• Consider ethylene (also called ethene): C2H4. Draw a Lewis structure, and use it to determine the geometry and hybridization of each of the carbon atoms. How can we describe a double bond in terms of the overlap of orbitals?

Molecular Orbitals

Molecular Orbital (MO) Theory

• Begins with the hypothesis that electrons in atoms exist in atomic orbitals • Assumes that electrons in molecules exist in molecular orbitals

• Rules• Combination of n atomic orbitals (mathematically adding and

subtracting wave functions) provides n MOs (new wave functions)• MOs are arranged in order of increasing energy

• It is possible to calculate reasonably accurate relative energies of a set of molecular orbitals

Molecular Orbital (MO) Theory (continued 1)

• Filling of MOs with electrons is governed by the same rules as for atomic orbitals

• Aufbau principle - Fill MOs beginning with the lowest energy unoccupied molecular orbital

• Pauli exclusion principle - No more than two electrons can be accommodated in a MO, and their spins must be paired

• Hund’s rule - When two or more MOs of equivalent energy are available, add one electron to each before any equivalent orbital is filled with two electrons, and the spins of the single electrons in degenerated orbitals should be aligned.

Molecular Orbital (MO) Theory (continued 2)

• Bonding molecular orbital: MO in which electrons have a lower energy than they would in isolated atomic orbitals

• Sigma (s) bonding molecular orbital: MO in which electron density is concentrated between two nuclei, along the axis joining them and is cylindrically symmetric

• Antibonding molecular orbital: MO in which electrons have a higher energy than they would in isolated atomic orbitals

• Indicated using an asterisk (*)

Features of MO Theory

• Molecular orbitals extend over entire molecules • All the orbitals of all the atoms take part in constructing molecular

orbitals• Molecular orbitals are created by the in-phase and out-of-phase addition of

all the atomic orbitals that are aligned to overlap on all atoms in a molecule

Combining VB and MO Theories

• VB theory views bonding as arising from electron pairs localized between adjacent atoms

• Pairs create bonds• Organic chemists commonly use atomic orbitals involved in three

hybridization states of atoms (sp3, sp2, and sp) to create orbitals that match the experimentally observed geometries

• To create orbitals that are localized between adjacent atoms, atomic orbitals are added and subtracted on the adjacent atoms, which are aligned to overlap each other

Combining VB and MO Theories (continued 1)

• Example - In methane, CH4, the sp3 hybrid orbitals point at the 1shydrogen orbitals, and the atomic orbitals are added and subtracted to create molecular orbitals

• The other resulting MO is higher in energy than the two atomic orbitals and is antibonding

• Only the lower-energy orbital is populated with electrons in methane• Population of the σ bonding orbital results in σ bond between the

C and the H

Figure 1.17 - Molecular Orbital Mixing Diagram for Creation of Any C—H σ bond

Combining VB and MO Theories (continued 2)

• An identical approach used to create C—H σ bonds is used to create C—C σ bonds

• CH3CH3 contains one C—C σ bond and 6 C—H σ bonds

Combining VB and MO Theories (continued 3)

• sp2 hybridization should be considered wherever there is a double bond• Consider ethylene, C2H4

• σ bond between the carbons is formed by overlapping sp2 hybrid orbitals along a common axis

• Each carbon also forms σ bonds with two hydrogens

Figure 1.21 - MO Mixing Diagram for the Creation of Any C—C π Bond

• Pi (π) bonding molecular orbital• MO with a nodal plane that cuts through both atomic nuclei, with

electron density above and below the nodal plane concentrated between the nuclei

Combining VB and MO Theories (continued 4)

• sp hybridization is appropriate wherever there is a triple bond• Example - A carbon-carbon triple bond consists of:

• One σ bond formed by overlapping of sp hybrid orbitals • Two π bonds formed by the overlap of a pair of parallel 2p atomic

orbitals

Molecular Orbitals: H2

Two atomic orbitals are combined, two new molecular orbitals must result. How does this work in forming H2?

H2 and He2

• This molecular orbital treatment can explain why H2 exists but He2 does not. We can define the bond order of a species as: Bond order = 1/2 (electrons in bonding orbitals – electrons in antibonding orbitals)

Phases and Overlap of Orbitals

• Why do both bonding and antibonding orbitals form from the combination of atomic orbitals?

• What is an antibonding orbital, anyway?

Forming σ-bonds From Hybridized Orbitals

• Construct an MO diagram for the C-C σ-bond in methane (CH4).

• Construct an MO diagram for the C-C σ-bond in ethane (C2H6).

Forming π-bonds From “Leftover” p Orbitals

• Construct an MO diagram for the C=C "-bond in ethene (H2C=CH2).

• Draw a complete MO diagram for all the bonds in ethene. What can we say, at this point, about the relative energy levels of the orbitals in this molecule

Energies of Atomic Orbitals

• The left chart shows the approximate energies of orbitals in several of the second- period elements. Can we make any generalizations about the energies of orbitals based on these observations?

• How would the charge on an atom affect the energies of its orbitals?

• To summarize: What are the three factors that will lead to lower orbital energies?

Forming Molecular Orbitals from Atomic Orbitals with Different Energies

• Construct an MO diagram for the C–Cl σ-bond in methyl chloride (CH3Cl):

• Construct an MO diagram for the C=O π-bond in formaldehyde (H2C=O):

• What generalizations can we make about molecular orbitals that are constructed from two atomic orbitals with different energies?

Energies of Molecular Orbitals

• Most organic molecules contain carbon, hydrogen, and several more electronegative elements such as O, N, Cl, Br, etc. In general, the energies of the molecular orbitals in such a molecule will have the following pattern: (X represents an electronegative atom)

• Explain why the energies of the molecular orbitals follow the pattern to the right.

