Chem 59-651 Bonding in MoleculesCovalent Bonding

Valence state electron configurations and Promotion Energies

Valence electrons and valence shell orbitals - Only valence electrons are used for bonding: ns, np, nd

- “Core” electrons are held too tightly (too low in energy)

- Filled nd orbitals are considered core electrons

- The promotion energy is the energy required to promote electrons from the ground state to a “valence state”, which is one type of excited state configuration that is used for bonding.

2s1 2p32s2 2p2E.g. C

ground state valence state

The term covalent implies sharing of electrons between atoms.

C*

Chem 59-651 Localized Bonding ModelsLocalized implies that electrons are confined to a particular bond or atom.

Octet rule: most main group atoms will tend to end up with an ns2 np6 electron configuration.

This is mostly true for the molecules of organic chemistry not necessarily for inorganic compounds.

The Lewis approach to bondingPairs of electrons are localized in bonds or as non-bonding “lone pairs” on atoms. Each bond is formed by a pair of electrons shared by two atoms.

ns np

G.N. Lewis

Chem 59-651 Rules for drawing Lewis diagrams a. Pick the central atom.

- Atoms that are present only once in the formula, especially heavy elements and metals, tend to be at the center of the structure. - Oxygen is often terminal and hydrogen almost always is. - Often the formula is written with the central atom first. (Sometimes there may be more than one central atom.)

b. Write out the valence shell electron configurations for the neutral central atom and the "terminal" atoms in their ground states.

c. If there is a negative charge distribute it among the terminal atoms in the first instance. Bear in mind that all the terminal atoms must make at least one covalent bond with the central atom, so do not create any noble gas configurations on them. Positive charge is best initially assigned by removing electrons from the central atom.

d. The total number of unpaired electrons on the terminal atoms will have to match the number of unpaired electrons on the central atom to account for the bonds and leave no unpaired electrons. If this is not the case, once the first three steps have been carried out, there are two strategies available:

e. Move electrons between the central atom and the terminal atoms as necessary. Make sure you keep track of the formal charges because you must be specific about their location. Enclosing a Lewis structure in brackets with the charge outside is not acceptable.

f. If and only if the central atom comes from the second period or below (Na onwards, n=3 and up), electrons can be placed into the nd subshell. (Whether the d orbitals play a significant role in bonding in main group compounds is debatable, but they do help to predict correct structure without invoking canonical structures with unreasonable charge separations.)

Chem 59-651 Typical Lewis structural types: Molecules that conform to the “Octet Rule”: saturated molecules

H NH

HH C

H

HH

1s

2s 2p

1s 1s

N

3 H

2s 2p

1s 1s 1s 1s

C

4 H

C*

ground state

valence state

NH3 CH4

These are typical of the molecules of organic chemistry.

Chem 59-651Molecules that conform to the “Octet Rule”: unsaturated molecules.

2s 2pN

Cl

Cl N O

3s 3pO

2s 2p

2s 2pN

N+

NO3-ClNO

O2s 2p

O-

2s 2p

O-

2s 2p

O NO

O

Chem 59-651 ResonanceResonance implies that there is more than one possible way to distribute the valence electrons in a Lewis structure. For an adequate description, each “canonical” structure must be drawn.

O NO

OO N

O

OO N

O

O

If different equivalent resonance structures are possible, the molecule tends to be more stable than one would otherwise expect. This is a quantum mechanical effect that we will talk about later.

O NO

O

Less favourablecanonical structure

I expect you to be able to: Draw Lewis structures (including resonance structures when necessary), determine bond orders, determine and place formal charges.

Chem 59-651 Molecules that don’t conform to the “Octet Rule”:

F ClF

F

H BH

H

Electron-deficient molecules Expanded valence shell molecules

3s 3pCl

Cl*

ClF3

F2s 2p

F2s 2p

F2s 2p

3d2s 2p

1s 1s 1s

B

3 H

B*

BH3

“Hypervalent molecules”“Lewis acids”

Chem 59-651Valence Shell Electron Pair Repulsion Theory

A basic geometry can be assigned to each non-terminal atom based on the number of “objects” attached to it. Objects include bonded atoms (single, double, triple, partial bonds) and “lone pairs” of electrons.

