8.4 Molecular Orbital Theory

Two hybridized, independently of which resonance form is considered.

The formation of sulfuric acid is the result of the reaction of sulfur dioxide with water.

Sulfur dioxide, SO2, is a major component of volcanic gases, as well as a product of the combustion of sulfur-containing coal.

The sulfur atom is surrounded by two bonds and one pair of electrons.

nitric acid, HNO3 is produced by the reaction of nitrogen dioxide, NO2, with atmospheric water vapor.

We can draw the Lewis structure, predict the electron-pair geometry, and come close to predicting bond angles for almost every covalent molecule.

The oxygen molecule O2 has a problem with its Lewis structure.

The electronic structure is in line with the rules of Lewis theory.

Each oxygen atom has eight electrons around it, and there is an O O double bond.
The magnetic behavior of oxygen is at odds with this picture.

O2 is attracted to magnetic fields.

The Lewis structure of O2 indicates that all electrons are pairs.

Magnetic susceptibility is the force experienced by a substance in a magnetic field.

Paramagnetic samples that are attracted to the magnet will appear heavier when compared to the weight measured in a magnetic field.
The increase in weight can be used to calculate the number of unpaired electrons.

A Gouy balance compares the mass of a sample in the presence of a magnetic field with the mass with the electromagnet turned off to determine the number of unpaired electrons.

There are two unpaired electrons in each O2 molecule.

The Lewis-structure model can't predict the presence of unpaired electrons.
In the presence of an inhomogeneous magnetic field, the apparent weight of most Molecules decreases slightly.
Paramagnetic and diamagnetic materials are not permanent magnets.
They can only show attraction or repulsion in the presence of a magnetic field.

Water has all thepaired electrons.

Living things have a large amount of water.
A frog will levitate if it is placed near a large magnet.
There are floating frog, strawberries, and more.

The paramagnetism of the oxygen molecule is explained by chemical bonding in the Mo theory.

It also explains the bonding in a number of other molecules, such as violations of the octet rule and more molecule with more complicated bonding, that are difficult to describe with Lewis structures.
It gives a model for describing the electrons in a molecule and their probable location.
Some substances are electrical conductors, others are semiconductors, and still others are insulators, thanks to MO theory.

The two bonding theories are summarized in Table 8.2.

Both theories give different ways of describing the structure.

Like electrons around isolated atoms, electrons around atoms in Molecules are limited to quantized energies.

When there are two electrons with the same spin, a molecule is full.

There are two identical atoms in a molecule.

There are several types of molecular orbitals in these diatomic molecules.

The wave function shows the wavelike properties of an electron.

There are combinations of atomic wave functions.

The waves are three-dimensional, and they combine with in-phase waves producing regions with a higher probability of electron density.

The orbital is an antibonding one.

The region between the two nuclei is close to the orbitals.
The two nuclei are pulled apart by the attractive force of the electrons.
Just as they fill lower-energy atomic orbitals before they fill higher-energy atomic orbitals, electrons fill the lower-energy bonding orbital before the higher-energy antibonding orbital.

The locations are indicated by the plus signs.

You can watch a visualization of the calculated atomic orbitals.

The phases are indicated by shading the orbital lobes.

Constructive wave interference increases the electron density when the same phase overlaps.

The destructive wave interference causes the regions of opposite phase to overlap.

A higher-energy, antibonding orbital is indicated by the asterisk.

When the p orbital contains electrons, there is a p bond.

The two atoms are held together by the help of electrons in this orbital.
There are two nodal planes created, one along the internuclear axis and the other between the nuclei, for the out-of-phase combination.

Combining the out-of-phase orbitals results in an antibonding orbital.

One is parallel to the axis and the other is not.
A bonding orbital is achieved by combining the in-phase orbitals.

The internuclear axis is located in a blue area near the two lobes of the orbital.

The antibonding orbitals are both degenerate and identical.

Predict what type of orbital would result from adding wave functions so each pair of orbitals shows up.

All of the orbitals have the same energy.

Only the correct alignment of the orbitals can combine.

It is a s orbital because it is located along the internuclear axis.

The internuclear axis is being bisected by an antibonding orbital.

Walter Kohn is a theoretical physicist.

The principles of quantum mechanics are combined with advanced mathematical techniques.
The density functional theory makes it possible to compute the properties of orbitals.
The chemistry prize was won by John Pople and Kohn in 1998 for their contributions to electronic structure.
Significant contributions to the physics of semiconductors were made by Kohn.

Walter Kohn was the first to develop methods to describe the structure of the atom.

He was part of the program that saved 10,000 children from the Nazis during World War II.

He discovered gold deposits in Canada and helped explain how instant film works.
He is still working on projects related to global warming and renewable energy.

There are many practical, real-world applications in the descriptions of bonding described in this chapter.

Drug design uses our understanding of chemical bonding to develop pharmaceuticals.
This area of study uses biology to identify specific targets, such as a binding site that is involved in a disease pathway.
Computational chemists can predict which structures will fit together and how effectively they will bind by modeling the binding site and potential drugs.
Candidate molecules are tested to determine side effects, how effectively they can be transported through the body, and other factors.
Computational chemistry has aided in the discovery of dozens of important new pharmaceuticals.

