Lecture 7 – Lewis Structures and Molecular Geometry

Lecture Preview

• What is a Lewis structure and how do we draw them?
• What is molecular geometry and what is VSEPR theory?
• How are Lewis structures and hybridization connected?
• How can we use 3D visualization resources to make our lives easier?

Lecture Content (Part 1)

In the previous lecture, we talked about 3 types of bonding, with covalent bonding being the one with the most concepts to cover.

In this lecture, we will do 3 things.

1. Formalize drawing molecular structures using Lewis structures
2. Predict molecular geometry using VESPR theory.
3. Utilize online resources to visualize 3D structures.

In the end, we will have the following.

Basically, we are getting more context and examples for the previous lecture to work with. We will live with Lewis structures as long as we are dealing with chemistry-related fields, like organic chemistry and biochemistry.

Lewis Structures

We have looked at Lewis structures already in the previous lecture. Just as a refresher, here are some Lewis structures we encountered in the previous lecture.

Those structures are from last lecture. If we look at those structures, we can observe what Lewis structures focus on.

• Lewis structures focus on valence electron activity. Core (non-valence) electrons are not drawn in a Lewis structure because in almost every case, core electrons do not directly participate in chemical reactivity.

• Lewis structures focus on molecules and covalent bonding and hybridization. Each line between atoms denotes 2 electrons – 1 electron from each atom.
  • There are Lewis structures for ionic compounds, but we won’t focus on that.
  • We will talk about how Lewis structures can imply hybridization.

• Lewis structures focus on lone pair electrons. The dots surrounding each atom are unshared (lone) electrons, and they always come in pairs.
  • If there is a situation where there is an odd number of lone electrons, 1 electron will be left out. That 1 electron makes the atom (and the corresponding molecule) a radical.

Although Lewis structures are extremely important in representing molecular structure, they have their disadvantages.

• Lewis structures cannot accurately reflect orbital sharing, especially pi bonding and above.
  • If there is a double bond, we simply draw 2 lines between the atoms. However, if we visualize the double bonding, we would see a sigma bond and a pi bond. The pi bond is not accurately visualized. (Take $O_2$ for example below)

• Lewis structures cannot accurately reflect unpaired lone electrons.
  • Lewis structures prioritize pairing up lone electrons, resulting in almost all unshared electrons being paired up. However, not every lone electrons are paired up. For example, $O_2$, according to its Lewis structure, has all of its electrons paired up. However, $O_2$ sometimes exhibit paramagnetism – a phenomenon only observed when there are unpaired electrons. As a result, Lewis structures do not accurately reflect unpaired lone electrons.

• Lewis structures cannot accurately describe resonance.
  • We will talk about resonance in this lecture, but first keep in mind that Lewis structures do not do resonance justice. It sometimes gives us a false idea that “this molecule looks like this all the time” when in reality “this molecule can be in a variety of conformations, with some being preferred over the others”.

Let’s quickly summarize how Lewis structures can and cannot do.

Despite the shortcomings of Lewis structures, we do not need to worry. Those shortcomings will be at most an inconvenience to us.

Counting Valence Electrons in a Lewis Structure

To correctly draw a Lewis structure, we need to ensure the valence electrons surrounding an atom obey certain rules. And those certain rules require us to count valence electrons surrounding an atom. Before we introduce the rules, let’s learn how to count them.

There are 2 methods of counting – a generous counting method and a less generous counting method.

• In the generous counting method, we count each covalent bond as 2 valence electrons for the atom of choice. Since covalent bonding is about sharing electrons, the shared electrons should be counted as valence electrons. Let’s call this the “total valence electron count” (TC).
• In the less generous counting method, we count each covalent bond as 1 valence electron for the atom of choice. Let’s call this the “formal valence electron count” (FC).

So, if we look at an oxygen molecule, we can count the valence electrons for each oxygen atom.

The Octet “Rule” and Formal Charges

Why do we need 2 different counts? It’s because we have 2 rules we need to follow. And these 2 rules require the 2 counting methods described above. The 2 rules are the octet rule and formal charge rule.

