Week 9 Hands-On Activity: Advanced WebMO Topics — Molecular Orbitals

5.3.13. Week 9 Hands-On Activity: Advanced WebMO Topics — Molecular Orbitals#

In this activity, you will use WebMO + Gaussian to carry out geometry optimizations and then separate molecular orbital calculations so that you can visualize and interpret canonical Hartree–Fock molecular orbitals. You will begin with H\(_2\), then move to C\(_2\)H\(_4\) (ethylene), and finally apply the same workflow independently to benzene.

5.3.13.1. Motivation#

At this point in the course, you have already used electronic structure methods to compute energies and optimized geometries. A major advantage of these calculations is that they also give access to the molecular orbitals built from the atomic orbital basis set. Visualizing these orbitals helps connect the math of quantum chemistry to chemical ideas you already know:

  • \(\sigma\) bonding vs. \(\pi\) bonding

  • bonding vs. antibonding orbitals

  • core orbitals vs. valence orbitals

  • occupied vs. virtual orbitals

  • how symmetry influences orbital shape

For simple molecules such as H\(_2\), the molecular orbitals are easy to interpret and connect directly to introductory bonding ideas. For larger molecules such as ethylene and benzene, the orbital pictures reveal how C–C \(\sigma\), C=C \(\pi\), C–H \(\sigma\), and \(\pi^\*\) antibonding orbitals emerge from combinations of atomic orbitals.

In our WebMO installation, molecular orbital visualization is most reliable when you first run a geometry optimization and then submit a separate Molecular Orbitals calculation using the optimized structure.

5.3.13.2. Learning Goals#

By the end of this activity, you should be able to:

  1. Build molecules in WebMO and check that the connectivity and geometry are reasonable.

  2. Run a geometry optimization at the HF/6-31G(d) level of theory.

  3. Run a separate Molecular Orbitals calculation starting from the optimized geometry.

  4. Visualize all occupied and several virtual orbitals in WebMO.

  5. Interpret the chemical nature of an orbital from its shape, nodal structure, and localization.

  6. Distinguish among:

    • core orbitals

    • C–H \(\sigma\) bonding orbitals

    • C–C \(\sigma\) bonding orbitals

    • C–C \(\pi\) bonding orbitals

    • antibonding orbitals such as \(\sigma^*\) and \(\pi^*\).

5.3.13.3. Before You Begin#

You will complete the following sequence for each molecule:

  1. Build the molecule

  2. Clean up / adjust the geometry if needed

  3. Submit a Geometry Optimization job at HF/6-31G(d)

  4. Open the completed optimized structure

  5. Submit a second job of type Molecular Orbitals at HF/6-31G(d)

  6. Open the results and visualize each orbital

  7. Record your observations

Important: In our version of WebMO, do not expect the molecular orbitals to be directly visualizable from the geometry optimization job alone. Run the separate Molecular Orbitals job after optimization.

5.3.13.4. Suggested Record-Keeping#

For each molecule, make a small table in your notes with columns such as:

Orbital number

Occupied / virtual

Approximate energy

Description

1

occupied

…

H–H \(\sigma\) bonding

2

occupied

…

C 1s-like core orbital

…

…

…

…

You do not need to memorize a fixed numbering convention across software versions. Instead, focus on the shape and chemical interpretation of each orbital.

5.3.13.5. Part 1. H\(_2\): The Simplest Molecular Orbital Picture#

5.3.13.5.1. Goal#

Use H\(_2\) to identify the basic difference between a bonding and antibonding molecular orbital.

5.3.13.5.2. Step 1. Build H\(_2\)#

  1. Open WebMO.

  2. Create a new job.

  3. Use the molecular builder to draw H\(_2\).

  4. Clean up the structure if needed.

5.3.13.5.3. Step 2. Run a Geometry Optimization#

Set up the job with:

  • Engine: Gaussian

  • Calculation type: Geometry Optimization

  • Method: Hartree–Fock (HF)

  • Basis set: 6-31G(d)

Submit the job and wait for completion.

5.3.13.5.4. Step 3. Run a Separate Molecular Orbitals Calculation#

After the optimization finishes:

  1. Open the optimized H\(_2\) job.

  2. Start a new job from the optimized structure.

  3. Select:

    • Calculation type: Molecular Orbitals

    • Method: HF

    • Basis set: 6-31G(d)

  4. Submit the job.

5.3.13.5.5. Step 4. Visualize the Orbitals#

Open the completed Molecular Orbitals job and inspect the orbitals one by one.

