Bonding and Physical Properties The Molecular Orbital Theory

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1 Bonding and Physical Properties The Molecular Orbital Theory Ø Developed by F. Hund and R. S. Mulliken in 1932 Ø Diagram of molecular energy levels Ø Magnetic and spectral properties Paramagnetic vs. Diamagnetic and Electronic transitions Ø Solid State onductance Ø Predicts existence of molecules Ø Bond Order

2 Linear ombination of Atomic Orbitals (LAO) The two ways of combining a simple wave and destructive overlap constructive overlap the two ways of combining a simple wave and The atomic orbitals of the individual atoms A and B may be represented by the wave functions ψ A and ψ B. The combination of them is the Molecular Orbital of the Molecule AB Therefore, the two molecular orbitals σ and σ* are formed as : Where the coefficients, indicate the contribution of the AO to the MO

3 t ti I t ti 1s 1s 1s 1s the two 1s orbitals combining to give a bonding orbital Destructive interaction nodal plane the two 1s orbitals combining to give an antibonding orbital

4 MO Diagram of Hydrogen Molecule: (empty) antibonding molecular orbital increasing energy 1s atomic orbital hydrogen atom A 1s atomic orbital hydrogen atom B bond order = (full) bonding molecular orbital the hydrogen molecule resulting from the combination of the two hydrogen atoms (no. of electrons in bonding MOs) (no. of electrons in antibonding bond order = (no. of electrons in bonding MOs) (no. of electrons in antibonding 2 MOs) 2 bond order (H2) 2 0 = = 1 2 i.e. a single bond

5 Prediction for the stability of a Molecule: H 2 + and H 2 -

6 Helium Molecule Possible? He 2 (full) antibonding molecular orbital increasing energy 1s atomic orbital helium atom A 1s atomic orbital helium atom B (full) bonding molecular orbital the hypothetical molecule resulting from the combination of the two helium atoms 2 2 bond order (He2) = = 0 i.e. no bond 2 MO Diagram of Helium Molecules

7 Molecular Orbital (MO) Formation Using 2s and 2p Atomic Orbital σ* σ we can rotate about this axis without changing the MOs both MOs have rotational symmetry about the axis through the two nuc these two pairs of p orbitals must side-on only these two p orbitals can overlap end-on two different ways that p orbitals can overlap with each other

8 2pσ * MO the end-on overlap of two 2p atomic orbitals to give the 2pσ * antibonding MO symmetrical cylindrically symmetrical about the internuclear axis in other words, these combinations have σ symmetry. The two molecular orbitals resulting nodal from plane the end-on combination of two 2p orbitals are labelled the 2pσ and the 2pσ* MOs nodal plane 2pσ * MO the end-on overlap of two 2pσ MO atomic orbitals symmetrical to give the 2pσ * antibonding MO the end-on overlap of two 2p atomic orbitals to give the 2pσ bonding MO symmetrical 2pσ MO symmetrical The side-on overlap of two p orbitals forms an MO that is no longer symmetrical about the internuclear axis. If we rotate about this axis, the phase of the orbital changes. The orbital is described as the end-on overlap of two 2p atomic orbitals to give the 2pσ bonding MO having π symmetry a π orbital is formed and the electrons in such an orbital make up a π bond. The side-on overlap of two p orbitals forms an MO that is no longer symmetrical about the internuclear axis. If we rotate about this axis, the phase of the orbital changes. The orbital is described as 2pσ MO symmetrical Since there are two mutually perpendicular pairs of p orbitals that can in this fashion, there the end-on overlap of two 2p atomic orbitals to give the having 2pσ bonding π symmetry a MO π orbital is formed and the electrons in such an orbital make up a π bond are a pair of degenerate mutually perpendicular π bonding MOs and a pair of degenerate mutually Since there are two mutually perpendicular pairs of p orbitals that can in this fashion, there perpendicular π* antibonding MOs. are a pair of degenerate mutually perpendicular π bonding MOs and a pair of degenerate mutually perpendicular π* antibonding MOs. the end-on overlap of two 2p atomic orbitals to give the 2pσ * antibonding MO 2pσ * MO symmetrical nodal plane nodal plane 2pπ * MO the side-on overlap of two 2p atomic orbitals to give the 2pπ* antibonding MO no symmetry If we rotate, the phase changes 2pπ * MO the side-on overlap of two 2p atomic orbitals to give the 2pπ* antibonding MO nodal plane no symmetry If we rotate, the phase changes 2pπ MO no symmetry If we rotate, the phase changes no symmetry If we rotate, the phase changes no symmetry 2pπ MO the side-on overlap of two 2p atomic orbitals to give the 2pπ bonding MO If we rotate, 2pπ * MO The two sorts of molecular the phase orbitals changes arising from the combinations of the p orbitals are not degen-