• The octet rule states that the total valence electron count for $C, O, N, F$ should be 8 for almost all circumstances.
  • The total valence electron count for $P, S, Cl, Br, I$ should be 8 for most circumstances.
  • The total valence electron count for $H$ should be 2 in molecules unless it’s a proton (0 total count).
  • Transition metals to not follow this rule.

• The formal charge rule states that the formal charge of most atoms should be 0 or close to 0.
  • We denote formal charge as $q^*$.
  • Transition metals to not follow this rule.

As we can see, the 2 rules are not necessarily “the golden standard” because exceptions are quite common. Consequently, we will view those 2 rules as more of “guidelines” than actual “rules”.

So, what is a formal charge?

Formal charge $q^*$ is a hypothetical charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity. It can be calculated using the following formula:

$q^* = \text{V} – \text{FC}$

which

• $q^*$ denotes the formal charge of an atom
• $\text{V}$ denotes the number of valence electrons of the neutral atom in isolation
• $\text{FC}$ denotes the formal valence electron count of the atom

The reason that we have an asterisk on $q$ is because the formal charge does not represent the actual charge of the atom. The formal charge gives us an idea of electron distribution among a molecule. If the formal charge of an atom is negative, then the electron may distribute more towards said atom. Alternatively, if the formal charge of an atom is positive, then the electron may distribute less around said atom.

We assign formal charges next to the atom, and we circle the charge to indicate that it’s a formal charge rather than an actual one.

With all that said, the priority of those guidelines when drawing Lewis structures are as follows.

• The octet rule has the highest priority. If we can have a Lewis structure with $TC = 8$ for all atoms (and 2 for hydrogen), we will default to that structure as the best Lewis structure. Although there are a good number of exceptions (especially when it comes to transition metals), we will assume said rule applies to $C, H, O, N, F$ and mostly $P, S, Cl, Br, I$.
• When the octet rule is followed, we adjust our Lewis structure to fit the formal charge rule.
  • If all formal charges can be 0, then let them be 0.
  • If there has to be formal charges, then minimize the number of atoms having formal charges.
  • Atoms with higher electronegativity handle negative formal charges better (because they are better at retaining electrons).
  • Adjacent atoms handle opposite formal charges better than those of the same sign (opposite signs compensate each other).

Drawing Lewis Structures

Now that the rules and guidelines are all set, how do we draw a Lewis structure?

We have the following steps to draw a Lewis structure. It’s like an algorithm. Let’s look at $N_2O$ as an example.

• Step 0: This is a preliminary step, but this step sets up a self-check for our Lewis structure. We will count the total valence electrons involved in the molecule (including the charge). Remember, a negative charge means that we need to add valence electrons; a positive charge means that we need to subtract valence electrons.

• Step 1: Identify which atom should be at the center.
  • Usually, the atom that has the most sharable electrons is the central atom.

In this case, nitrogen will be the central atom (3 sharable electrons from nitrogen > 2 sharable electrons from oxygen)

• Step 2: Identify how many electrons can be shared from the branching atoms, and use that to make covalent bonds with the central atom. Also, using the octet rule, fill out the lone pairs for the branching atoms.
  • Since the left nitrogen has 3 sharable electrons, it will make a triple bond. It needs 1 lone pair (2 electrons) to fill the octet.
  • Since the right oxygen has 2 sharable electrons, it will make a double bond. It needs 2 lone pairs (4 electrons) to fill the octet.
  • Don’t worry about the central atom yet.

• Step 3: Look at the central atom, and apply the octet rule on it (unless it’s an exception).
  • If there are too many electrons, break some bonds and move those electrons to the other atom.
  • If there are too few electrons, add lone pairs.
  • In this case, the central nitrogen atom has 2 too many electrons. So, we need to break 1 bond. We can break the N-N bond or the N-O bond.

• Step 4: Calculate the formal charges for each atom.

Atom	V	FC	$q^*$
Left N	5	5	0
Central N	5	4	1+
Right O	6	7	1-

Atom	V	FC	$q^*$
Left N	5	6	1-
Central N	5	4	1+
Right O	6	6	0

• Step 5: Determine which structure of the best according to the guidelines.
  • Since the difference between the 2 structures is where the negative formal charge lands, we can analyze that.
  • Since electronegative atoms handle negative formal charges better, the structure to the left is the best Lewis structure.

