Molecular geometry

Chapter Ten

Chemical Bonding II :

Molecular Shapes,

Valence Bond Theory, and Molecular Orbital Theory

TMHsiung ©2014 Chapter 10 Slide 1 of 80

Contents

1.

Artificial Sweeteners: Fooled by Molecular Shape

2.

VSEPR Theory: The Five Basic Shapes

3.

VSEPR Theory: The Effect of Lone Pairs

4.

VSEPR Theory: Predicting Molecular Geometries

5.

Molecular Shape and Polarity

6.

Valence Bond Theory : Orbital Overlap as a

Chemical Bond

7.

Valence Bond Theory: Hybridization of Atomic

Orbitals

8.

Molecular Orbital Theory : Electron Delocalization


1.

Artificial Sweeteners: Fooled by Molecular Shape



The sugar molecule (the key ) enters the active site

(the lock

─ sugar receptor protein) of taste cell, resulting in ion channels opened, nerve signal transmission, and reaching the brain a sweet taste .



Artificial sweeteners such as aspartame and saccharin bind to the active more strongly than sugar.



Similarities in the shape of sucrose and artificial sweeteners give those sweeteners the ability to stimulate a sweet taste sensation.




*****

Valence Shell Electron Pair Repulsion (VSEPR) theory : A theory that allows prediction of the shapes of molecules or polyatomic ion based on the idea that electrons ˗ either as lone pairs or as bonding pairs

˗ repel one another .

•

Electron geometry : The geometrical arrangement of electron groups in a molecule.

•

Molecular geometry : The geometrical arrangement of atoms in a molecule.




VSEPR theory proceeding i) Write a best Lewis structure ii) Determine VSEPR notation :

A X m

E n

:

A: Central atoms

X: Terminal atoms

E: Lone pairs electrons

H

2

O for example:

A X

2

E

2

*****


iii) Determine the electron geometry

*****



An electron group can be:

- either single bond or a multiple bond

- a (resonance) hybrid bond

- a lone pairs of electron

- a unpaired single-electron



Repulsion force in general:

LP vs. LP > LP vs. BP > BP vs. BP

* Lone Pairs (LP), Bonding Pairs (BP)

Angle for repulsion forces : 90 ° > 120 ° > 180 °



For central (interior) atom belong to third-period or higher element with VSEPR notation such as AX

5

,

AX

4

E, AX

3

E

2

, AX

6

, AX

5

E, AX

4

E

2 require an expanded octet such as 3d orbital .



Multiple bond occupy more space than single bond


iv) Determine the molecular geometry

*****



Structures for the central atom without lone-pair electrons ( AX n type ), electron geometry and molecular geometry are identical .



Structures for the central atom with lone-pair electrons ( AX n

E m type ) type), electron geometry and molecular geometry are different .


*****


*****


*****

* Count only electron groups around the central atom. Each of the following is considered one electron group : a lone pair , a single bond , a double bond , a triple bond , or a single electron .


2.

VSEPR Theory: The Five Basic Shapes

( All electrons around the central atom are bonding group )



Two Electron Groups (AX

2

): Linear




Three Electron Groups (AX

3

): Trigonal Planar

TMHsiung ©2014 Chapter 10

* double bond contains more electron density than the single bond

Slide 12 of 80



Four Electron Groups (AX

4

): Tetrahedral



Five Electron Groups (AX

5

): Trigonal Bipyramidal




Six Electron Groups (AX

6

): Octahedral


Example 10.1

VSEPR Theory and the Basic Shapes

Determine the molecular geometry of NO

3

−

.

Solution

NO

3

− has 5 + 3(6) + 1 = 24 valence electrons . The Lewis structure has three resonance structures:

Use any one of the resonance structures to determine the number of electron groups around the central atom. The nitrogen atom has three electron groups .

The electron geometry is trigonal planar :

The molecular geometry is also trigonal planar.


3.

VSEPR Theory: The Effect of Lone Pairs

( Some electrons around the central atom are lone pairs )



Four Electron Groups with Lone Pairs

AX

3

E

AX

2

E

2


* Effect of Lone Pairs on Molecular Geometry




Five Electron Groups with Lone Pairs

AX

4

E

AX

3

E

2

AX

2

E

3




Six Electron Groups with Lone Pairs

AX

5

E

AX

4

E

2


4. VSEPR Theory: Predicting Molecular Geometries

Example 10.2

Predicting Molecular Geometries

Predict the geometry and bond angles of PCl

3

.