9 2pσ 2 2pπ 3 2p 3 2p 2 2pπ increasing energy of orbitals 2s 2pσ 2sσ 2sσ 2s nonbonding lone pair two π bonds N N nonbonding lone pair the 1sσ and 1sσ* MOs are much lower in energy than the other MOs one σ bond 1sσ 1s 1s atomic orbitals on atom A 1sσ atomic orbitals on atom B molecular orbitals resulting from the combination of atomic orbitals

10 Molecular Orbital Diagram of Oxygen Molecule O 2 Bond Order = (6-2)/2 = 2 Paramagnetic in Nature

11 Molecular Orbital Diagram of Heteronuclear Diatomic Molecules E = 0 less energy needed to ionize a carbon atom energy needed to ionize an oxygen atom more energy needed to ionize a fluorine atom energy 2p x 2p y 2s 2p z atomic orbitals for carbon 2p x 2p y 2p z 2s atomic orbitals for oxygen O 2p x 2p y 2p z 2s atomic orbitals for fluorine F

12 increasing energy s orbital on less Energies of AOs both the same AO on atom B is a little lower AO on atom B is a lot lower electronegative element in energy than AO on atom A in energy than AO on atom A ψ A AO on AO atom on A atom A φ 2 φ 2 ψ A ψ B AO on ψ B AO on atom A atom A molecular orbitals from elements of different electronegativity MOs MOs ψ B AO on AO on atom B atom B ψ A φ 2 ψ A φ 2 MOs ψ B AO on atom B s orbital on more electronegative element AO on atom A ψ B φ 1 AO on These three different cases where the two φ φ 1 combining atom orbitals B differ greatly in φenergy, 1 only a little, 1 MOs or not at all φ 1 are summarized below. ψ A ions φ 2 AO on atom B Energies large of interaction AOs both between the same AOs AO on less atom interaction B is a little between lower AOs in energy than AO on atom A AO on AOs atom are too B is far a apart lot lower in energy to in energy interact than AO on atom A bonding MO much lower in energy bonding MO is lowered only by a the filled orbital on the anion has the φ φ than 2 2 AOs ψ A small amount relative to AO on same energy as φ 2 the AO on atom B atom B ψ A Molecular Orbital of the Molecule AB Formed in combination of two atomic orbitals of A and B atoms which have different Elcetronegativity ψ B antibonding MO is much higher in antibonding MO is raised in energy the empty orbital on the cation has ψ B σ ψ A

13 Molecular Orbital Diagram of HF Molecule

14 atoms. ompare this with the π bond that results from combining an oxygen p AO with a carbon p AO. π* π* O π* O energy energy p AO on p AO on carbon carbon A A p AO p AO on on carbon carbon BB energy arbon p AO Oxygen p AO π π O π O - Π Molecular Orbital -O Π Molecular Orbital Now the bonding MO (π) is made up with a greater contribution from the oxygen p orbital than from the carbon p orbital. If this MO contained electrons, there would be more electrons around the oxygen atom than around the carbon. This O π bond is covalent but there is also some electrostatic contribution to its bond strength. This electrostatic interaction actually makes a O double bond much stronger than a double bond (bond strength for =O, about kj mol 1 ; for =, kj mol 1 : compare also a O single bond, kj mol 1 with a single bond, kj mol 1 ). Because the electrons in the populated MO (π) are associated more with the oxy- (+) R 2 ( O

15 LUMO Lowest Unoccupied Molecular Orbital HOMO Highest Occupied Molecular Orbital Energy Molecular Orbital Diagram of arbon Monoxide

Molecular-Orbital Theory

Prof. Dr. I. Nasser atomic and molecular physics -551 (T-11) April 18, 01 Molecular-Orbital Theory You have to explain the following statements: 1- Helium is monatomic gas. - Oxygen molecule has a permanent