• Step 6: This is where we need to use the number from Step 0. Let’s check if our Lewis structure has the same number of valence electrons as the one we calculated from step 0.

$8 \text{ from the covalent bonds } + 8 \text{ from the lone pairs } = 16 \text{ from Step 0}$

After this, we have our Lewis structure for $N_2O$.

This looks like a lot to deal with, but in reality, once we get familiarized with the process, we can streamline this process and pump out Lewis structures very quickly. However, do note that our step-by-step guide here doesn’t work very well with molecules with only 2 atoms. To write a Lewis structure for molecules with 2 atoms, just stick with the sharing orbital diagrams.

Also, here is an extremely important note about Lewis structures.

• The structures in Step 4 are all valid Lewis structures. Some aren’t the best structures, but they are valid structures. When we ask for Lewis structures, we usually ask for the “best” Lewis structure. However, we cannot make this mode of questions restrict our way of viewing other equally valid Lewis structures.
• We will explore this note further when we talk about resonance.

We will focus on a lot of examples in discussion. For now, let’s continue discussing molecular geometry.

Molecular Geometry

Molecular geometry can be nicely predicted by a theory we will be introducing: VSEPR theory.

VSEPR (pronounced “vesper”) is the abbreviation of Valence Shell Electron Pair Repulsion. In this theory, we count the number of electron domains surrounding the atom of interest in the molecule. By figuring out how many electron domains there are, we can predict the molecular (and electron) geometry of the molecule.

• A covalent bond group counts as 1 electron domain. More specifically…
  • Single bonds count as 1 electron domain.
  • Double bonds count as 1 electron domain.
  • Triple bonds count as 1 electron domain as well.
• Lone electron pairs also count.

The gist of this theory is that, since electrons repel each other, the electron pairs will repel each other such that they will be in a position where they are as far from each other as possible, thus determining the geometry.

A quick side note: molecular geometry is not the same as electron geometry. We’ll see the differences soon.

Counting Electron Domains and Predicting Geometry

Let’s explore the possible geometric options using VSEPR. Here’s a brief preview of what we will be discussing. Important and not-very-relevant geometries are labeled. Despite some geometries being labeled as “not very relevant”, we will still occasionally encounter them. So, basic understanding of those geometries is still highly recommended.

When the atom of interest has 2 electron domains:

Here, there is only one possible scenario.

• The atom of interest is covalently bonded to 2 other atoms + 0 lone pairs.
  • In this case, the molecular geometry is linear. To be as far from each other as possible, the 2 other atoms will position themselves at the opposite sides of the atom of interest.
  • As a result, the covalent bonds will be 180 degrees apart.
  • The electron geometry will be linear as well.

Below is an example of a linear molecular geometry – the carbon is attached to 2 oxygens. There are 2 electron domains because there are 2 covalent bond groups (2 double bonds, one on each side).

When the atom of interest has 3 electron domains:

There are 2 scenarios to be considered in this case.

When the atom of interest has 4 electron domains:

There are 3 scenarios in this case.

• The atom of interest is covalently bonded to 2 other atoms + 2 lone pairs.
  • The molecular geometry will be bent, with each covalent bond groups slightly less than 109.5 degrees apart because lone pair electrons have greater repulsion.
  • The electron geometry will still be bent.

When the atom of interest has 5 electron domains:

To be honest here, we would rarely deal with atoms with more than 4 electron domains. We’ll still learn about them, but focus more on the 2, 3, and 4 electron domain geometries.

There are 4 scenarios in this case.

When the atom of interest has 6 electron domains:

There are 5 scenarios in this case.

• The atom of interest is covalently bonded to 4 other atoms + 2 lone pairs.
  • The molecular geometry will be square planar, with covalent bond group angles being 90 degrees apart.
  • The electron geometry will be still be octahedral.

This concludes the list of different geometries detailed by the VSEPR theory. Let’s do a summary, with electron geometries in parenthesis.

As we can see from the numerous structures,

• Molecular geometry focuses on the geometry of covalent bonds.
• Electron geometry focuses on the geometry of covalent bonds + lone pairs.

We want to learn about molecular geometry because it determines the shape of the molecule, which can affect how it fits in with other molecules. We want to learn about electron geometry because it determines how lone pairs are positioned – they can react with other molecules.

