the resulting orbital is lower in energy: called bonding molecular orbital. If waves interact destructively, the resulting orbital is higher in energy: an antibonding molecular orbital.
- 17. +. +. . . + -bonding b Amplitudes are added Molecular Orbital: 1. Bonding MO: Constructive interference = A+B Constructive interference
- 18. The electron remains between the two nuclei Nuclei are shielded from each other The electrons spend much time in this MO. It interacts strongly with both nuclei therefore attract two nuclei togather, so MO is called Bonding MO. The energy of the molecule is lower Bonding MO . . +
- 19. Amplitudes of wave functions subtracted. Molecular Orbitals: 2. Antibonding MO: Destructive interference +. -. . . node antibonding + - = A-B Destructive Interference
- 20. The electrons are excluded from internuclear region. The electrons remain outside of the area between two nuclei. Both nuclei repels to each other No shielding of Nuclear charge. Therefore this MO is destabilizing the bond so called Antibonding MO. The energy of the molecule is higher . . + - Antibonding MO
- 21. 2AO =2MO
- 22. Comparison of AO & MO AO MO Monocentric Bi/polycentric Under influence of one nuclei Under influence of more than one nuclei e.g. are S, Px,Py,Pz,dxy,dyx,dxz, dx2-y2,dz2 Bonding MO, antobonding MO, nonbonding MO, sigma MO, pi MO.
- 23. BMO ABMO Addition overlap Substraction overlap viewed as constructive interference of waves = A+B viewed as distructive interference of waves = A-B Lower in energy Higher in energy Electron in bMO shield nuclear charge between two nuclei i.e. binds two nuclei, so called bonding MO. Electron in abMO cannot shield nuclear charge between two nuclei (i.e cannot bind), so called bonding MO. Nuclear density concentrated between internuclear line joining two nuclei. Nuclear density concentrated outside of nuclear line. Electron in BMO increases bond order Electron in ABMO decreases bond order
- 24. Points to remember in MOT Two atomic orbitals combine => two molecular orbitals result. Of each pair of molecular orbitals, one is a bonding molecular orbital. The bonding orbital is at a lower energy than the separate atomic orbitals. Electrons in a bonding orbital increase the stability of the molecule. The second orbital is an antibonding orbital. The antibonding orbital is at a higher energy than the AOs. Electrons in an anti bonding orbital decrease the stability of the molecule.
- 25. Molecular Orbitals Two AOs in hydrogen atoms combine to form … … a bonding molecular orbital, lower in energy than the AOs, and … … an antibonding molecular orbital, higher in energy than the AOs. Electron density between the nuclei is increased. Electron density between the nuclei is decreased.
- 26. Types of Overlap: 1.s-s Constructive interference from the 1s orbitals (1s) Destructive inteference form the 1s orbitals ( ) The molecular orbital has a nodal plane bisecting the internuclear axis. A node or nodal plan is a region in which the probability of finding an electron is zero. * s 1 * s 1
- 27. 2. px-px Head-on overalp produces sigma molecular orbitals . Constructive interference from the 2px orbitals Destructive interference for the 2px orbitals
- 28. 3. py-py/pz-pz These atomic orbitals overlap ‘side-on’ forming molecular orbitals The bonding combination is The antibonding combination is Termed as molecular orbitals because they have a nodal plane along the internuclear axis y p 2 * p 2 y
- 29. Constructive interference from the 2py/2pz orbitals Destructive interference from the 2py/2pz orbitals
- 30. Types of overlap (sigma and pi) The two px orbitals combine to form sigma bonding and antibonding MOs. The two py orbitals and the two pz orbitals give pi bonding and antibonding MOs.
- 31. H2 Molecule: (2 nuclei and 2 electron) Let the two Hydrogen in H2 be labeled as HA and HB. Therefore e-s in their AO’s can be described by wave functions as A & B. The overlap of AO can be visualized as overlap of two waves, A and B . The overlap is given by algebric addition of two waves (i.e. addition followed by subtraction) = CAA ± CBB Where C is extent of overlap
- 32. A and B are same atomic orbitals (except for their different origin) = A± B This is LCAO. It has two terms = A+ B (Addition) & = A- B (Substraction) The addition gives Bonding Orbital (BMO). The substraction gives Antibonding Orbital (AbMO). Order of filling e- is same as that AO. BMO have low energy than individual energy of AO. AbMO have high energy than that of individual AO.