— σ* C–H — σ* C–C — σ* C–X

— π* C=C— π* C=X

— C nonbonding orbital (lone pair OR carbocation)

— X nonbonding orbital (lone pair)

— π C=C— π C=X

— σ C–H — σ C–C — σ C–X

Energy-Level Diagrams for Simple Molecules • Construct an approximate energy-level diagram for acetonitrile, CH3CN, using the

following steps: • Step 1. Draw a complete Lewis structure for the molecule, including all lone pairs. • Step 2. Make a list of all the molecular orbitals in the molecule. Count the orbitals to make

sure that you haven’t forgotten any! (How many molecular orbitals must there be?) • Steps 3&4. Arrange the molecular orbitals in order using the general order on the

previous page. • Step 5. Fill the molecular orbitals with the correct number of electrons. • Step 6. Check your energy-level diagram:

• Does it have the correct number of orbitals?• Does it have the correct number of electrons?• Are all the bonding orbitals filled with electrons? (They should be!) • Are all the antibonding orbitals vacant? (They should be!)• Count the total number of filled bonding orbitals: is that equal to the total number of bonds in the Lewis structure?

What Happens when Two Molecules React? • Consider a general reaction between molecules A and B to yield products C and D:

• Each of the reacting species (A and B) has many molecular orbitals, filled and unfilled. What happens when these two molecules interact (when they come close together)?

There are three basic types of interactions between the orbitals of A and the orbitals of B, depending on whether the orbitals are filled or unfilled. What can we say about these three types of interactions?

filled-filledunfilled-unfilledfilled -unfilled

Frontier Orbitals

Frontier Orbitals: The Importance of the HOMO and LUMO • It turns out that the interaction between orbitals that

are close in energy is more important than the interaction between orbitals that are far apart in energy. Why is this the case?

• Because of the above observation, we can understand most of the reactivity of organic molecules by examining only a small number of orbitals, known as the frontier orbitals. These are:

HOMO (Highest Occupied Molecular Orbital) LUMO (Lowest Unoccupied Molecular Orbital)

• Show the interaction between the HOMO and the LUMO of molecules A and B. Why is this interaction the single most important orbital interaction for these species?

Finding the HOMO and LUMO• Given the order of the energies of molecular

orbitals of organic compounds, we can make some simple generalizations that will help us locate quickly the HOMO and LUMO for a given molecule. What are those generalizations? What should we look for?

• Using those guidelines, find the HOMO and LUMO for the following species:

— σ* C–H — σ* C–C — σ* C–X

— π* C=C— π* C=X

— C nonbonding orbital (lone pair OR carbocation)

— X nonbonding orbital (lone pair)

— π C=C— π C=X

— σ C–H — σ C–C — σ C–X

The Shapes of Frontier Orbitals: Overlap Matters

• Draw “cartoon orbitals” to represent the shapes of the specified orbitals in the following molecules:

the HOMO of CH3OH the HOMO of ethylene (H2C=CH2)

the LUMO of the tert-butyl carbocation ((CH3)3C+)

the LUMO of methyl bromide (CH3Br) the LUMO of formaldehyde (H2C=O)

Molecules with Several Possible Frontier Orbitals• Most organic molecules have several possible HOMO’s and several

possible LUMO’s. Consider the following molecules. Why can’t we simply specify a single HOMO or a single LUMO for these species? Identify all the possible HOMO’s and LUMO’s in these species.

Arrows: Non-bonding HOMO and Non-Bonding LUMO

• For the following species: 1) Identify the possible HOMO’s and LUMO’s2) Select the likely nucleophile and electrophile from these two species 3) Show how these species will react using curved arrows4) Predict the immediate product of that reaction

Arrows: Non-bonding HOMO and Antibonding LUMO

• For the following species: 1) Identify the possible HOMO’s and LUMO’s2) Select the likely nucleophile and electrophile from these two species 3) Show how these species will react using curved arrows4) Predict the immediate product of that reaction

Predicting Reactions Using Frontier Orbitals

• Here are two species you have never seen before. Using Frontier Molecular Orbital Theory (FMO Theory), predict the first step of the reaction between these two species. Draw the curved-arrow mechanism that shows how they react, and predict the immediate product of that reaction.

Functional Groups

Functional Groups

• Atoms or groups of atoms within a molecule that show a characteristic set of physical and chemical properties.

• Why are functional groups important?• Allow the division of organic compounds into classes• Exhibit characteristic chemical reactions• Basis for naming organic compounds

• A major topic for organic chemistry is to study the structure and properties of functional groups.

• A list of major functional groups is on the inside front cover.

Alcohols

• Contain an —OH (hydroxyl) group bonded to a carbon atom with four single bonds

• Classified as primary (1°), secondary (2°), or tertiary (3°) depending on the number of carbon atoms bonded to the carbon bearing the —OH group

Amines

• Contain an amino group, a nitrogen atom bonded to one, two, or three carbon atom(s) by single bonds

• Classified into primary (1°), secondary (2°), and tertiary (3°) amines

Aldehydes and Ketones

• Contain a carbonyl (C═O) group

Carboxylic Acids

• Contain a carboxyl (—COOH) group

Carboxylic Esters

• Derivatives of carboxylic acids in which the carboxyl hydrogen is replaced by a carbon-containing group

• Commonly known as esters

Carboxylic Amides

• Derivatives of carboxylic acids in which the —OH of the carboxyl group is replaced by an amine

• Commonly known as amides

Summary of the Introduction of Functional Groups

Name Structure Example IUPAC Name

Alcohol

Amine

Aldehyde

Ketone

Carboxylic Acid

Carboxylic Ester

Carboxylic Amide