Ch.10 - Molecular Shapes & Valence Bond TheoryWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Molecular Orbital Theory allows us to predict the distribution of electrons within a molecule. This allows us to predict properties such as bond order, magnetism and shape

Molecular Orbital (MO) Theory

Concept #1: Understanding Molecular Orbital Theory

Transcript

We've talked about one theory before, we've talked about VSEPR theory. Remember VSEPR means: valence shell electron pair repulsion and this has to do with molecular geometry. When we draw a compound, the lone pair electrons want more space for themselves, so they push all the other bonds away from them. When we're doing electronic geometry and molecular geometry and drawing Lewis dot structure, we're following VSEPR theory.
Now we're going to talk about the second type of theory, atomic theory or molecular orbital theory. We're going to say in the molecular orbital theory electrons are seen as being delocalized, or spread out over molecule instead of concentrated in a covalent bond.
Let's say we have a compound, hydrogen connected to Cl. Their forming a covalent bond with each other and realize that when it comes to a covalent bond, we have to see it as this, we have two forces basically fighting against each other.
We're going to have a bonding orbital is the region of high electron density between nuclei where a bond forms. The bond that we're forming is forming because we have bonding orbitals connecting together. We're going to say opposed to that, fighting against the bonding orbital, is the anti-bonding orbital. This is the region of zero electron density between the nuclei where a bond cannot form.
What this means is that every time we're forming a covalent bond between nonmetals, there are forces that want to keep the bond together and at the same time there are forces that exist that want nothing but to destroy that bond. These two bonding forces are basically fighting against one another. If bonding forces are greater, the bond forms. If anti-bonding forces are greater, the bond doesn't form. If they're equal the bond doesn't form. We want the bonding forces to always be greater so that a bond can be made.
How do we determine who's greater? The way we determine is by using these and these are our molecular orbital diagrams. I know it sucks, it looks crazy, but you have to memorize them. It's similar to the electron configuration that we learned earlier, except now we're doing molecular orbital electron configurations. But if you remember how to do electron configuration, this is very similar to it.
We're going to say the MO on the left side has atomic orbitals and molecular orbitals. The part that we're really concerned with are the molecular orbitals right here. These atomic orbitals on the left on the right to it, those come from the electron configurations which we use earlier. But it's the central parts of each of these MO diagrams that we're concerned with.
Here's the thing, we're going to say the one on the left deals with hydrogen, H2, to N2 on the periodic table. So hydrogen all the way to nitrogen, deals with the one on the left. The one on the right deals with O2, F2 and Ne2. Basically, for these molecular orbital diagrams, we're dealing with diatomic molecules. Remember, we know that there is only certain types of elements that can be diatomic molecules. Have No Fear Of Ice Cold Beer. That's the sentence we learned to remember the diatomic molecules.
Here's the thing, when we were doing MO theory we're going to treat all these elements whether they're diatomic or not, because neon normally isn't diatomic, but for the molecular orbital diagram, we treat it as though it's diatomic.
This is the way it's going to work. The way we look at this is, technically we start out with s1s because electron configuration begins with one s, but here this molecular orbital diagram shows us 2s at the beginning. This s here means sigma, so sigma 2s.
Here we have an s with a star, so this is sigma star 2s. When we see a star, that star signifies we have anti-bonding, so a star means anti-bonding. Here the 2s, molecular orbital is a bonding orbital and the sigma 2s molecular orbital is anti-bonding orbital.
We then go up to p, 2p. This p means pi. We have a pi 2p molecular bonding orbital, then we have sigma 2p bonding orbital, then we have a pi star, which means anti-bonding, orbitals and a sigma star 2p anti-bonding orbital. We're going to do just like we do with electron configuration to solve this.

In MO theory, electrons are seen as being delocalized or spread out over a molecule instead of concentrated in a covalent bond. 