VSEPR theory lets us predict the shape of a molecule based on the electron configurations of the constituent atoms. It is based on maximizing the distance between points on a spherical surface.

Octahedraltrigonal bipyramidal*

tetrahedraltrigonalplanar

linearGeometry

65432Number of Objects

Chem 59-651

AX6

(octahedral)AX5E

(square pyramidal)AX4E2

(square planar)AX3E3

(T-shaped)

AX5

(t.b.p. or square

pyramidal)AX4E

(seesaw)AX3E2

(T-shaped)AX2E3

(linear)

AX4

(tetrahedral)AX3E

(pyramidal)AX2E2

(bent)

AX3

(trig. planar)AX2E(bent)

AX2Formula (Shape)

Octahedraltrigonal bipyramidal

tetrahedraltrigonalplanar

linearGeometry

65432Number of Objects

The geometry around an atom is described by the general formula:

AXmEn

Where X is a bonded atom, E is a lone pair and (m+n) is the number of objects (sometimes called the steric number, SN) around the central atom A.

Chem 59-651

Geometry

Number of Objects

squareanti-prismatic

pentagonalbipyramidal

87

XeF5- NMe4

+

Xe-

F F F F F

Xe is described as AX5E2 and has a pentagonal planar shape derived from the pentagonal bipyramidal geometry.

Less common geometries

Chem 59-651Refinement of VSEPR theory predicted geometries

The relative steric demand of objects is different and amount of repulsion caused by the object will alter the arrangement of the atoms around the central atom.

Incr

easi

ng s

teric

dem

and Lone pair of electrons

Multiple bond polarized toward central atom

Normal single bond

Long single bondpolarized away from central atom

109.5°

106.6°

104.5°

CH4

NH3

OH2

Chem 59-651 Valence Bond TheoryValence bond theory (VBT) is a localized quantum mechanical approach to describe the bonding in molecules. VBT provides a mathematical justification for the Lewis interpretation of electron pairs making bonds between atoms. VBT asserts that electron pairs occupy directed orbitalslocalized on a particular atom. The directionality of the orbitals is determined by the geometry around the atom which is obtained from the predictions of VSEPR theory.

In VBT, a bond will be formed if there is overlap of appropriate orbitals on two atoms and these orbitals are populated by a maximum of two electrons.

σ bonds: symmetric about the internuclear axis

πbonds: have a node on the inter-nuclear axis and the sign of the lobes changes across the axis.

Chem 59-651 Valence Bond Theory Detailed valence bond theory treatment of bonding in H2.

HA 1s1 HB 1s1

φA (1)

Ψ1 = φA(1) φB(2)

VBT considers the interactions between separate atoms as they are brought together to form molecules.

φB (2)

Atomic wavefunction on atom B

electron

Ψ2 = φA(2) φB(1)

Ψ+ = N (Ψ1 + Ψ2) (bonding, H-H)

Ψ- = N (Ψ1 - Ψ2) (anti-bonding)

Quantum mechanics demands that electrons can be interchangeable so we must use a linear combination of Ψ1 and Ψ2.

Ψ3 = φA(1) φA(2) (ionic H- H+)

Ψ4 = φB(1) φB(2) (ionic H+ H-)

Ψmolecule = N [Ψ1 + Ψ2] + (C [Ψ3 + Ψ4])

Ψmolecule = N [Ψcovalent + (C Ψionic)]

N is a normalizing coefficientC is a coefficient related to the amount of ionic character

Chem 59-651 Valence Bond Theory Valence bond theory treatment of bonding in H2 and F2 – the way it is generally used.

HA 1s1 HB 1s1

φA α φB β

This gives a 1s-1s σ bond between the two H atoms.

For VBT treatment of bonding, people generally ignore the anti-bonding combinations and the ionic contributions.

F2s 2p

F2s 2p

2pz 2pz

Z axis

This gives a 2p-2p σ bond between the two F atoms.

Chem 59-651Valence bond theory treatment of bonding in O2

This gives a 2p-2p σ bond between the two O atoms.

O2s 2p

O2s 2p2pz 2pz

Z axis

Z axis

2py 2py

This gives a 2p-2p πbond between the two O atoms. In VBT, πbonds are predicted to be weaker than σbonds because there is less overlap.