Solution

Step 1 PCl

3 has 26 valence electrons .

Lewis structure for the molecule:

Step 2 The central atom (P) has four electron groups .

Step 3 Three of the four electron groups around P are bonding groups and one is a lone pair.

Step 4 The electron geometry is tetrahedral

The molecular geometry is trigonal pyramidal


Example 10.3

Predicting Molecular Geometries

Predict the geometry and bond angles of ICl

4

−

.

Solution

Step 1 ICl

4

− has 36 valence electrons .

Lewis structure for the molecule:

Step 2 The central atom (I) has six electron groups.

Step 3 Four of the six electron groups around I are bonding groups and two are lone pairs.

Step 4 The electron geometry is octahedral

The molecular geometry is square planar .




Representing Molecular Geometries on Paper

Examples:




Predicting the Shapes of Larger Molecules

Example:


Example 10.4

Predicting the Shape of Larger Molecules

Predict the geometry about each interior atom in methanol (CH

3

OH) and make a sketch of the molecule.

Solution

The Lewis structure of CH

3

OH.

Three-dimensional sketch of the molecule:


*****



Memo for VSEPR



Without lone-pair electrons

VSEPR

Notation

AX

2

AX

3

AX

4

AX

5

AX

6

Electron

Geometry

Linear

Trigonal planar

Molecular

Geometry

Linear

Trigonal planar

Tetrahedral Tetrahedral

Trigonal bipyramidal Trigonal bipyramidal

Octahedral Octahedral




With lone-pair electrons

VSEPR

Notation

AX

2

E

AX

3

E

AX

2

E

2

AX

4

E

AX

3

E

2

AX

2

E

3

AX

5

E

AX

4

E

2

Electron

Geometry

Trigonal planar

Tetrahedral

Tetrahedral

Trigonal bipyramidal



Octahedral

Octahedral

*****

Molecular

Geometry

Bent

Trigonal pyramidal

Bent

Seesaw

T-shaped

Linear

Square pyramidal

Square planar


5. Molecular Shape and Polarity



Bond dipole versus Molecular dipole



Bond dipole : A separation of positive and negative charge in an individual bond .



Molecular dipole :

• For diatomic molecule: molecular dipole is identical to bond dipole.

• For a molecule consisted by three or more atoms, molecular dipole is estimated by the vector sum of individual bond dipole moment ( net dipole moment ).




Polar molecule versus Nonpolar molecule



Polar molecule : A molecule in which the molecular dipole is nonzero .



Nonpolar molecule : A molecule in which the molecular dipole is zero .



Molecular p olarity prediction

•

Draw the Lewis structure for the molecule and determine its molecular geometry .

•

Determine if the molecule contains polar bonds by electronegativity values.

•

Determine if the polar bonds add together to form a net dipole moment .




Examples

CO

2

Molecular geometry: linear

(net) dipole moment: m

= 0 D

Nonpolar molecule

*****

TMHsiung ©2014

H

2

O

Molecular geometry: bent

(net) dipole moment: m

= 1.84 D

Polar molecule

Chapter 10 Slide 29 of 80

Example 10.5

Determining if a Molecule Is Polar

Determine if NH

3 is polar .

Solution

Lewis structure:

Determine if the molecule contains polar bonds .

The electronegativities of nitrogen and hydrogen are 3.0 and 2.1, respectively.

Determine if the polar bonds add together to form a net dipole moment . The three dipole moments sum to a net dipole moment.

Ans: The molecule is polar .




Polarity effects of the intermolecular forces

Example 1: For H

2

O

Example 2: Like dissolves like

Polar molecules interact strongly with other polar molecules excluding the nonpolar molecules and separating into distinct regions.




Quantum-Mechanical Approximation Technique



Perturbation theory (used in valence bond theory ): A complex system (such as a molecule) is viewed as a simpler system (such as two atoms) that is slightly altered or perturbed by some additional force or interaction (such as the interaction between the two atoms).



