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) Orbital overlap Constructive Interference Bonding Overlap Wavefunction ( ) Atom (1) 1s 1s 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. -4-3 -2-1 0 1 2 3 4 z (Angstroms) 1
Orbital overlap Destructive Interference Wavefunction ( ) Antibonding Overlap 1s 1s Atom (1) Atom (2) -4-3 -2-1 0 1 2 3 4 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. Pi (π)( ) Bonding side on overlap Sigma (σ)( ) Bonding head on overlap p z p z Bonding pi molecular Constructive Interference Bonding sigma molecular Constructive Interference p z p z Antibonding pi molecular Destructive Interference Destructive Interference Bonding sigma molecular 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 s 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 s 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. 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 s, interatomic distance, or size of s) b. The electronegativities become different 2
Cr 3 [Cr(NH 3 ) 6 ] 3 Octahedron 3 :NH 5 d-s d on Cr (Cr 3 d 3 ion) 3 electrons in the d-s : :NH 3 N H 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 s (d z2, d x2-y2 ) Δ Crystal Field Splitting Energy t 2g s (d xz, d yz, d xy ) Metal (Cr) d-s Metal d MO s Energy Ligand MO s Ligand (N) lone-pair s Bonding (σ) Metal-Ligand MO s Absorption Spectra Cr 3 Solutions 1.4 1.2 [Cr(H2O)6]3 Antibonding (σ*) Metal-Ligand MO s 1.0 0.8 0.6 0.4 [Cr(OH)4(H2O)2]1- [CrO4]2- Metal d MO s Δ oct 0.2 0.0 250 350 450 550 650 750 850 wavelength (nm) 3
[CrO 4 ] 2- t 2 s (more antibonding) e s (antibonding) Metal (Cr) d-s Energy Oxygen 2p MO s e s (bonding) 12 Oxygen 2p s (4 oxygens x 3 p s) t 2 s (bonding) Absorption Spectra CrO 2-4 Solutions Antibonding Cr 3d s 1.4 [Cr(H2O)6]3 1.2 1.0 0.8 0.6 1 0.4 0.2 0.0 250 350 450 550 650 750 850 wavelength (nm) Oxygen 2p MO s Absorption Spectra CrO 2-4 Solutions Antibonding Cr 3d s 1.4 [Cr(H2O)6]3 1.2 1.0 [Cr(OH)4(H2O)2]1- [CrO4]2- [Cr(OH)4(H2O)2]1- [CrO4]2-0.8 0.6 2 0.4 0.2 0.0 250 350 450 550 650 750 850 wavelength (nm) Oxygen 2p MO s 4
Charge Transfer Salts, ACrO 4 The 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? CrO 2-4 vs. MnO 2-4 5
Antibonding (e) Cr dx 2 -y 2, dz 2 Antibonding (e) Mn dx 2 -y 2, dz 2 O 2p [CrO 4 ] 2- O 2p [MnO 4 ] - As the cation oxidation state increases [i.e. Cr(VI) Mn(VII)] d-s become more electronegative (lower in energy) Energy Gap decreases Absorption shifts to longer wavelengths 100 SrMoO 4 SrCrO 4 Series 90 Reflectance 80 70 60 50 40 30 20 10 [CrO 4] 2- SrCrO4 SrCr0.9Mo0.1O4 SrCr0.8Mo0.2O4 SrCr0.5Mo0.5O4 SrCr0.2Mo0.8O4 SrCr0.1Mo0.9O4 SrMoO4 CrO4(2-) SrMoO 4 0 250 350 450 550 650 750 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 s are always much smaller than the s and p, but the 3d s are particularly small 6
Antibonding (e) Cr dx 2 -y 2, dz 2 Antibonding (e) Mo dx 2 -y 2, dz 2 O 2p [CrO 4 ] 2- O 2p [MoO 4 ] 2- Mo 4d s are larger than the Cr 3d s d-s interact more with O 2p s more antibonding 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-s are larger Metal-ligand antibonding interactions are stronger e g (σ*) s are more antibonding Low spin configurations are always observed 7