Molecular Orbital Theory: Videos & Practice Problems

Molecular Orbital Theory explains how valence electrons of atoms combine to form molecular orbitals, which are either bonding or antibonding. Bonding molecular orbitals, symbolized by the sigma (σ) sign, have high electron density that promotes bond formation and increases molecular stability. In contrast, antibonding molecular orbitals, indicated by a sigma star (σ*) sign, possess a node of low electron density that prevents bond formation and decreases stability. Electrons are distributed into these molecular orbitals following the Aufbau principle, Pauli Exclusion Principle—stating each orbital can hold two electrons with opposite spins—and Hund's Rule, which fills degenerate orbitals singly before pairing. This framework is essential for understanding the delocalization of electrons in molecules and the formation of stable chemical bonds.

Electron Orbital Diagrams

Understanding molecular orbital theory begins with a solid grasp of electron orbital diagrams, which illustrate how electrons are arranged in atoms. Electrons fill orbitals according to the Aufbau principle, which dictates the order of filling from lower to higher energy levels, starting with the 1s orbital, followed by 2s, 2p, and so forth.

Each orbital can accommodate a maximum of two electrons, as stated by the Pauli exclusion principle. These two electrons must have opposite spins, represented by one electron spinning up and the other spinning down. This principle is crucial for determining the spin quantum number (m_s), which can take values of +1/2 or -1/2.

Additionally, Hund's rule plays a significant role in the filling of orbitals. It states that when electrons occupy orbitals of the same energy (known as degenerate orbitals), they will first fill each orbital singly with parallel spins before pairing up. For example, in a p orbital, the filling sequence would be up (↑) for each of the three p orbitals before any down (↓) spins are added.

This foundational knowledge of electron configurations and the principles governing them is essential for delving into molecular orbital theory, where the interactions between atomic orbitals lead to the formation of molecular orbitals.

Electron Orbital Diagram Example

The electron orbital diagram for a nitrogen atom, which has an atomic number of 7, illustrates the arrangement of its 7 electrons according to the principles of quantum mechanics. Following the Aufbau principle, electrons fill the lowest energy orbitals first. For nitrogen, the filling sequence begins with the 1s orbital.

In the 1s orbital, two electrons are placed with opposite spins, represented as:

1s² (↑↓)

Next, we move to the 2s orbital, which also accommodates two electrons with opposite spins:

2s² (↑↓)

At this point, we have accounted for 4 electrons (2 in 1s and 2 in 2s). The remaining 3 electrons will occupy the 2p orbitals. According to Hund's rule, which states that electrons will fill degenerate orbitals singly before pairing up, we distribute the next three electrons across the three 2p orbitals:

2p³ (↑ ↑ ↑)

Thus, the complete electron configuration for nitrogen can be summarized as:

1s² 2s² 2p³

This configuration highlights that nitrogen has a total of 7 electrons, with the 2p orbitals being half-filled, which is characteristic of its chemical properties and reactivity.

Atomic Orbitals Example

Molecular orbital theory provides a framework for understanding how atoms combine their electrons to form molecules. When two atoms, such as oxygen, come together, their electron configurations interact, leading to the formation of molecular orbitals. For oxygen, which has an atomic number of 8, the electron configuration is represented as 1s² 2s² 2p⁴.

To visualize this, we can create vertical electron orbital diagrams for two oxygen atoms. Each oxygen atom contributes its own set of orbitals. The 1s orbitals are filled first, with two electrons represented as one up and one down spin (1s²). The 2s orbitals are filled similarly (2s²), followed by the 2p orbitals. Since the 2p orbitals are degenerate, we apply Hund's rule, which states that electrons will fill each orbital singly before pairing up. Thus, for the 2p⁴ configuration, we fill the orbitals as follows: up, up, up, and then down for each of the two oxygen atoms.

At this stage, we have two separate electron orbital diagrams for the oxygen atoms. The next step involves combining these diagrams to form molecular orbitals, which will provide a new description of the electrons in the resulting molecule. This process will reveal how the atomic orbitals merge and what new bonding characteristics emerge from this electron pooling.

Molecular Orbital Diagram

Molecular orbital diagrams are essential for understanding chemical bonding, as they illustrate how valence electrons from atomic orbitals combine to form molecular orbitals. These molecular orbitals arise from the interaction of electrons between two atoms, allowing us to visualize the bonding characteristics of molecules.

To construct a molecular orbital diagram, one must first determine the number of valence electrons for the elements involved. For example, oxygen, which has the electron configuration of 1s² 2s² 2p⁴, possesses 6 valence electrons, as it is located in group 6A of the periodic table.