Variational method (used in molecular orbital theory ): The energy of a trial function (educated function) within the Schrodinger equation is minimized.




Schrodinger equation revisited

H



= E



•

H (Hamiltonian operator), a set of mathematical operations that represent the total energy (kinetic and potential) of the electron within the atom.

•

•

E is the actual energy of the electron.

 is the wave function , a mathematical function that describes the wavelike nature of the electron.



Perturbation theory: Approach by small changes to a known system in which Hamiltonian operator is modified.



Variational method: Approach by combining systems of comparable weighting in which wave function is modified.




Valence bond theory versus molecular orbital theory



Valence bond theory (VB): An advanced model of chemical bonding in which electrons reside in quantum-mechanical orbitals localized on individual atoms that are a hybridized blend of standard atomic orbitals ; chemical bonds result from an overlap of these orbitals .



Molecular orbital theory (MO): An advanced model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule. In the simplest version, the molecular orbitals are simply linear combinations of atomic orbitals.


6. Valence Bond Theory: Orbital Overlap as a

Chemical Bond



Valence bond theory describes that covalent bonds are formed when atomic orbitals on different atoms overlap.

 Simple Atomic Orbitals (AO’s) Overlap

Bonding in H

2 for example

• A covalent bond is formed by the pairing of two electrons with opposing spins in the region of overlap of atomic orbitals between two atoms.

• This overlap region has a high electron charge density.

• The overall energy of the system is lowered .



 Acceptable simple Atomic Orbitals (AO’s) Overlap

Bonding in H

2

S for example

• Predicted H˗S˗H angle is 90 o , actual H˗S˗H angle is 92 o , therefore, the simple AO overlap is acceptable for H

2

S molecule.




Unacceptable simple

Atomic Orbitals (AO’s)

Overlap

Example 1: CH

4

C

Example 2: NH

3 and H

2

O

• Ground-state electron configuration of C for example, it should form only

2 bonds

• Actually, the central atom of

H

2

S, H and CH

2

O, NH

3

,

4

, are sp 3 hybridization


7. Valence Bond Theory: Hybridization of Atomic

*****

Orbitals



Hybridization: A mathematical procedure in which standard atomic orbitals are combined to form new, hybrid orbitals .

•

Hybridizing is mixing different types of orbitals in the valence shell to make a new set of degenerate orbitals such as sp, sp 2 , sp 3 , sp 3 d, sp 3 d 2 .

•

Hybrid orbitals minimize the energy of the molecule by maximizing the orbital overlap in a bond.

•

Those central atoms are available hybridized , however, those terminal atoms are supposed to be unhybridized .




General statements regarding hybridization

•

Hybridization is employed for central atom

***** only, thus, the hybrid orbital describes the electron geometry for central atom.

•

Number of hybrid orbitals = Number of standard atomic orbitals combined = Number of

σ bond + Number of lone pairs.

•

Number of hybridization obitals of a central atom = 2 → sp ; = 3 → sp 2 ; = 4 → sp 3 ; = 5 → sp 3 d ; =

6 → sp 3 d 2 .

•

Hybrid orbitals may overlap with standard atomic orbitals or with other hybrid orbitals to form

σ bond

.

•

Molecular geometry is described by the relative atomic position around central atom.


 sp 3 hybridization (C for example) one s orbital with three p orbitals combine to form four sp 3 hybrid orbitals ( degenerate ).



Examples of sp 3 hybridization (for central atom)

Central atom

Molecule

Standard orbitals

Hybrid

Orbital

Geometry

*****

σ σ σ σ

C

N

H

H

C H

H

H

..

N H

H

2s

2s

2p

2p lone sp 3

σ σ σ sp 3 lone lone

σ σ

O H

..

O

..

H 2s

2p sp 3


 sp 2 hybridization (B for example ) one s orbital with two p orbitals combine to form three sp 2 hybrid orbitals


Examples of sp 2 hybridization (for central atom)

Central atom

Molecule

Standard orbitals

Hybrid

Orbital

σ σ σ

Unhybridized

Orbital

*****

B

F B F

F 2s

2p

2p sp 2

σ σ σ π

C

H

C C

H

H

H 2s

2p

2p sp 2 lone

σ σ π

N H

..