An important target for pharmaceutical research is the molecule shown.

Scientists have been able to greatly reduce the progress of the disease by designing molecule that bind to thisprotein.

The horizontal lines represent one orbital that can hold two electrons.

The center of the picture shows the combination of the atomic orbitals.
The lines show which of the atomic orbitals are related to each other.
One lower-energy (bonding) molecular orbital and one higher-energy (antibonding) orbital result is required for each pair of atomic orbitals that combine.

The distribution of electrons can be predicted by filling the orbitals in the same way that we fill atomic orbitals.

The OpenStax book is available for free at http://cnx.org/content/col11760/1.9 and each orbital can hold a maximum of two electrons with opposite spins.

Just as we write electron configurations for atoms, we can do the same with the electronic configuration.

For clarity, we place parentheses around the same energy.
parentheses separate each orbital because they are at a different energy.
The core electrons can be omitted from the diagrams and configurations.

The diagram shows the orbitals of the valence shell only.

The same principle and rule are used to fill the molecular orbitals.

The number of electrons in the filled diagram is shown.

Bond order is the number of bonding pairs of electrons between two atoms.

A single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3.
The bond order is usually the same when we use the description of the distribution of electrons.
Both methods describe the same phenomenon, but the MO technique is more accurate and can handle cases when the Lewis structure method fails.

An electron contributes to an antibonding interaction if it occupies an antibonding orbital.

The destabilizing electrons are subtracted from the stabilizing electrons in the advanced theories of covalent bonding.

We divide by two to get the bond order.

A stable bond does not have a bond order of zero if the distribution of electrons in themolecular orbitals between two atoms is such that the resulting bond would have a bond order of two.

The energy of a H2 molecule is lower than that of two H atoms.

A single upward arrow shows one electron in an orbital, and two upward and downward arrows show two electrons of opposite spin, in this configuration.

H2 is predicted to be a stable molecule with lower energy than the separated atoms.

The H-H bond is a single bond because of the bond order being equal to 1.

The stabilizing effect of the two electrons in the lower-energy bonding orbital would be offset by the destabilizing effect of the two electrons in the higher-energy antibonding molecule.

There is no driving force for the formation of the diatomic molecule because of the zero net energy change.

The bond order in a dihelium molecule would be zero.

No bond is formed between two atoms with a bond order of zero.

He2 won't be a stable molecule since it has equal numbers of bonding and antibonding electrons according to the diagram.

The atoms of the second period of the periodic table are Li2, Be2, B2, C2, N2, O2, F2, and Ne2.

The Be2 molecule and Ne2 molecule would not be stable.
We can see this by looking at the electron configurations.

We predict electron configurations of atoms.

The lowest possible energies are assigned to valence electrons.

When there are two or more degenerate molecular orbitals, electrons fill each of them singly before any pairs of electrons take place.

S bonds are more stable than p bonds formed from atomic orbitals.

S orbitals are usually more stable than p orbitals.
This is not always the case.
The generic diagram shown in the previous section is consistent with the Ne2 order.

Adding or subtracting electrons from the diagram for the neutral molecule can be used to get the molecular orbital diagram.

The second period shows the MO diagrams for each diatomic molecule.

The effective nuclear charge increases and the atomic radius decreases.

This can be used to practice labeling and filling.

The result is that the ss orbital becomes more stable and the sp orbital becomes less stable.

The antibonding orbitals also undergo s-p mixing, with the ss* becoming more stable and the sp* becoming less stable.

The MO pattern occurs as expected, with the sp orbital lower in energy than the sp orbitals.

The sp orbital is higher in energy than the pp orbital when s-p mixing occurs.

The pattern where the sp orbital is raised above the pp set is where all of the other period 2 diatomic molecules have s-p mixing.

The Be2 and Ne2 molecule have a bond order of 0 and do not exist.

The two atoms have the same electron.

The Li2 molecule would be stable because both valence electrons were in a bonding orbital.
The molecule is present at a temperature near the boiling point of the element.
The other molecules in Table 8.3 with a bond order greater than zero are also known.

We expect the two electrons that occupy these two degenerate orbitals to be unpaired, and this molecular electronic configuration for O2 is in accord with the fact that the oxygen molecule has two unpaired electrons.

The unpaired electrons of the oxygen molecule provide support for the theory.

The bonding orbital is lower in energy than the original atomic orbitals because they are in-phase.

The antibonding orbital has higher energy than the original atomic orbitals because they are out-of-phase.

There are a lot of atoms in a small sample, and therefore a lot of atomic orbitals that can be combined into a single molecule.

Antibonding orbitals will result.
The allowed energy levels for all the bonding orbitals are so close together that they form a band.
The antibonding orbitals are very close together and form a band.

The orbitals are called bands because they are so close to each other.

