Valence bond theory: sticks

no more

Electrons are not simply dots

And bonds are not sticks

Learning objectives

Describe principles of valence bond theory

Predict hybridization of orbitals based on

Lewis dot structures and electronic

geometry

Describe difference between sigma and pi

bonding

Taking it to the next level:

acknowledging orbitals

VSEPR is quite successful in predicting

molecular shapes based on simplistic Lewis

dot approach and repulsion of charge

groups

But orbital model has electrons occupying

atomic orbitals

How do we reconcile the observed shapes

of molecules with the atomic orbital model?

Valence bond theory

Valence bond theory is the simplest approach to an orbital picture of covalent bonds

Valence electrons occupy atomic orbitals (basic s, p, d, f or hybridized versions of them)

Covalent bond is formed by overlap of atomic orbitals containing one electron from each atom

Bonding orbitals contain two electrons paired

Bonding electrons are localized between two atoms

Lone pairs occupy single atomic orbitals, spins paired

Bond strength is proportional to amount of orbital overlap

Shape of molecule determined by geometry of overlapping atomic orbitals

Overlap of two 1s orbitals in H2

This is a visual representation of a

mathematical operation involving the wave

functions of each orbital

Overlap of two 2p orbitals directed along the bond

axis (sigma bond)

Overlap of p and s orbitals

Limits on qualitative approach

Valence bond theory is a mathematical

model that yields bond lengths, bond

energies, and bond angles using the wave

functions of the bonding atoms

Qualitative approach shows the overlap of

atomic orbitals and approximate geometry of

bonds that result

Problems with tetrahedral bonds

In CH4 the bonds are

all equivalent and at

angles of 109.5°

The 2p orbitals in C

are at 90° - far from

optimum for overlap

The ground state

configuration is 2s22p2

Reconcile these facts

with known structure

Hybridization: problem resolved

The wave mechanics permits

mixing atomic orbitals to

produce “hybrid” orbitals

Hybridization alters shape and

energy of original ao’s

In case of C, two 2s and two 2p

are mixed to produce four

homogeneous sp3 hybrid orbitals

sp3 hybridization

Formally, one 2s electron is promoted to empty 2p orbital (energy cost, repaid on bond formation)

The four basis orbitals are then “hybridized” to yield set of four sp3 hybrid orbitals

This is qualitative explanation of a mathematical operation in wave mechanics

Tetrahedral directions and sp3

hybrids

sp3 hybridization

produces four wave

functions that have

greater density along

the tetrahedral bonding

directions

Improves overlap with

atomic orbitals on

bonded atoms

Valence bond picture of CH4

Each C sp3 hybrid contains one electron

Each H 1s contains one electron

Lone pairs occupy sp3 hybrid orbitals

Valence bond picture of the tetrahedral electronic

geometry provides same results for molecules with

lone pairs

Lone pairs occupy same sp3 hybrid orbitals as

bonding pairs

Do molecules with four charge

groups always use sp3 hybrids?

H – S – H bond angle

is 92º

Better result with S – H

bonds using 2p orbitals

rather than sp3 hybrids

(angle is 109.5º)

Bonding orbitals more

“p-like”

Lone pair electrons

more “s-like”

Notes on hybridization

The total number of orbitals is unchanged before and after Four ao’s (s + 3 x p) give four hybrid orbitals (4 x sp3)

Three ao’s (s + 2 x p) give three sp2 hybrids

Two ao’s (s + p) give two sp hybrids

Electron capacity remains unchanged

Unique hybridization scheme for each electronic geometry (five total)

Same hybridization scheme for given electronic geometry

Number of ao’s in hybridization scheme = number of charge groups round central atom

sp hybridization for linear geometry

One s and one p orbital

sp2 hybridization for trigonal planar

One s and two p

orbitals

Sigma and pi bonding

Sigma bonds (along

internuclear axes)

describe electronic

geometry

“Surplus” p orbitals

overlap in parallel

arrangement above

and below internuclear

axis (pi bonds)

Comparison of pi and sigma bonding

Pi bond

Orbital overlap above

and below inter-nuclear

axis

Sigma bond

Orbital overlap along

inter-nuclear axis

Sigma bond slightly

stronger than pi bond

Valence bond picture of ethylene

H2C=CH2

Three sigma bonds

between C and 2 x H + C

Six electrons around C

Pi bond between C and C

Two electrons around C

Two + six = eight (full

octet)

Contrast with Lewis model:

Lewis: 4 dots shared

Valence bond: sigma + pi

bonds

Valence bond picture of acetylene

HC≡CH Sigma bonds between C

and H (purple and blue) and C and C (purple) 4 electrons around C

Two pi bonds between C and C (red) 4 electrons around C

Four + four = eight (complete octet)

Multiple bonds and implications for

structure

Single bond allows rotation about C – C axis

Double bond is rigid

Double bonds and geometrical

isomers

Isomers: same atoms,

different forms

CH2ClCH2Cl has just

one form

CHClCHCl has two

isomers

Expanded octets:

Beyond coordination number 4

Invoke empty d orbitals (impossible for second row elements) One d orbital for trigonal

bipyramidal sp3d

Two d orbitals for octahedral sp3d2

Number of orbitals in hybrid always equals number of charge clouds

Trigonal bipyramid –sp3d

Octahedral –sp3d2

Shortcomings of valence bond

The orbitals are restricted to atoms

Bonds are limited to two atoms

Cannot accommodate the concept of delocalized electrons – bonds covering more than two atoms

Problems with magnetic and spectroscopic properties

Enter the LCAO: Linear Combination of Atomic Orbitals (MO theory)