The Lewis approach and VBT predict that O2 is diamagnetic –this is wrong!

(the choice of 2py is arbitrary)

O OLewis structure

Double bond: σ bond + πbondTriple bond: σ bond + 2 πbond

Chem 59-651 DirectionalityThe bonding in diatomic molecules is adequately described by combinations of “pure” atomic orbitals on each atom. The only direction that exists in such molecules is the inter-nuclear axis and the geometry of each atom is undefined in terms of VSEPR theory (both atoms are terminal). This is not the case with polyatomic molecules and the orientation of orbitals is important for an accurate description of the bonding and the molecular geometry.

Examine the predicted bonding in ammonia using “pure” atomic orbitals:

H NH

H

1s

2s 2p

1s 1s

N

3 HThe 2p orbitals on N are oriented along the X, Y, and Z axes so we would predict that the angles between the 2p-1s σ bonds in NH3 would be 90°. We know that this is not the case.

106.6°

Chem 59-651 HybridizationThe problem of accounting for the true geometry of molecules and the directionality of orbitals is handled using the concept of hybrid orbitals. Hybrid orbitals are mixtures of atomic orbitals and are treated mathematically as linear combinations of the appropriate s, p and d atomic orbitals.

Linear sp hybrid orbitals

A 2s orbital superimposed on a 2px orbital Ψ1

12

12

= +φ φs p

Ψ212

12

= −φ φs p

The two resultant sp hybrid orbitals that are

directed along the X-axis (in this case)

The 1/√2 are normalization coefficients.

Chem 59-651 Orthogonality and NormalizationTwo properties of acceptable orbitals (wavefunctions) that we have not yet considered are that they must be orthogonal to every other orbital and they must be normalized. These conditions are related to the probability of finding an electron in a given space.

Ψ Ψn m∂τ∫ = 0Orthogonal means that the integral of the product of an orbital with any other orbital is equal to 0, i.e.:

Normal means that the integral of the product of an orbital with itself is equal to 1, i.e.:

where n ≠ m and δτ means that the integral is taken over “all of space” (everywhere).

Ψ Ψn n∂τ∫ = 1

This means that we must find normalization coefficients that satisfy these conditions. Note that the atomic orbitals (φ) we use can be considered to be both orthogonal and normal or “orthonormal”.

Chem 59-651 Example of the orthogonality of Ψ1 and Ψ2

Ψ112

12

= +φ φs p Ψ212

12

= −φ φs p

Ψ Ψ1 212

12

12

12

∂τ φ φ φ φ ∂τ∫ ∫= +

−

s p s p

( ) ( ) ( ) ( )Ψ Ψ1 212

12

12

12

∂τ φ φ ∂τ φ φ ∂τ φ φ ∂τ φ φ ∂τ∫ ∫ ∫ ∫∫= − + −s s s p s p p p

( ) ( ) ( ) ( )Ψ Ψ1 212

1 12

0 12

0 12

1∂τ∫ = − + −

Ψ Ψ1 212

12

0∂τ∫ = − =

Thus our hybrid sp orbitals are orthogonal to each other, as required.

Chem 59-651

2s 2p

1s 1s

Be

2 H

Be*

BeH2

BeH H

HybridizationValence bond theory treatment of a linear molecule: the bonding in BeH2

The promotion energy can be considered a part of the energy required to form hybrid orbitals.

The overlap of the hybrid orbitals on Be with the 1s orbitals on the H atoms gives two Be-H (sp)-1s σ bonds oriented 180° from each other. This agrees with the VSEPR theory prediction.

sp 2p

Be* (sp)

Chem 59-651Valence bond theory treatment of a trigonal planar molecule: the bonding in BH3

H BH

H

2s 2pB

B*

Ψ113

16

12

= − +φ φ φs p px y

Ψ213

16

12

= − −φ φ φs p px y

Ψ313

26

= +φ φs px

This gives three sp2 orbitals that are oriented 120° apart in the xy plane – be careful: the choice of axes in this example determines the set of coefficients.

B* (sp2)sp2 2p

Chem 59-651

1s 1s 1s

3 H

B*

The overlap of the sp2 hybrid orbitals on B with the 1s orbitals on the H atoms gives three B-H (sp2)-1s σ bonds oriented 120° from each other. This agrees with the VSEPR theory prediction.