Example #1: Use a MO diagram to write the electron configuration of each of the following:

C22-

Example #2: Use a MO diagram to write the electron configuration of each of the following:

F2+

Bond Order

Concept #2: Calculating Bond Order

Transcript

So remember, we say that there's Vesper theory and then there's molecular orbital theory, molecular orbital Theory uses these molecular orbital diagrams in order to write the electron configurations of these diatomic compounds, and we're going to say the molecular orbital diagram that we have, the one on the left and the one on the right, can be connected to a new idea bond order. Now, first remember that the one on the Left deals with H2 to N2 and then one on the on the right deals with O2, F2 and Ne2, and we're going to say bond order equals half times the number of electrons in bonding molecular orbitals minus the number of electrons in the anti-bonding molecular orbitals. Remember, the ones with stars are the anti-bonding molecular orbitals, the ones with no stars in them, those are our regular bonding molecular orbitals. Now, we're going to say based on our answers that we get from using this equation, our compound could be stable and exist or it can be unstable and not exist, we're going to say a bond order greater than 0 means that the compound is stable and exists. So, once, we write out the electron configuration using our molecular orbital diagrams, we would then use the bonding order formula, if the answer we get is greater than 0 that compound exists, if we get a bond order equal to 0 then that means the compound is unstable and it does not exist in reality and we're going to say in general the greater the bond order the stronger the bond, this ties into single bonds, double bonds, triple bonds.

So, remember let's say we have two carbons single bonded to each other, we have two carbons double bonded to each other and we have two carbons triple bonded to each other, we would say that the bond order of the two carbons that are single bonded is one, the bond order of the double bond is two because there's two bonds and the bond order of the triple bond is three, triple bonds are stronger than double bonds stronger than single bonds because the more bonds you put on top the more you layer the stronger the bond. So, this has to do a little bit with bond order, we're also going to say that the stronger the bond is the shorter the bond will be. So, although the triple bond is the strongest it's also the shortest. So, you've got to give up something to be that strong of a bond, we're going to say the single bond is the easiest to break but it is the longest and also remember, that if you have a single bond then you have one Sigma bond, if you have a double bond it's one Sigma and one pi, and if you have a triple bond it's one Sigma and two PI's, you always have one Sigma bond it forms the bond that connects the elements, the pi bonds are just overlapping orbitals that protect that Sigma bond, protect that single bond.

By calculating the bond order it is possible to determine the stability of the bonds within a molecule. 

Practice: Use a MO diagram to determine if the following compound exists or not. 

