1. Lecture 24 Valence bond theory

2. Valence bond theory
There are two major approximate theories of chemical bonds: valence bond (VB) theory and molecular orbital (MO) theory.
While it is computationally less widely used than MO, VB has a special appeal to organic chemists studying reaction mechanisms and remains useful and important.
The concepts of spn hybridization and lone pairs are introduced.

3. Orbital approximation
In polyelectron atoms, we used the orbital approximation – an approximate separation of variables – where we filled hydrogenic orbitals with electrons to construct atomic wave functions.
For polyatomic molecules, can we also use orbital approximation? Can we use hydrogenic atomic orbitals to construct molecular wave functions?

4. Singlet and triplet He (review)
In the orbital approximation for (1s)1(2s)1 He, there are four different ways of filling two electrons:
Anti-symmetric
Triplet
more stable
Anti-symmetric
Singlet
Anti-symmetric

5. Cross-section of wave function
VB theory for H2
Let us construct the molecular wave function of H2 using its two 1s orbitals A and B. HA HB a b a b HA HB
Cross-section of wave function

6. VB theory for H2 singlet more stable triplets enhanced! depleted!
electron
density
triplets
depleted!
electron
density

7. Fair-use image from Wikipedia
Covalent bond
electron
density
Enhanced electron density between nuclei shields nucleus-nucleus repulsion. The greater the overlap of two AO’s, the stronger the bond.
Two singlet-coupled (α1β2 − β1α2) electrons for one bond (Lewis structure).
G. N. Lewis
Fair-use image from Wikipedia

8. σ and π bonds σ bond π bond
A π bond is weaker than σ bond because there is less orbital overlap in π.
σ bond
π bond

9. Public image from WikipediaN2
N is (1s)2(2s)2(2px)1(2py)1(2pz)1
N2 forms one σ bond and two π bonds. Altogether three-fold covalent bonds (triple bonds).
Fritz Haber
N2 + 3H2 → 2NH3
Public image from Wikipedia

10. H2O O is (1s)2(2s)2(2px)2(2py)1(2pz)1.
The two unpaired electrons in 2p orbitals can each form a σ bond with H (1s)1.
This explains the HOH angle of near 90º.

11. NH3 N is (1s)2(2s)2(2px)1(2py)1(2pz)1.
The three unpaired electrons in 2p orbitals can each form a σ bond with H (1s)1.
This explains the pyramidal structure with the HNH angle of near 90º.

12. Promotion and hybridization
C (1s)2(2s)2(2px)1(2py)1 is known to form four equivalent bonds as in CH4.
valence 2p 2s 1s
Still not equivalent
Promotion – we invest a small energy in C for a bigger energy gain (4 bonds instead of 2) in CH4

13. sp3 hybridization
From one s and three p orbitals, we form four equivalent bonds by linearly combing (hybridizing) them: z y x
These are orthonormal

14. CH4 With the sp3 hybridization, C is (1s)2(sp3)1(sp3)1(sp3)1(sp3)1.
The four unpaired electrons in the four sp3 orbitals can each form a σ bond with H (1s)1.
This explains the tetrahedron structure of CH4 with the HCH angle of º.

15. sp2 hybridization
From one s and two p orbitals, we form three equivalent bonds by linearly combing them: y x
These are orthonormal

16. Industrial production of ethylene
CH2=CH2
With the sp2 hybridization, C is (1s)2(2pz)1 (sp2)1(sp2)1(sp2)1.
Three unpaired electrons in three sp2 orbitals can each form a σ bond with H(1s)1 or C(sp2)1. C(2pz)1 additionally forms a π bond.
This explains the planar structure of ethylene with the HCH and CCH angles of near 120º.
George O. Curme, Jr.
Industrial production of ethylene
Public image

17. sp hybridization
From one s and one p orbital, we form two equivalent bonds by linearly combing them:
These are orthonormal

18. CHΞCH With the sp hybridization, C is (1s)2(2pz)1(2py)1(sp)1(sp)1.
Two unpaired electrons in two sp1 orbitals can each form a σ bond with H(1s)1 or C(sp)1. C(2pz)1 and (2py)1 form two π bonds.
This explains the linear structure of acetylene.
cf. H2O

19. Lone pairs Revisit H2O. O is (1s)2(2s)2(2px)2(2py)1(2pz)1.
Two unpaired electrons each form a covalent bond: O(2py)1H(1s)1 and O(2pz)1H(1s)1
Two valence electrons that do not participate in chemical bond are called a lone pair: O(2s)2 and O(2px)2.
Lone pairs are part of electron density not shielding nucleus-nucleus repulsion and are also not stabilized by nuclear charges. They are naked electron pairs that repel other lone pairs or bonding electron pairs.

20. Lone pairs in H2O
Two different views of H2O: nonhybridized versus sp3 hybridized
The observed HOH angle is 104.5º, closer to the sp3 picture, suggesting that lone-pair repulsion plays a significant role.
sp3 picture suggests HOH angle ~ 109.5º
Nonhybridization suggests HOH angle ~ 90º

21. Lone pairs in NH3
Two different views of NH3: nonhybridized versus sp3 hybridized
The observed HNH angle is 107º, much closer to the sp3 picture, suggesting that a dominating role of lone-pair repulsion.
sp3 picture suggests HNH angle ~ 109.5º
Nonhybridization suggests HNH angle ~ 90º

22. Lone pairs in H2X
The larger the central atom in the isovalence H2X series, the more widely spread valence p and s orbitals and the smaller the lone-pair repulsions. H2Te has no need to promote and hybridize (HTeH angle of 89.5º) to minimize the lone-pair repulsion, whereas H2O can lower its energy by promoting and hybridizing into sp3 and separating the lone pairs more widely.
H2X
HXH angle
H2O
104.5
H2S
92.2
H2Se
91.0
H2Te
89.5

23. Challenge homework #7
C is (1s)2(2s)2(2px)1(2py)1. Is methylene CH2 bent (nonhybridized p, sp2, sp3) or linear (sp1)?
Find the answer in the following paper and report.
“Methylene: A Paradigm for Computational Quantum Chemistry” by Henry F. Schaefer III, Science, volume 231, page 1100, 7 March 1986.

24. Summary
VB theory is an orbital approximation for molecules. The orbitals used are hydrogenic atomic orbitals.
VB theory explains the Lewis structure (two singlet-coupled electrons – α and β spins – per bond).
This explains σ and π bonds, promotion and spn hybridization, lone pairs.
Lone-pair repulsion is important in determining molecular structures.