- 33. How to draw MO Diagram? High energy Antibinding MO, (AbMO) Energy a Low energy bonding MO, (BMO) b 1S1 H 1S1 H AO of one H atom AO of other H atom MO of H2 Molecule
- 34. Bond Order and Bond Stability 2 electrons g antibondin of # electrons bonding of # order bond *BO gives the number of bonds formed between atoms. *BO=0 means no bonding (as there are same number of electron in bonding and antibonding orbitals) *More the bond order, more the stability of molecule. *More the bond order, shorter the bond length & greater the bond energy. *Bond energy is the amount of energy necessary to break a mole of bonds.
- 35. Molecular Orbital Diagrams: a) Homonuclear Diatomic Molecules b) Homonuclear Diatomic Molecules Draw the energy level diagrams / Molecular Orbital Diagram (MOD) and write the MO electron configurations H2 He2 Be2 N2 O2 and O2 -
- 36. In H2 the two electrons go into the bonding molecular orbital and none in the antibonding MO. The bond order is = 1 2 (2 - 0) = 1 a) Homonuclear Diatomic Molecules 1. H2 molecule
- 37. Electronic Configuration: He(2): 1s2 In the case of He2, the bond order would be 1 2 (2 - 2) = 0 • Bond order is zero. • That is no bond between two He atom. • Therefore, He2 does not exist. a) Homonuclear Diatomic Molecules 2. He2 Molecule
- 38. 1. Principle energy level n =2
- 39. a) Homonuclear Diatomic Molecules 3. Li2 molecules 1s2, *1s2, 2s2 Bond order: 1 Li Energy Li Li2 1s 1s 1g 1u* 2s 2s 2g 2u*
- 40. 1s2, *1s2, 2s2, *2s2 Bond order: 0 Be Energy Be Be2 1s 1s 1g 1u* 2s 2s 2g 2u* a) Homonuclear Diatomic Molecules 4. Be2 Molecules
- 41. Energy Diagram for Homonuclear Molecules
- 42. Simplified a) Homonuclear Diatomic Molecules 5. O2 Molecule
- 43. Homonuclear Diatomics • Energy level sequence: • 1s 1s* 2s 2s* 2p y(2p) = z(2p) y*(2p) z*(2p)2p*.
- 44. b) Heteronuclear Diatomic Molecules Molecular orbital diagrams for heteronuclear molecules is different than homonuclear ones The more electronegative elements are lower in energy than those of the less electronegative element. A few diatomics have unpaired electrons in the MO’s. These diatomics would be classified as being paramagnetic. Diamagnetic species have no unpaired electrons.
- 45. Heteronuclear Diatomic Molecules The energy differences between bonding orbitals depend on the electronegativity differences between the two atoms The larger the difference the more polar the bond that is formed (ionic character increases) The difference reflects the amount of overlap between the bonding orbitals. If the difference is too great the orbitals cannot overlap effectively and nonbonding orbitals will be formed.
- 46. Energy Level Diagram for NO
- 48. Summary Explains the distributions and energy of electrons in molecules Useful for describing properties of compounds Bond energies, electron cloud distribution, and magnetic properties etc The electron in an atomic orbital is described as a wave function utilizing the Schröndinger equation. The ‘waves’ have positive and negative phases. To form molecular orbitals, the wave functions of the atomic orbitals must
- 49. Summary How the phases or signs combine determine the energy and type of molecular orbital. Bonding orbital – the wavefuntions are in- phase and overlap constructively (they add). Bonding orbitals are lower in energy than AOs Antibonding orbital – the wavefunctions are out-of-phase and overlap destructively (they subtract) Antibonding orbitals are higher in energy than the AO’s When two atomic orbitals combine, one bonding and one antibonding MO is