Molecular Orbital Theory and Charge Transfer Excitations

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1 Molecular Orbital Theory and Charge Transfer Excitations Chemistry 123 Spring 2008 Dr. Woodward Molecular Orbital Diagram H 2 Antibonding Molecular Orbital (Orbitals interfere destructively) H 1s Orbital H 1s Orbital Energy Bonding Molecular Orbital (Orbitals interfere constructively) 1

2 Orbital overlap Constructive Interference Bonding Overlap Wavefunction ( ) Atom (1) 1s Atom 1 1s Atom 2 Atom (2) Constructive Interference Between the nuclei the wavefunctions add together. Electron density maximized in the internuclear region. This type of overlap leads to formation of a covalent bond z (Angstroms) Orbital overlap Destructive Interference Wavefunction ( ) Antibonding Overlap 1s Atom 1 1s Atom 2 Atom (1) Atom (2) z (Angstroms) Destructive Interference Between the nuclei the wavefunctions cancel each other out. Electron density pushed away from internuclear region. This type of overlap works against formation of a covalent bond. 2

3 Pi (π)( ) Bonding side on overlap Sigma (σ)( ) Bonding head on overlap Atom 1 p z orbital Atom 2 p z orbital Bonding pi molecular orbital Constructive Interference Atom 1 p y orbital Atom 2 p y orbital Bonding sigma molecular orbital Constructive Interference Atom 1 p z orbital Atom 2 p z orbital Antibonding pi molecular orbital Destructive Interference Atom 1 p y orbital Atom 2 p y orbital Destructive Interference Bonding sigma molecular orbital Principles of MO Theory 1. Conservation of Orbitals: The number of Molecular Orbitals is equal to the number of Atomic Orbitals. 2. Conservation of Electrons: The number of electrons occupying the molecular orbitals is equal to the sum of the valence electrons on the constituent atoms. 3. Pauli Exclusion Principle: Each MO can hold two electrons of opposite spin. 4. Hunds Rule: When orbitals are degenerate (at the same energy) all electron spins are the same direction (up) until we have to start putting two electrons in the same orbital. 5. Principle of Orbital Mixing: The splitting between bonding and antibonding MO s decreases as: a. The spatial overlap decreases (due to orientation of the orbitals, interatomic distance, or size of orbitals) b. The orbital electronegativities become different 3

4 Cr 3 [Cr(NH 3 ) 6 ] 3 Octahedron 3 :NH 5 d-orbitals d on Cr (Cr 3 d 3 ion) 3 electrons in the d-orbitals : :NH 3 H N H H 6 Ligand Orbitals Nitrogen lone pairs (all containing 2 e - ) Only sigma interactions are allowed [Cr(NH 3 ) 6 ] 3 Antibonding (σ*) Metal-Ligand MO s e g orbitals (d z2, d x2-y2 ) Δ Crystal Field Splitting Energy t 2g orbitals (d xz, d yz, d xy ) Metal (Cr) d-orbitals Metal d MO s Energy Ligand MO s Ligand (N) lone-pair orbitals Bonding (σ) Metal-Ligand MO s 4

5 Absorption Spectra Cr 3 Solutions [Cr(H2O)6]3 Antibonding (σ*) Metal-Ligand MO s 1.0 [Cr(OH)4(H2O)2]1- [CrO4]2- absorbance Metal d MO s Δ oct wavelength (nm) [CrO 4 ] 2- t 2 orbitals (more antibonding) e orbitals (antibonding) Metal (Cr) d-orbitals CT Energy Oxygen 2p MO s e orbitals (bonding) 12 Oxygen 2p orbitals (4 oxygens x 3 p orbitals) t 2 orbitals (bonding) 5

6 Absorption Spectra CrO 2-4 Solutions Antibonding Cr 3d orbitals 1.4 [Cr(H2O)6] absorbance CT wavelength (nm) Oxygen 2p MO s Absorption Spectra CrO 2-4 Solutions Antibonding Cr 3d orbitals 1.4 [Cr(H2O)6] [Cr(OH)4(H2O)2]1- [CrO4]2- [Cr(OH)4(H2O)2]1- [CrO4]2- absorbance CT wavelength (nm) Oxygen 2p MO s 6

7 Charge Transfer Salts, ACrO 4 The absorbance of SrCrO 4 is similar to a concentrated solution of CrO 4 2- ions. Charge Transfer Excitations and Periodic Trends We can expect charge transfer transitions when we have a d 0 cation in a high oxidation state. How does the charge transfer change as we move around the periodic table? 7

8 CrO 2-4 vs. MnO 2-4 Antibonding (e) Cr dx 2 -y 2, dz 2 Antibonding (e) Mn dx 2 -y 2, dz 2 CT CT O 2p [CrO 4 ] 2- O 2p [MnO 4 ] - As the cation oxidation state increases [i.e. Cr(VI) Mn(VII)] d-orbitals become more electronegative (lower in energy) CT Energy Gap decreases Absorption shifts to longer wavelengths 8

9 100 SrMoO 4 SrCrO 4 Series 90 Reflectance [CrO 4 ] 2- absorbance SrCrO4 SrCr0.9Mo0.1O4 SrCr0.8Mo0.2O4 SrCr0.5Mo0.5O4 SrCr0.2Mo0.8O4 SrCr0.1Mo0.9O4 SrMoO4 CrO4(2-) 10 SrMoO Wavelength (nm) SrCrO 4 Orbital Radii Group 6 Cr 4s r 1.63 Å Mo 5s r 1.75 Å W 6s r 1.65 Å Cr 3d r 0.46 Å Mo 4d r 0.73 Å W 5d r 0.78 Å The d orbitals are always much smaller than the s and p, but the 3d orbitals are particularly small 9

10 Antibonding (e) Cr dx 2 -y 2, dz 2 Antibonding (e) Mo dx 2 -y 2, dz 2 CT CT O 2p [CrO 4 ] 2- O 2p [MoO 4 ] 2- Mo 4d orbitals are larger than the Cr 3d orbitals d-orbitals interact more with O 2p orbitals more antibonding CT Energy Gap increases Absorption shifts to shorter wavelengths 2 nd nd & 3 rd Row Transition Metals e g (σ*) [Co(H 2 O) 6 ] 3 Δ 2.25 ev [Rh(H 2 O) 6 ] 3 Δ 4.23 ev 2 nd and 3 rd row transition metals d-orbitals are larger Metal-ligand antibonding interactions are stronger e g (σ*) orbitals are more antibonding Low spin configurations are always observed 10