The energy of the two bands is lower in the valence band.
The size of the band gap between the two bands determines the type of solid.
Only a small amount of energy is required to move electrons from the valence band to the conduction band in a conductor.
Poor conductors of electricity are caused by the large band gap in an insturment.
Semiconductors conduct electricity better than conductors, but not as well.

In order to conduct electricity, electrons must move from the filled band to the empty band.

The energy difference between the top of the band and the bottom of the band determines how easy it is to move electrons between the bands.
The band gap is small and only a small amount of energy is required in a conductor.
They are good conductors of electricity because of the small energy difference.
Poor conductors of electricity are a result of the band gap being so large that very few electrons move into the band.
Semiconductors conduct electricity when moderate amounts of energy are provided to move electrons out of the valence band and into the conduction band.
Silicon is found in many electronics.

Semiconductors are used in a variety of devices.

Light can move electrons out of the valence band and produce electricity from solar cells.
The generated electricity can be used to power a light or a tool, or it can be stored for later use.
Solar cells can convert up to 42% of the energy in sunlight into electricity.

Draw a diagram of the O2 molecule.

The bond order for O2 can be calculated from this diagram.

The diagram predicts two unpaired electrons.

N2 is the main component of air.

Predict the bond order from the diagram of the N2 molecule.

N2 is diamagnetic and has a bond order of 3.

The ion should be stable since this has six more bonding electrons than antibonding.

The basic ideas of the diatomic examples presented here are used to create molecular orbital diagrams for more than two atoms.

Computers are required to calculate how the atomic orbitals combine with more atoms.

There are three-dimensional drawings of the orbitals for C6H6.

The based on the same energies.

The overlap of two separate atomic orbitals on different atoms creates a region with one pair of electrons shared between the two atoms.

The s bond is formed when the orbitals overlap along an axis.
They form a p bond when they overlap in a fashion.

We can use hybrid orbitals, which are mathematical combinations of some or all of the atomic orbitals, to describe the electron density.

These hybrid orbitals can either be sigma bonds directed toward other atoms of the molecule or lone pairs of electrons.
The geometry of the regions of electron density can be used to determine the type of hybridization around a central atom.

A s bond is located along the axis between two atoms and one or two p bonds.

The s bonds are usually formed by the overlap of hybridized atomic orbitals, while the p bonds are usually formed by the side-by-side overlap of un hybridized orbitals.
When there are multiple un hybridized orbitals, the placement of p bonds can vary.

The behavior of electrons in a molecule in terms of combinations of the atomic wave functions is described in the MO theory.

The atoms in the molecule may be extended over the resulting molecular orbitals.
Bonding molecular orbitals are formed by in-phase combinations of atomic wave functions.
Out-of-phase combinations of atomic wave functions and electrons make a molecule less stable.
The s MOs are located along the internuclear axis.

The electronic structure of diatomic molecules can be described by applying a theory called molecular orbital theory to the electrons of the atoms.

The rules that apply to filling atomic orbitals are the same rules that apply to filling molecular orbitals.
Those with all-paired electrons are repelled by a magnetic field, while materials with unpaired electrons are attracted to it.
Predicting the magnetic properties of the molecule is possible with the help of molecular orbital theory.

Draw a curve that shows the energy of the system at different distances.

The minimum energy of this curve can be found in two ways.

The bonding in F2 is explained by the valence bond theory.

The bonds have an overlap of atomic orbitals.

The bonding in O2 is explained by the valence bond theory.

The bonds in O2 have an overlap of atomic orbitals.

Predict the number of s and p bonds for each molecule by drawing the Lewis structures for CO2 and CO.

There are four different shapes for a molecule with the formula.

Give the shape and the central A atom for each.

CH3SCH2 CH2 CH(NH2CO2H) is an amino acid.

A Lewis structure of this compound can be drawn.

It was thought that the noble gases couldn't form compounds after they were discovered.

We know that the belief is incorrect.

A mixture of xenon and fluorine gases is found to slowly produce a white solid after being placed on a windowsill.
The compound contains 77.55% Xe and 22.45% F.

Consider HNO2 and nitrous acid.

Strike-anywhere matches have a layer of P4S3.

The heat produced by striking the match causes these two compounds to react and set the wooden stem of the match on fire.

There is a ion in 3.

P4S3 has an unusual structure.

The following molecule has a carbon atom.

Write Lewis structures.

On the basis of hybrid orbitals, it's explained that the stable molecules of NF3 and PF3 are not the same molecule as the one that doesn't exist.

N2F4 and N2F2 are fluoro derivatives of nitrogen.

Each bond is created by which orbitals overlap.

The compound acetonitrile, H3CCN, is a useful solvent that can be used to dissolution salts and organic compounds.

It's present in paint strippers.

It's not necessary to hybridize the nitrogen atom.

H2 C + C + CH2 gives the hybridization of each carbon atom in the molecule allene.

The diagram shows how many carbon atom electrons are in each orbital.

Predict the valence electron molecular orbital configurations for the following to see if they will be stable or unstable.

Determine the bond order of each member of the following groups, and determine which member of each group is predicted to have the strongest bond.

Predict if the MO diagram for S2 would show s-p mixing.