H BH

H

Valence bond theory treatment of a trigonal planar molecule: the bonding in BH3

sp2 2p

Chem 59-651

H CH

HH

2s 2p

C

C*

Valence bond theory treatment of a tetrahedral molecule: the bonding in CH4

Ψ114

14

14

14

= + + +φ φ φ φs p p px y z

Ψ214

14

14

14

= + − −φ φ φ φs p p px y z

Ψ314

14

14

14

= − − +φ φ φ φs p p px y z

Ψ414

14

14

14

= − + −φ φ φ φs p p px y z

This gives four sp3 orbitals that are oriented in a tetrahedral fashion.

sp3

C* (sp3)

Chem 59-651

2s 2p

1s 1s 1s 1s

C

4 H

C*

Valence bond theory treatment of a tetrahedral molecule: the bonding in CH4

The overlap of the sp3 hybrid orbitals on C with the 1s orbitals on the H atoms gives four C-H (sp3)-1s σ bonds oriented 109.47° from each other. This provides the tetrahedral geometry predicted by VSEPR theory.

HCH

HH

sp3

C* (sp3)

Chem 59-651Valence bond theory treatment of a trigonal bipyramidal molecule:

the bonding in PF53s 3p

P

P*3d

P* (sp3d) 3d

3dz23pz 3py 3px3s sp3dz2

The appropriate mixture to form a trigonal bipyramidal arrangement of hybrids involves all the ns and np orbitals as well as the ndz2

orbital.

PF5 has an VSEPR theory AX5 geometry so we need hybrid orbitals suitable for bonds to 5 atoms. ns and npcombinations can only provide four, so we need to use nd orbitals (if they are available).

Chem 59-651

Ψ113

16

12

= + +φ φ φs p px y

Ψ213

16

12

= + −φ φ φs p px y

Ψ313

26

= −φ φs px

Valence bond theory treatment of a trigonal bipyramidal molecule

These coefficients are exactly the same as the result for the trigonal planar molecules because they are derived from the same orbitals (sp2)

Ψ412

12 2

= +φ φp dz z

Ψ512

12 2

= − +φ φp dz z

These coefficients are similar to those for the sp hybrids because they are formed from a combination of two orbitals (pd).

The orbitals are treated in two different sets.

Remember that d orbitals are more diffuse than s or p orbitals so VBT predicts that the bonds formed by hybrids involving d orbitals will be longer than those formed by s and p hybrids.

Chem 59-651Valence bond theory treatment of a trigonal bipyramidal molecule:

the bonding in PF5

F2s 2p

F2s 2p

F2s 2p

3dP* (sp3d)

F2s 2p

F2s 2p

The overlap of the sp3d hybrid orbitals on P with the 2p orbitals on the F atoms gives five P-F (sp3d)-2p σ bonds in two sets: the two axial bonds along the z-axis (180° from each other) and three equatorial bonds in the xy plane (120° from each other and 90° from each axial bond). This means that the 5 bonds are not equivalent!

Chem 59-651An alternative, and maybe more reasonable, version of VBT

treatment of a trigonal bipyramidal molecule:The d orbitals are too high in energy to mix effectively with the s and p orbitals, so the trigonal bipyramidal molecule is actually composed of an equatorial set of trigonal(sp2) hybrids and the axial bonds come from an MO interaction between the two ligand orbitals and the pz orbital on the central atom.

Ψ112

12

= +φ φp pzFa zFb

Ψ212

12

= −φ φp pzFa zFb

σ φ= +12

121 3Ψ pzP

σ φ* = −12

121 3Ψ pzP

Chem 59-651The square pyramidal AX5 geometry requires mixing with a different d orbital than in the trigonal bipyramidal case.

Sb(C6H5)5

You should consider what orbital(s) would be useful for such a geometry and we will see a way to figure it out unambiguously when we examine the symmetry of molecules.

d orbitals

Chem 59-651Valence bond theory treatment of an octahedral molecule:

the bonding in SF63s 3pS

S*3d

S* (sp3d2) 3d

F F F F F F

The overlap of the sp3d2 hybrid orbitals on S with the 2p orbitals on the F atoms gives six S-F (sp3d2)-2p σ bonds 90° from each other that are equivalent. You can figure out the normalization coefficients. As in the case of the TBP, there is also an MO approach that does not require d orbitals.