N

..

N H 2s

2p sp 2

2p


 sp hybridization (Be for example) one s orbital with one p orbitals combine to form two sp hybrid orbitals


Examples of sp hybridization (for central atom)

Central atom

Molecule

Standard orbitals

Hybrid

Orbital

Unhybridized

Orbital

*****

σ σ

Be Cl Be Cl

2s

2p sp

σ σ

2p

π π

C

H C C H

2s

2p sp

2p


*****



About Multiple Covalent Bond

 σ

(sigma) bond: The first covalent bond formed by end-to-end overlap of standard or hybridized orbitals between the bonded atoms: s + s, s + p, p + p ( end-to-end ), s + hybrid orbital p + hybrid orbital, hybrid orbital + hybrid orbital

 π

(Pi) bond : The second (and third , if present) bond in a multiple bond, results from side-by-side overlap of unhybridized p orbitals : p + p ( side-by-side )



Summary:

Single bonds: one σ bond

Double bond: one σ bond and one π bond

Triple bond: one σ bond and two π bonds




Sigma Bonding and Pi Bonding




VB theory of bonding in ethylene (H

2

C=CH

2

) example of sp 2 hybridization and a double bond

• Lewis structure

• A π-bond has two lobes (above and below plane), but is one bond , side-by-side overlap of 2p–2p


Continued

• All six atoms in

C

2

H

4 lie in the same plane




VB theory of bonding in Acetylene (HC



CH) example of sp hybridization and a triple bond

• Lewis structure

• Two π-bonds from 2p–2p overlap forming a cylinder of πelectron density around the two carbon atoms


Continued




VB theory of bonding in Formaldehyde (H

2

C=O) example of sp 2 hybridization and a double bond

• Lewis structure


Continued

σ σ σ π

• Valence bond model




Bond Rotation

* Rotation around s bond does not require breaking the bond, however, p bond interact above and below the internuclear axis, so rotation around the axis requires the breaking the bond.

* In general, bond energy of p bonds are weaker than that of s bonds because the side-to-side orbital overlap tends to be less efficient than the end-to-end orbital overlap.




cis versus trans Isomers




Expanded Octet hybridization

 sp 3 d hybridization, AsF

5 for example


Continued


 sp 3 d 2 hybridization, SF

6 for example


Continued




*****

Example for hybridization/electron geometry types versus molecular geometry

Example Number of

σ + lone

2

Hybridization sp

4

5 sp sp 3

3 d

VSEPR notation

AX

2

AX

3

AX

2

E

AX

4

AX

3

E

AX

2

E

2

AX

5

AX

4

E

AX

3

E

2

AX

2

E

3

AX

6

AX

5

E

AX

4

E

2

Electron geometry

Linear

Molecular geometry linear

Trigonal planar

Tetrahedral

Trigonal planar

Angular

Tetrahedral

Trigonal pyramidal

Angular

Trigonal bipyramidal Trigonal bipyramidal

Seesaw

T-shaped

Linear

Octahedral Octahedral

Square pyramidal

Square planar

ClBe -Cl

B Cl

3

S O

2

C H

4

N H

3

H

2

O

P Br

5

S F

4

Cl F

3

Xe F

2

S F

6

Br F

5

Xe F

4




Procedure for Hybridization and Bonding

Scheme

*****

1. Write the Lewis structure for the molecule.

2. Use VSEPR theory to predict the electron geometry about the central atom .

3. Select the correct hybridization for the central atom based on the electron geometry .

4. Sketch the molecule , beginning with the central atom and its orbitals. Show overlap with the appropriate orbitals on the terminal atoms.

5. Label all bonds using the

σ or π notation followed by the type of overlapping orbitals.


Example 10.7

Hybridization and Bonding Scheme

Write a hybridization and bonding scheme for acetaldehyde,

Solution

Step 1 Lewis structure

Step 2 The leftmost carbon atom, tetrahedral electron geometry .

The rightmost carbon atom, trigonal planar geometry .

Step 3 The leftmost carbon atom, sp 3 hybridized

The rightmost carbon atom, sp 2 hybridized .


Continued

Step 4 The appropriate orbitals on the terminal atoms.

Step 5 Type of overlapping orbitals.

