LCAO-molecular orbitals

1. LCAO-molecular orbitals • In MO Theory, atomic orbitals on the constituent atoms are combined to form bonding, non-bonding and anti-bonding orbitals for the molecule H2 He2

2. Valence Bond (“hybridization”) theory • Valence Bond (VB) theory is driven by the shape of the molecule (Chapter 10.7) • VB Theory begins with two steps: • hybridization (combination of AOs on the same atom such that new AOs, known as hybrid orbitals, are formed that POINT IN THE RIGHT DIRECTION) • hybrid orbitals and/or AOs on different atoms are combined to make sigma bonds with electron density localized between the two bonding atoms • Pi bonds are formed from unhybridized atomic p orbitals • Key differences between MO and VB theory: • MO theory has electrons distributed over molecule • VB theory localizes an electron pair between two atoms • MO theory combines AOs on DIFFERENT atoms to make MOs (LCAO) • VB theory combines AOs on the SAME atom to make hybridized atomic orbitals (hybridization) • In MO theory, the symmetry (or antisymmetry) must be retained in each orbital. • In VB theory, all orbitals must be looked at at once to see retention of the molecule’s symmetry.

3. H—Be—H and sp hybridization • In the method of hybrid orbitals, we “create” two hybrid atomic orbitals specifically designed to fit the shape of the molecule, in this case linear, using atomic orbitals of an excited state Be atom! • Unused AOs are left behind as unhybridized atomic orbitals • The energy of the hybrid atomic orbitals are intermediate between those of the original constituent AO’s • The hybrid orbitals combine with other orbitals, atomic or hybrid, in the usual fashion, creating both bonding and anti-bonding molecular orbitals, which are localized molecular orbitals

5. BH3 and sp2 hybridization • BH3 is trigonal planar with three equal B—H bonds • To get this shape, we need to combine the 2s with two 2p AO’s to generate three equivalent hybrid atomic orbitals • Combination with the H 1s leads to bonding and anti-bonding molecular orbitals, which are localized molecular orbitalspointing to the corners of a triangle

7. CH4 and sp3 hybridization • CH4 is tetrahedral with four equal C—H bonds • To get this shape, we need to combine all the n=2 AO’s to generate four equivalent hybrid atomic orbitals • Combination with the H 1s leads to bonding and anti-bonding molecular orbitals, which are localized molecular orbitalspointing to the corners of a tetrahedron

8. Compare to the LCAO model of CH4 4σ 3σ 4σ 2σ 3σ 1σ 2σ 2σ 1σ 1σ

9. VB theory is built on VSEPR shapes • Recap: Molecular Geometry and Electron Group Geometry (Chapter 10) Hybridization: sp sp2 sp2

10. VB theory is built on VSEPR shapes • VB theory is useless beyond 4 electron groups! • Thus we need only consider 2, 3, and 4 electron groups from Chapter 10, section 7 Hybridization: sp3 sp3 sp3

11. Summary of the VB (Hybrid AO) method • The normal atomic orbitals have shapes that do not correspond to chemical bonds • Atomic orbitals are essentially spherical • Bonds are oriented towards the Terminal Atoms • Hybrid Atomic Orbitals (HAO) are mathematically valid mixtures of the original atomic orbitals • They are “manufactured” by promoting electrons to the desired excited state • This energy has to be “paid” for – it is obtained by the bond energy that results from good chemical bonds formed when the geometry “fits” • Remember that the method results in multiple equal – and hence degenerate – HAO’s that differ only in their orientation • Bonds can be formed from the “overlap” between any of the following: • HAO with HAO • HAO with AO • AO with AO

12. Two central atoms: ethane • If we treat ethane by the VSEPR theory, we find that bothcarbon atoms are tetrahedral • The shape of the molecule is shown in the diagram: theonly additional information required is the conformationwhich is adjusted to minimize contacts between the atoms – this is known as the staggered conformation • We can thus explain the bonding in ethane by using sp3 hybrid orbitals on each carbon atom • The H atoms bond using their 1s atomic orbitals • In all there are 14 electrons or 7 electron pair bonds in the molecule Ignore the “tail ends” of the HAO Rotation…

13. Bonding in Ethane Lewis structure (including all lone pairs) VSEPR Geometry (including 3D) Hybridization at central atoms

14. Double bonds: ethene • If we treat ethane by the VSEPR theory, we find that bothcarbon atoms are trigonal planar • The shape of the molecule is shown in the diagram: theonly additional information required is the conformationwhich is planar. Why does this geometry occur? • We can explain the bonding in ethene by using sp2 hybrid orbitals on each carbon atom, which leavesone atomic p orbital unused on each C atom, while H atoms use their 1s atomic orbitals • In all there are 6 electron pair bonds in the molecule, 5 in σ orbitals, 1 in the π orbital The sigma skeleton of ethene The pi bond of ethene

15. Planarity in double bonds: ethene again • We can now explain the origin of theplanar structure of ethene • Only when the two CH2 fragments are co-planarcan there be efficient overlap between the unhybridized p orbitals leading to the π bond • As shown in the bottom diagram: if ethene isrotated by 90° along the C—C bond, the atomicp orbitals have zero net overlap • Such an arrangement is know as an orthogonalinteraction of wavefunctions, and does not leadto any net bonding • Double bonds impose coplanar conformationson the joining atoms • This is true for all double-bonded molecules, and is a powerful confirmation of the bonding theories that we have developed • Note that a double bond is always the sum of a sigma + a pi bond • Single bonds are always sigma bonds, so that in ethane, all the bonds are sigma

19. Bonding in Allene (H2C=C=CH2) Lewis Structure VSEPR Geometry Hybridization σ bonding π bonding