3dz23pz 3py 3px3s sp3d23dx2-y2

Chem 59-651

sp2 2pN*(sp2)

Cl

Cl N O

3s 3pO

2s 2p

2s 2pN

Valence bond theory treatment of π-bonding: the bonding in ClNO

πσ σ

NCl O

A drawing of the VBT πbond in ClNO.

There are three “objects” around N so the geometry is trigonal planar. The shape is given by AX2E (angular or bent).

The overlap of the sp2 hybrid orbitals on N with the 3p orbital on Cl and the 2p orbital on O give the two σ bonds and it is the overlap of the “left over” p orbital on N with the appropriate orbital on O that forms the (2p-2p) πbond between the two atoms.

Chem 59-651

2s 2pN

N+

O-

2s 2p

O-

2s 2pO

2s 2p

O NO

O

Valence bond theory treatment of π-bonding: the bonding in the nitrate anion

There are three “objects” around N so the geometry is trigonal planar. The shape is given by AX3 (trigonal planar).

sp2 2pN+*(sp2)

π

σ

σσ

The overlap of the sp2 hybrid orbitals on N with the the 2p orbitals on the O give the three (sp2-2p) σ bonds and it is the overlap of the “left over” p orbital on N with the appropriate orbital on the uncharged O atom that forms the (2p-2p) πbond.

N OOO

VBT gives only one of the canonical structures at a time.

Chem 59-651

2s 2pEach C

Valence bond theory treatment of π-bonding: the bonding in ethene

There are three “objects” around each C so the geometry is trigonal planar at each carbon. The shape is given by AX3 for each carbon.

sp2 2pC*(sp2)

The overlap of the sp2 hybrid orbitals on C with the the 1s orbitals on each H give the four terminal (sp2-1s) σ bonds. The double bond between the C atoms is formed by a (sp2- sp2) σ bond and the (2p-2p) πbond.

C CH

H H

H

1s 1s 1s 1s

4 H

sp2 2p

C*(sp2)

σ σ

σ σ

σ

π

Each C*

C CHH

HH

Chem 59-651Valence bond theory treatment of π-bonding: the bonding in SOCl2

3s 3pS

S*3d

ClSOCl

There are four “objects” around S so the geometry is tetrahedral and the shape is given by AX3E (pyramidal).

sp3 3dS*(sp3)

O2s 2p

Cl ClS

OClCl

σ πσ σ

The overlap of the sp3 hybrid orbitals on S with the 3p orbitals on Cl and the 2p orbital on O give the three σ bonds and, because the lone pair is located in the final sp3 hybrid, it is the overlap of the “left over” d orbital on S with an appropriate p orbital on O that forms the (3d-2p) πbond in the molecule.

Chem 59-651

3s 3pCl

Cl*3d

Valence bond theory treatment of bonding: a hypervalent molecule, ClF3

F ClF

F

3dCl* (sp3d)

F F F

The overlap of the sp3d hybrid orbitals on Cl with the 2p orbitals on the F atoms gives three P-F (sp3d)-2p σ bonds in two sets: the two axial bonds along the z-axis (less than 180° from each other because of the repulsion from the lone pairs) and the one equatorial bond halfway between the other Cl bonds. Again, the bond lengths will not be the same because there is more d contribution to the axial hybrid orbitals.

There are five “objects” around Cl so the geometry is trigonal bipyramidal and the shape is given by AX3E2 (T-shaped). Consider this: Why are such molecules T-shaped instead of pyramidal?

Chem 59-651 Summary of Valence Bond Theory

1. Write an acceptable Lewis structure for the molecule.

2. Determine the number of VSEPR objects around all central atoms and determine the geometry around the atom.

3. Construct hybrid orbitals suitable for the predicted bonding.

4. Link orbitals together to make bonds.

5. Describe the bonding. Include the names of the orbitalsinvolved in each bond. Draw pictures of the bonds formed by the overlap of theseorbitals.

BeH H

Two objects around Be, so AX2 (linear)

Two orbitals pointing 180° from each other needed, so use two sp hybrids

Two (sp-1s) Be-H σ bonds.

Be HH

sp 1s