Hybridization in VSEPR Theory

Surprisingly, hybridization can also be determined using VSEPR theory. Here is a quick review of hybridization from last lecture. We’ll focus on hybridization between s and p orbitals.

Not surprisingly, we can see the connections between VSEPR theory and hybridization.

• During hybridization, orbitals are hybridized to form orbitals of the same energy level, rearranging electrons. This rearrangement causes electrons to position themselves in different ways to maximize their distance from each other.

Lecture Content (Part 2)

Ideally, there should be around 30-45 minutes left for this lecture. We will be using this time to look at different molecules and their geometries. This part of the lecture will be interactive.

• We will be using https://molview.com to help us draw and visualize molecules.
• While drawing and visualizing, we will document the geometries and hybridization of certain atoms of interest.
  • It is highly encouraged to just drag the 3D model and spin around, looking at the molecule from different views.
  • Try to see how other atoms are geometrically affected from VSEPR theory.
• The same molecules listed here will also be available on the lecture worksheet.

Lewis Structure and Molecular Geometry Exercises

There are 10 Lewis structures listed below. We will be completing the following steps for each Lewis structure.

• Task 1: Draw the Lewis structure on the 2D molecule drawing panel.
  • While copying, observe how the octet “rule” is satisfied.
  • We need to add the hydrogen atoms manually, add formal charges manually, and add lone pairs manually, if applicable. The software doesn’t do it for us.
  • If there is formal charge on an atom, think about why that is the case ($q^* = V – FC$).
  • Don’t worry about the names of the molecules.

• Task 2: Look at the rendered 3D structure on the other panel.
  • Find at least 3 atoms of interest that have at least 2 electron domains (some atoms are labeled already, use the “marker” feature to replicate in the software).
  • Label those atoms of interest, and for each labeled atom, identify the molecular and electron geometry surrounding it, as well as its hybridization.

• Task 3: Go to the lecture worksheet.
  • Document relevant information from Task 1 and Task 2.
  • Try to see if we’re getting more familiar with Lewis structures.

This is one of the many exercises we will do just to get ourselves comfortable with Lewis structures and molecular geometry. We will go through a lot of exercises in upcoming lectures. Those upcoming lectures will, respectively, focus less on introducing new content and more on establishing fundamentals.

For the molecules below, just search it up using the search bar. It will give you the structure. However, add in missing hydrogen atoms and lone pairs if applicable – we haven’t learned how to simplify the structures yet.

Also, for those who are already informed about resonance structure (we’ll talk about it next lecture), don’t worry about it – use electron domains to solve it.

Molecules 7-10 are important biochemical molecules used as medication or found in our bodies.

• Aspirin is an NSAID (non-steroidal anti-inflammatory drug) used for pain relief, anti-inflammatory effects, and blood thinning (antiplatelet properties). It works by inhibiting cyclooxygenase (COX) enzymes, reducing prostaglandin production.

• Penicillin inhibits bacterial cell wall synthesis by targeting the peptidoglycan layer, leading to bacterial death. It laid the foundation for modern antibiotics, with derivatives like amoxicillin and methicillin expanding its spectrum.

• Cortisol is a glucocorticoid hormone that regulates metabolism, immune response, and stress adaptation. It is used medically as hydrocortisone to treat inflammation, allergies, and adrenal insufficiency. It is synthesized from cholesterol, which is the precursor for all steroid hormones (e.g., testosterone, estrogen, aldosterone).

• Dopamine plays a major role in the reward system, affecting motivation, addiction, and learning. Low dopamine levels are associated with Parkinson’s disease and depression. High dopamine activity is linked to schizophrenia and certain addictions.

Getting used to the molecular and electron geometry will be pretty useful in the future, so we will take our time on this part of the lecture.

Summary

This lecture, alongside the previous lecture and the next lecture, is very important for organic chemistry and biochemistry, as well as chemistry in general. We will definitely summarize those lectures together multiple times in the future, so don’t worry about not getting it immediately. We will also provide a lot of practice during lecture time.

Before next lecture, try to see if at least half of the following concepts seem familiar. The concepts listed will be focused more on covalent bonds.