As you view each orbital, ask:

  • Is electron density concentrated between the two nuclei?

  • Is there a node between the nuclei?

  • Is the orbital occupied or unoccupied?

5.3.13.5.6. Questions for H\(_2\)#

Record answers to the following:

  1. How many occupied molecular orbitals does H\(_2\) have?

  2. What is the nature of the lowest-energy occupied orbital?

  3. What is the nature of the first unoccupied orbital?

  4. Which orbital would you call the H–H \(\sigma\) bonding orbital?

  5. Which orbital would you call the H–H \(\sigma^*\) antibonding orbital?

5.3.13.5.7. What You Should Observe#

For H\(_2\), the key ideas are:

  • The lowest occupied MO should be a bonding \(\sigma\) orbital

  • The lowest virtual MO should be an antibonding \(\sigma^*\) orbital

  • The bonding orbital has electron density between the nuclei

  • The antibonding orbital has a node between the nuclei

5.3.13.6. Part 2. C\(_2\)H\(_4\) (Ethylene): Separating \(\sigma\), \(\pi\), Core, and Antibonding Orbitals#

5.3.13.6.1. Goal#

Use ethylene to distinguish among multiple classes of orbitals:

  • carbon core orbitals

  • C–H \(\sigma\) bonding orbitals

  • C–C \(\sigma\) bonding orbital

  • C–C \(\pi\) bonding orbital

  • low-lying antibonding orbitals, especially \(\pi^*\)

5.3.13.6.2. Step 1. Build Ethylene#

Create a new WebMO job and draw C\(_2\)H\(_4\).

Tips:

  • Make sure the molecule is ethylene, not ethane.

  • Confirm there is a C=C double bond.

  • Use a clean planar geometry.

5.3.13.6.3. Step 2. Run a Geometry Optimization#

Use:

  • Engine: Gaussian

  • Calculation type: Geometry Optimization

  • Method: HF

  • Basis set: 6-31G(d)

Submit and wait for the optimized structure.

5.3.13.6.4. Step 3. Run a Molecular Orbitals Calculation#

Start a second job from the optimized structure with:

  • Calculation type: Molecular Orbitals

  • Method: HF

  • Basis set: 6-31G(d)

Submit the job.

5.3.13.6.5. Step 4. Visualize All Orbitals#

Open the molecular orbital results and inspect every occupied orbital plus the first few virtual orbitals.

For each orbital, decide whether it is primarily:

  • localized near one carbon nucleus (core-like)

  • distributed along a C–H bond (C–H \(\sigma\) bonding)

  • concentrated along the C–C internuclear axis (C–C \(\sigma\) bonding)

  • above and below the molecular plane (C–C \(\pi\) bonding)

  • antibonding with a nodal surface (\(\pi^*\) or \(\sigma^*\))

5.3.13.6.6. Ethylene Analysis Prompts#

As you inspect the orbitals, answer the following:

  1. How many occupied orbitals are present?

  2. Which orbital(s) appear to be the carbon 1s core orbitals?

  3. Which occupied orbitals correspond mainly to C–H \(\sigma\) bonding?

  4. Which occupied orbital corresponds mainly to the C–C \(\sigma\) bond?

  5. Which occupied orbital corresponds to the C–C \(\pi\) bond?

  6. What is the nature of the LUMO?

  7. Do the first few virtual orbitals look more like \(\pi^*\) or \(\sigma^*\) orbitals?

5.3.13.6.7. Orbital Interpretation Tips#

Use these visual clues:

  • Core orbitals: very compact and localized close to the carbon nuclei

  • \(\sigma\) orbitals: electron density lies along the line connecting nuclei

  • \(\pi\) orbitals: electron density is above and below the molecular plane, with a nodal plane containing the bonded nuclei

  • Antibonding orbitals: contain additional nodes in the bonding region

5.3.13.7. How to View and Interpret Orbitals in WebMO#

When your Molecular Orbitals job is complete:

  1. Open the job results.

  2. Locate the Molecular Orbitals section in the calculated quantities.

  3. Click the View icon for an orbital, or select orbitals within the molecule viewer.

  4. Rotate the molecule to inspect the orbital from multiple directions.

  5. Compare occupied and unoccupied orbitals.

5.3.13.7.1. Practical Viewing Advice#

  • Rotate the molecule so you can clearly see the bond axis and the molecular plane