O2 2- and B-

Which statement about bonding molecular orbitals is incorrect? a. Electrons in bonding orbitals tend to stabilize the molecule. b. Only s bonds can result from bonding molecular orbitals. c. In a bonding molecular orbital, the electron density is high between the two atoms. d. Bonding molecular orbitals result from addition of the wave functions of the atomic orbitals. e. The relative numbers of electrons in bonding versus antibonding orbitals determines the overall stability of the molecule.
According to the molecular orbital (MO) theory, overlap of two s atomic orbitals produces which of the following? a) one antibonding molecular orbital and one hybrid orbital b) two antibonding molecular orbitals c) one bonding molecular orbital and one antibonding molecular orbital d) two bonding molecular orbitals and one antibonding molecular orbital e) two bonding molecular orbitals and two antibonding molecular orbitals
How many electrons can be placed into each MO of a molecule?
Draw a picture that shows all three 2p orbitals on one atom and all three 2p orbitals on another atom. Imagine the atoms coming close together to bond.How many 2p bonds can the two sets of 2p orbitals make with each other?
What is a chemical bond according to molecular orbital theory?
What is an antibonding molecular orbital?
When applying molecular orbital theory to heteronuclear diatomic molecules, the atomic orbitals used may be of different energies.If two atomic orbitals of different energies make two molecular orbitals, how are the energies of the molecular orbitals related to the energies of the atomic orbitals?
The organic molecules shown beloware derivatives of benzene in which additional six-membered rings are "fused" at the edges of the hexagons. The compounds are shown in the usual abbreviated method for organic molecules.Benzene, naphthalene, and anthracene are colorless, but tetracene is orange. What does this imply about the relative HOMO-LUMO energy gaps in these molecules? See the "Chemistry Put to Work" box in the textbook on Orbitals and Energy.
For each of these contour representations of molecular orbitals, identify: The type of MO (sigma or pi)
For each of these contour representations of molecular orbitals, identify: The type of MO (sigma or pi)
True or false: Boron contains 2s 22p1 valence electrons, so only one p orbital is needed to form molecular orbitals.
The following is part of a molecular orbital energy-level diagram for MOs constructed from 1s atomic orbitals.What labels do we use for the two MOs shown?
The molecular orbitals depicted below are derived from  n = 2 atomic orbitals. Which is highest in energy?
The molecular orbitals depicted below are derived from  n = 2 atomic orbitals. Which is lowest in energy?
Consider the following electron configuration:(σ3s)2 (σ3s*)2 (σ3p)2 (π3p)4 (π3p*)4Give four species that, in theory, would have this electron configuration.
In which MO is the overlap of atomic orbitals greater, a σ2p or a π2p?
The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.23 in the textbook. Construct a molecular-orbital diagram for a chain containing eight lithium atoms and use it to answer the following questions.How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?
Sketch each molecular orbital.a. σ2sb. σ2s*c. σ2pd. σ2p*e. π2pf. π2p*
Sketch the molecular orbital and label its type (σ or π; bonding or antibonding) that would be formed when the following atomic orbitals overlap. Explain your labels.
Sketch the bonding and antibonding molecular orbitals that result from linear combinations of the 2pz atomic orbitals in a homonuclear diatomic molecule. (The 2pz orbitals are those whose lobes are oriented perpendicular to the bonding axis.) How do these molecular orbitals differ from those obtained from linear combinations of the 2py atomic orbitals? (The 2py orbitals are also oriented perpendicular to the bonding axis, but also perpendicular to the 2pz orbitals.)
Can a molecule with an odd number of electrons ever be diamagnetic? Explain why or why not.
Can a molecule with an even number of electrons ever be paramagnetic? Explain why or why not.
Why are bonding molecular orbitals lower in energy than the parent atomic orbitals?
How many electrons does it take to fill (c) the MOs formed from combination of the 1s orbitals of two atoms?
How many electrons does it take to fill (a) the MOs formed from combination of the 2p orbitals of two atoms;
The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown on the picture below.Choose the correct molecular-orbital diagram for a chain containing six lithium atoms.
Which of the following statements is TRUE?a. When two atomic orbitals come together to form two molecular orbitals, one molecular orbital will be lower in energy than the two separate atomic orbitals and one molecular orbital will be higher in energy than the separate atomic orbitals.b. A bond order of 0 represents a stable chemical bond.c. Electrons placed in antibonding orbitals stabilize the ion/molecule.d. The total number of molecular orbitals formed doesn't always equal the number of atomic orbitals in the set.e. All of the above are true.
For each of these contour representations of molecular orbitals, identify:The atomic orbitals (s or p) used to construct the MO
Which of the following is not addressed by molecular orbital theory?A. magnetic properties of moleculesB. electron partial delocalization / resonanceC. spectral properties of moleculesD. molecular geometry
How many electrons does it take to fill the MOs formed from combination of the 2s orbitals of two atoms?
For each of these contour representations of molecular orbitals, identify:The atomic orbitals (s or p) used to construct the MO
We have learned that the Lewis model portrays a chemical bond as the transfer or sharing of electrons represented as dots. Valence bond theory portrays a chemical bond as the overlap of two half-filled atomic orbitals. What is a chemical bond according to molecular orbital theory?
The electronic band structure of nickel.If the metal were potassium rather than nickel, which bands- 4s, 4p, and/or 3d -would be partially occupied?
How is the number of molecular orbitals approximated by a linear combination of atomic orbitals related to the number of atomic orbitals used in the approximation?
Although I3- is known, F3- is not.Another classmate says F3-– does not exist because F is too small to make bonds to more than one atom. Is this classmate possibly correct?
Which of these molecular electron configurations describe an excited state? Check all that apply.a. (σ1s)2(σ1s*)2(σ2s)2(σ2s*)2(σ2p)2(π2p)4b. (σ1s)2(σ1s*)2(π2p)1c. (σ1s)2(σ1s*)2(σ2s)2(σ2s*)2(σ2p)2(σ2p*)1d. (σ1s)2(σ1s*)2(σ2s)1(σ2s*)1
 All of the following statements concerning molecular orbital (MO) theory are correct EXCEPTa. The Pauli exclusion principle is obeyed.b. Hund’s rule is obeyed.c. The combination of two atomic orbitals creates one molecular orbital.d. A bonding molecular orbital is lower in energy than its parent atomic orbitals.e. Electrons are assigned to orbitals of successively higher energy. 
Sketch each molecular orbital. Choose the appropriate labels to their perspective targets.δ2sδ*2sδ2pπ*2pδ*2pπ2p