TMHsiung ©2014 Chapter 10

*****

Slide 65 of 80

8. Molecular Orbital Theory: Electron Delocalization

Chemical Bond



Molecular Orbital (MO) : A model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule .

• The molecular orbitals are linear combinations of atomic orbitals (LCAO) .

• Because the orbitals are wave functions , the waves can combine either constructively or destructively .




MOs formed by combining two 1s AOs




MOs formed by combining two set 2p AOs

 σ

2p and σ

2p

*: end-to-end overlap of

AOs

 π

2p and π

2p

*: side-by-side overlap of

AOs




Summarizing LCAO–MO Theory:

*****

•

The total number of MOs formed from a particular set of AOs always equals the number of AOs in the set.

• When two AOs combine to form two MOs, one MO is lower in energy (the bonding MO ) and the other is higher in energy (the antibonding MO ).

•

When assigning the electrons of a molecule to MOs, fill the lowest energy MOs first with a maximum of two spin-paired electrons per orbital.

•

When assigning electrons to two MOs of the same energy, follow Hund’s rule —fill the orbitals singly first, with parallel spins, before pairing.




Applications of MOs

• Estimate the bond order:

Bond Order (BO) =

(Σ bonding e

– － Σ antibonding e –

)/2

• Predict the existence of molecule

•

Estimating bond length and bond energy

• Predicting magnetic properties

*****




1st Period Homonuclear Diatomic MOs

H

2 and He

2 for example:

σ

1s

*

AOs of H

σ

1s

(two 1s AOs) MOs of H

2

BO = (2−0)/2 = 1

H

2 molecule does exist

Diamagnetic

σ

1s

*

AOs of He

σ

1s

(two 1s AOs) MOs of He

2

*****

BO = (2−2)/2 = 0

He

2 molecule does not exist




2nd Period Homonuclear Diatomic MOs

 Effects of 2 s –2 p

Mixing: Increasing energy difference, decreasing the degree of mixing.


*****

Continued




Predicting magnetic properties by MOs

Lewis structure

..

For O

2

:

..

..

O O

..

 Experiment showed O

2 is paramagnetic



MO prove O

2 have unpaired electrons




2nd Period Heteronuclear Diatomic MOs



NO for example

• Oxygen is more electronegative than nitrogen, so its atomic orbitals are lower in energy than nitrogen’s atomic orbitals.

• The lower energy atomic orbital makes a greater contribution to the bonding molecular orbital and the higher energy atomic orbital makes a greater contribution to the antibonding molecular orbital.




HF for example


Example 10.10

Molecular Orbital Theory

Draw an MO energy diagram and determine the bond order for the N

2

−

Do you expect the

N

2

− bond to be stronger or weaker than in the N diamagnetic or paramagnetic ?

2 ion . molecule ? Is

Solution

The N

2

− ion has 11 valence electrons

(5 for each nitrogen atom plus 1 for the negative charge). Assign the electrons to the molecular orbitals beginning with the lowest energy orbitals and following

Hund’s rule.

The bond order is 2.5, bond order for N

2

N

2

− molecule is 3, the bond is ion has one unpaired electron and is therefore paramagnetic .

weaker .


Example 10.11

Molecular Orbital Theory for Heteronuclear Diatomic

Molecules and Ions

Use molecular orbital theory to determine the bond order of the CN

− ion. Is the ion paramagnetic or diamagnetic ?

Solution

Number of valence electrons

= 4 (from C) + 5 (from N) +

1 (from negative charge) = 10

Write an energy level diagram

Since the MO diagram has no unpaired electrons, the ion is diamagnetic .




Polyatomic Molecules

Example: O

3

Lewis model

Example: C

6

H

6

VB model MO model

TMHsiung ©2014

Lewis model

Chapter 10

MO model

Slide 79 of 80

End of Chapter 10


Molecular geometry

Chapter Ten

Chemical Bonding II :

Molecular Shapes,

Valence Bond Theory, and Molecular Orbital Theory

Contents

End of Chapter 10

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Molecular geometry

Chapter Ten

Chemical Bonding II :

Molecular Shapes,

Valence Bond Theory, and Molecular Orbital Theory

Contents

End of Chapter 10

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