  • For ethylene, view the molecule both:

    • edge-on, to highlight the \(\pi\) orbital above/below the plane

    • face-on, to see symmetry and nodal structure

  • It is often helpful to compare:

    • HOMO vs. LUMO

    • occupied \(\pi\) vs. unoccupied \(\pi^*\)

    • bonding vs. antibonding pairs

5.3.13.7.2. What to Pay Attention To#

For each orbital, note:

  • where the orbital is localized

  • whether density lies between nuclei

  • whether a nodal plane or nodal surface is present

  • whether the orbital looks chemically bonding, nonbonding, or antibonding

5.3.13.8. Checkpoint Questions#

Before moving to the assignment, make sure you can answer the following in complete sentences:

  1. Why is the lowest occupied orbital of H\(_2\) considered bonding?

  2. What visual feature distinguishes a bonding orbital from an antibonding orbital?

  3. In ethylene, what visual feature identifies the \(\pi\) bond?

  4. Why are carbon core orbitals easy to distinguish from valence orbitals?

  5. Why is the first unoccupied \(\pi^\*\) orbital in ethylene an antibonding orbital?

You should be ready to explain these using orbital shape and nodal structure, not only by quoting orbital energies.

5.3.13.9. Short Assignment: Benzene Molecular Orbitals#

5.3.13.9.1. Objective#

Apply the same workflow to benzene, C\(_6\)H\(_6\), and interpret the pattern of occupied and low-lying unoccupied molecular orbitals.

5.3.13.9.2. What to Do#

  1. Build benzene in WebMO.

  2. Run a Geometry Optimization at HF/6-31G(d).

  3. Run a second Molecular Orbitals job at HF/6-31G(d) using the optimized structure.

  4. Visualize:

    • all occupied orbitals

    • the first few unoccupied orbitals

5.3.13.9.3. What to Turn In#

Submit a short write-up that includes:

5.3.13.9.3.1. 1. Workflow summary#

State briefly that you:

  • built benzene

  • optimized the geometry

  • ran a separate Molecular Orbitals job

  • visualized the occupied and low-lying virtual orbitals

5.3.13.9.3.2. 2. Occupied orbitals#

Report:

  • the number of occupied orbitals

  • the general types present, such as:

    • carbon core orbitals

    • C–H \(\sigma\) bonding orbitals

    • C–C \(\sigma\) bonding orbitals

    • delocalized \(\pi\) bonding orbitals

5.3.13.9.3.3. 3. Lowest unoccupied orbitals#

Describe the first few unoccupied orbitals and explain why they are identified as \(\pi^\*\) antibonding orbitals.

5.3.13.9.3.4. 4. Orbital interpretation#

In a few sentences, explain:

  • how benzene’s occupied \(\pi\) orbitals differ from its unoccupied \(\pi^\*\) orbitals

  • how delocalization appears in the orbital pictures

5.3.13.9.4. Guiding Questions for Benzene#

Use these questions to structure your write-up:

  1. How many occupied molecular orbitals are there in benzene?

  2. Which occupied orbitals are clearly core orbitals?

  3. Which occupied orbitals are part of the \(\sigma\) framework?

  4. How many occupied orbitals are clearly part of the delocalized \(\pi\) system?

  5. What is the character of the lowest unoccupied orbitals?

  6. Why do the first few virtual orbitals have \(\pi^*\) character rather than looking like localized C–H antibonding orbitals?

5.3.13.9.5. Submission Format#

A concise submission is fine. One to two pages total is enough, provided your descriptions are clear and chemically specific.

5.3.13.10. Optional Extension#

If you finish early, compare the MO pictures of:

  • H\(_2\)

  • ethylene

  • benzene

and comment on how increasing molecular size and conjugation changes the orbital pattern.

In particular, think about:

  • how the number of orbitals grows

  • how \(\pi\) orbitals evolve from localized to delocalized

  • how the virtual orbitals begin to form recognizable antibonding families

5.3.13.11. End-of-Activity Reflection#

After completing the activity, you should be able to answer:

  • What information do molecular orbital pictures add beyond a molecular geometry?

  • Why is a separate MO calculation useful in our version of WebMO?

  • How can you identify a \(\pi\) bonding orbital, a \(\pi^*\) antibonding orbital, and a \(\sigma\) bonding orbital from the picture alone?

These are exactly the kinds of visual and conceptual connections that make computational chemistry useful for interpreting chemical bonding.

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