Background Information

In the previous lab, we used molecular modeling software (Avogadro for most of you) to quickly build structures of molecules that would show reasonably correct molecular geometries, including shapes, bond lengths, and distances. We compared the values generated to experimental data, and probably found that molecules were fairly accurate when simple, but errors increased with complexities like more atoms and pi (double) bonds.

The molecular models used in Avogadro and other free modeling tools are generated and optimized using molecular mechanics – in the very simplest version each atom is treated as a single point with a defined charge, and each bond is treated like a spring. Atoms are not single points, they don’t always have fixed charge, and their bonds can be influenced by the rest of the atom. All of these assumptions lead to cumulative errors that can be fairly significant in certain cases.

A much more robust way to model data is to use Molecular Orbitals (MOs), the simplest versions of which we talked about in Chapter 5.4. Molecular Orbitals, like the atomic orbitals we talked about in Chapter 3.1-3.3, must consider how every single electron in a system affects every other electron. We saw that this was impossibly difficult to accomplish with anything more certain than probability densities as soon as we had two electrons, like in Helium. Molecular orbitals generally have at least two electrons and two atoms and are even more complex. We use computational packages to generate molecular orbital information by solving Schrödinger’s equation under a set of assumptions. The nature of these assumptions and the mechanics of the calculation are the subject of Physical Chemistry II or Modern Physics, but we can run the packages and use the orbitals generated to inform our understanding of chemistry right now.

Obviously, we can’t run complex computations every time we want to see whether an atom is likely to have a dipole. Even though we can get better information from Molecular Orbital Theory, models like Valence Bond Theory give us answers that are relatively close most of the time, and way more accessible. Molecular Orbital Theory gives us much better answers when we want to talk about bonds broken and bonds formed, charged species, and anything that has pi-bonds, but we can only use it qualitatively without calculations, like we did in chapter 5.4. This lab gives a first glimpse at how useful the information given by Molecular Orbital Theory can be.

Molecular orbitals are often used to predict reaction energies and directions. Reactions occur when electrons move from one orbital into another to form a new bond. The electrons that are most reactive are the highest energy electrons. We talk about the orbitals that contain electrons as occupied molecular orbitals, the highest energy electrons then are in the Highest energy Occupied Molecular Orbital (HOMO). The orbitals that are empty (unoccupied molecular orbitals) are able to receive electrons, with the Lowest energy Unoccupied Molecular Orbital (LUMO) being the most reactive. This leads to a few key points:

• In general, reactivity can be explained by electrons moving from a HOMO to a LUMO that it can overlap in symmetry. You can see in the figure below that a reaction is allowed if the overlap would be all in phase between overlapping orbitals, but if some would be in phase and some would be out of phase, it would not be allowed.
• When a bonding orbital is the HOMO and contributes electrons to a LUMO, a new bond is formed and the bonding orbital that was the source of the electrons is now empty (a bond is broken).
• When the LUMO is an antibonding orbital, the bond(s) that it is associated with are broken when electrons are added from the HOMO. In the example of the next page, the C-Cl bond is responsible for the LUMO, and will be broken when HO^- reacts.

The interactions between atoms are defined by symmetry – interactions like those shown between the \(\ce{HO^{\text{-}}}\) and the \(\ce{CH3Cl}\) on the above left are all one phase along the bond axis, and are considered to have sigma symmetry (think “s” orbital). Sigma symmetry can interact with symmetry. If the HO^- is trying to interact with the LUMO from on top, as shown in (b), the C-Cl bond has two different phases along the proposed interaction (pi symmetry, like a p-orbital).

In Avogadro, all occupied orbitals get displayed as “HOMO -X”, with the actual HOMO labeled “HOMO” and the next highest energy labeled “HOMO-1”, then “HOMO-2”, etc.

Similarly, all unoccupied orbitals get displayed as “LUMO +X”, with the actual LUMO labeled “LUMO”, and the next lowest energy labeled “LUMO+1”, etc.

In this lab, we will be trying to identify the symmetries of HOMO and LUMO interactions in order to understand the geometry of some common reactions in organic chemistry.

Start by opening the file for ethene, \(\ce{H2C=CH2}\). These files are all generated as “.log”, which will probably not default to opening in Avogadro. It is easier to open Avogadro first and then choose the file. When the file opens, you should have a screen similar to the screen on the right. The HOMO and LUMO and several orbitals above and below are shown in green, which means that the file has already rendered (drawn) those MOs. If you click on that row, the MO will display over the ball and stick model. You can show other rows by clicking them and then clicking “render” on the bottom right. Play around with the controls a little bit and then watch the video attached to this lab about interpreting the MO diagrams.

Fill out the information requested for the actual HOMO and LUMO in each molecule. The first row follows the discussion in the video.

1. Ethene and butadiene react via a reaction process called a “Diels-Alder Reaction”. Compare the energy differences of the LUMO of ethene and the HOMO of butadiene vs the LUMO of Butadiene and the HOMO of ethene. Which is more significant? Which interaction is more likely (Hint: less energy is better and faster)?

2. If adding an atom or group of atoms to butadiene decreased the energy of its LUMO, do you think this reaction would be faster or slower? Why or why not?

3. Draw the LUMO of butadiene or printscreen with a view that clearly shows the symmetry (probably from the side). Draw the HOMO of ethene or printscreen with a view that shows the symmetry (again probably from the side).

4. The first and last carbons for butadiene will interact with the carbons of ethene from either above or below (not straight alongside, since the hydrogens are in the way). Based on the orbital pictures from 2, what symmetry do you expect the interactions to have (remember – sigma has no nodes in the direction of interaction for a circular cross-section, pi has one node for a hamburger-shaped cross-section)?

5. What type of bond would form between the end carbons of the molecules (same as last answer)?

6. The LUMO of butadiene has both bonding and antibonding intereactions. Labelling the carbons 1-4, which carbons have antibonding (out of phase) interactions? Which carbons have bonding interactions?

7. Which bonds do you expect to be broken? Where should there be a new bond formed?

8. The pi electrons in the ethene are part of the HOMO. What does this predict about the second bond of ethene (see bullet points at end of first page)?

9. The Diels-Alder reaction and product is shown below. Does the product shown match what you’d expect for your answers to questions 4-8?

10. For the next questions we’ll be looking at the molecules BH₃ (borane) and isoprene. Compare the energy differences of the LUMO of borane and the HOMO of isoprene vs the LUMO of isoprene and the HOMO of borane. Which is more significant? Which interaction is more likely (Hint: less energy is better and faster)?

11. The LUMO of borane is more or less an empty p-orbital. Isoprene’s HOMO is a full pi-orbital, but its shape is influenced by the adjacent CH₃ groups. Based on the shape of the HOMO, which carbon of isoprene’s double bond has the most electron density with which to interact with borane?

12. The reaction of a double bond, such as that in isoprene is called a “hydroboration” and is fairly selective for which carbon of the double bond gets the boron. A reaction scheme is shown below. Does it match your expectations based on 10 and 11? Why or why not?

This lab is intended to get you thinking about how electron spaces like molecular orbital can shape the reactivity of molecules in preparation for organic chemistry next year. Anytime we use MOs for now, we will continue to walk through each step – what are the HOMO and LUMO that would likely interact? With what symmetry would they interact? Which areas of the molecule are most reactive? How do we see these in the product? We won’t use these except in guided settings until organic chemistry.