Lecture 24Valence bond theory

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.

Orbital approximation In polyelectron atoms, we used the orbital

approximation – forced 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?

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

Anti-symmetric

Anti-symmetric

Singlet

Triplet more stable

VB theory for H2

Let us construct the molecular wave function of H2 using its two 1s orbitals A and B.

(1) (2) (1) (2)A B

VB theory for H2singlet

more stable

triplet

en n

e

en n e

Covalent bond )1()2()2()1()2()1()2()1( ABBA

(1)Enhanced electron probability density between nuclei (shielding nucleus-nucleus repulsion). The greater the overlap

of two AO’s the stronger the bond.(2)Two singlet-coupled (α1β2−β1α2) electrons for one bond

(Lewis structure).

σ and π bonds A π bond is weaker than σ bond because

there is less orbital overlap in π.

σ bond π bond

N2

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).

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.

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.

Promotion and hybridization C (1s)2(2s)2(2px)1(2py)1 is known to form four

equivalent bonds as in CH4.

1s

2s

2pvalence

1s

2s

2pvalence

Promotion – we invest a small energy in C for a bigger energy gain (4 bonds instead of 2) in CH4

Still not equivalent

sp3 hybridization From one s and three p orbitals, we form four

equivalent bonds by linearly combing them:

xy

z

These are orthonormal

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 precisely 109.47º.

sp2 hybridization From one s and two p orbitals, we form three

equivalent bonds by linearly combing them:

x

y

These are orthonormal

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.

sp hybridization From one s and one p orbital, we form two

equivalent bonds by linearly combing them:

These are orthonormal

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

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 thus not being stabilized by nuclear charges. They are naked electron pairs that repel other lone pairs or bonding electron pairs.

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

sp3 lone pairsp3 lone pair

2s lone pair

2pz lone pair

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

sp3 lone pair2s lone pair

Lone pairs in H2X The larger the central atom in

the isovalence H2X series, the more widely spread valence p and s orbitals become and the lone-pair repulsions decrease. H2Te has no need to promote and hybridize (HTeH angle of 89.5º), whereas H2O gains greatly by promoting and hybridizing into sp3 and separating the lone pairs widely.

H2X HXH angle

H2O 104.5

H2S 92.2

H2Se 91.0

H2Te 89.5

Homework challenge #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.

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.