MOLECULAR STRUCTURE CHAPTER 14 Experiments show O 2 is paramagnetic

Objectives: Extend atomic concepts to electronic structures of molecules Utilize two quantum mechanical theories of molecular electronic structure Valence bond theory Bonding as a result of a shared electron pair between two atoms Molecular orbital theory Concept of atomic orbital extended to molecular orbital Molecular orbital is a wavefunction spread over entire molecule

Hybridization – mixing of two or more atomic orbitals to form a new set of hybrid orbitals. 1.Mix at least 2 nonequivalent atomic orbitals (e.g. s and p). Hybrid orbitals have very different shape from original atomic orbitals. 2.Number of hybrid orbitals is equal to number of pure atomic orbitals used in the hybridization process. 3.Covalent bonds are formed by: a.Overlap of hybrid orbitals with atomic orbitals or b.Overlap of hybrid orbitals with other hybrid orbitals

Fig 11.7 An sp 3 orbital formed from superposition of s and three p orbitals on same atom Four LCAOs give four equivalent hybrid MOs: h 1 = s + p x + p y + p z h 2 = s - p x - p y + p z h 3 = s - p x + p y - p z h 4 = s + p x - p y - p z

Fig 11.8 Each sp 3 hybrid orbital forms a σ bond by overlap with an H 1s orbital 109.5° e.g., wavefunction for overlap of hybrid h 1 and H 1s: Ψ = h 1 (1)A(2)+ h 1 (2)A(1)

Fig 11.9 More detailed representation of formation of an sp 3 hybrid orbital

Fig An sp 2 orbital formed from superposition of s and two p orbitals on same atom Three LCAOs give three equivalent hybrid MOs: h 1 = s + √ 1/2 p y h 2 = s + √ 3/2 p x - √ 1/2 p y h 3 = s - √ 3/2 p x - √ 1/2 p y Remaining unhybridized p orbital

Fig Representation of double bond in C 2 H 4

Fig Representation of triple bond in C 2 H 2

# of Lone Pairs + # of Bonded Atoms HybridizationExamples sp sp 2 sp 3 sp 3 d sp 3 d 2 BeCl 2 BF 3 CH 4, NH 3, H 2 O PCl 5 SF 6 How do I predict the hybridization of the central atom? Count the number of lone pairs AND the number of atoms bonded to the central atom

Summary of Valence Bond Theory Developed substantially by Linus Pauling (1935) Bonding pair of electrons localized between two atoms Includes concepts of σ and π bonds and hybridization Discrepancies between theoretical and observed bond angles (e.g., H 2 O and NH 3 ) Does not address magnetic properties of molecules

Molecular Orbital Theory Developed much more fully than VB theory Concept of atomic orbital extended to molecular orbital Molecular orbital is a wavefunction spread over entire molecule Bonding pair of electrons delocalized over entire molecule Includes concepts of σ and π bonds, bond order, anti-bonding orbitals, and resonance Allows prediction of magnetic properties of molecules

Born-Oppenheimer approximation The nuclei are relatively massive and may be treated as stationary while the electrons move in their field.

The hydrogen molecule-ion, H 2 + where:

Fig (a) Amplitude of bonding MO in H 2 + A B Fig (b) Contour rep of the amplitude Ψ ± = N(A ± B) Electron may be found in AO on atom A and in AO atom B, then overall Ψ ± is a superposition of both AOs:

Fig General shape of the boundary surface of a σ orbital

Fig General shape of the boundary surface of a σ orbital Probability density: Ψ 2 + = N 2 (A 2 + 2AB + B 2 ) Constructive: Ψ + = N(A + B) Overlap density

Fig Calculated and experimental molecular potential energy curves for H 2 +

Fig Constructive interference when two H1s orbitals overlap to form a σ orbital Superposition: Ψ ± = N(A ± B) Constructive: Ψ + = N(A + B)

Fig Destructive interference when two H1s orbitals overlap to form a σ * orbital Superposition: Ψ ± = N(A ± B) Destructive: Ψ - = N(A - B) Probability density: Ψ 2 - = N 2 (A 2 - 2AB + B 2 ) node

Fig (a) Amplitude of antibonding MO in H 2 + Fig (b) Contour rep of the amplitude

Fig General shape of the boundary surface of a σ * orbital Destructive: Ψ - = N(A - B) Probability density: Ψ 2 - = N 2 (A 2 - 2AB + B 2 )

Fig Partial explanation of the origin of bonding and antibonding effects σ σ*σ*

Fig MO energy level diagram for H 2 constructed from overlap of H1s orbitals D o = 7.18 x J = 36,130 cm -1

Fig MO energy level diagram for He 2 constructed from overlap of H1s orbitals Bond order: b = ½(n – n*)