When filling in the molecular orbital diagram, three fundamental principles guide the process:

• Aufbau Principle: Electrons fill the lowest energy orbitals first before moving to higher energy levels.
• Hund's Rule: For degenerate orbitals (orbitals of the same energy), one electron is placed in each orbital before pairing occurs.
• Pauli Exclusion Principle: No two electrons in the same orbital can have the same spin; they must have opposite spins.

In the case of two oxygen atoms, the filling of molecular orbitals begins with the lowest energy levels. The process involves placing electrons in the molecular orbitals according to the aforementioned principles. Starting with the 1s and 2s orbitals, the electrons are filled as follows:

1. Place one electron in each of the available molecular orbitals until all are half-filled (following Hund's Rule).

2. Once half-filled, begin pairing the electrons in the orbitals, ensuring that each pair has opposite spins (as per the Pauli Exclusion Principle).

For the two oxygen atoms, the filling sequence would result in a total of 8 electrons being distributed across the molecular orbitals. The final arrangement would show the electrons filled in a manner that reflects the bonding characteristics of the oxygen molecule.

As one delves deeper into molecular orbital theory, the complexity and variety of molecular orbitals become more apparent, enhancing our understanding of molecular structure and stability.

Molecular Orbital Theory

When examining the combination of valence electrons between elements, two primary types of molecular orbitals come into play: bonding molecular orbitals and antibonding molecular orbitals. Bonding molecular orbitals are characterized by regions of high electron density between atoms, which facilitate bond formation. In contrast, antibonding molecular orbitals, denoted with an asterisk (*), represent areas of low electron density, also referred to as nodes, that inhibit bond formation.

Understanding the stability of these orbitals is crucial; filled bonding molecular orbitals enhance stability, while filled antibonding molecular orbitals diminish it. This interplay creates a dynamic where one force promotes bond formation, while the other works against it. In a molecular orbital diagram, electrons are described as delocalized, meaning they are spread throughout the molecule rather than localized around individual atoms. Valence electrons from atomic orbitals combine to form these molecular orbitals.

For instance, in the case of hydrogen and helium, their valence electrons occupy 1s atomic orbitals. In a molecular orbital framework, the bonding molecular orbital is represented as σ_1s, while the antibonding molecular orbital is represented as σ_1s* (sigma star 1s). This notation indicates the nature of the molecular orbitals formed from the atomic orbitals of the respective elements. The distribution of electrons from atomic orbitals into these molecular orbitals is essential for understanding molecular bonding and stability.

Molecular Orbital Diagram Example

To construct the molecular orbital diagram for the dihelium cation (He₂⁺), we begin by determining the total number of valence electrons. Each helium atom has an atomic number of 2 and possesses 2 valence electrons. Therefore, for two helium atoms, the total is 2 × 2 = 4 valence electrons. However, since the cation has a +1 charge, indicating the loss of one electron, we are left with 3 valence electrons for He₂⁺.

Next, we construct the molecular orbital diagram by considering the energy levels of the valence electrons. For period 1 elements like helium, we start with the 1s molecular orbitals. The filling of these orbitals follows three key principles: the Aufbau principle, the Pauli exclusion principle, and Hund's rule. According to the Aufbau principle, we fill the molecular orbitals from the lowest energy level to the highest.

With 3 valence electrons, we begin filling the molecular orbitals. The first two electrons will occupy the bonding molecular orbital (σ_1s) with one electron spin-up and one spin-down. The third electron will then occupy the antibonding molecular orbital (σ^*_1s) with a single spin, resulting in a half-filled state.

In summary, the molecular orbital diagram for He₂⁺ will show the bonding molecular orbital σ_1s fully filled and the antibonding molecular orbital σ^*_1s half-filled, reflecting the distribution of the 3 valence electrons.

Here’s what students ask on this topic:

What is molecular orbital theory?

Molecular Orbital Theory (MOT) is a principle for understanding the chemical bonding in molecules. It describes how atomic orbitals combine to form molecular orbitals, which are the energy states of electrons in a molecule. In MOT, when two atoms bond, their atomic orbitals overlap to create molecular orbitals that are spread out over the entire molecule, rather than being localized around individual atoms.

There are two types of molecular orbitals that can form: bonding orbitals, which have lower energy and can lead to a stable bond by housing paired electrons, and antibonding orbitals, which have higher energy and can destabilize a molecule if they contain electrons. Electrons fill the molecular orbitals starting with the lowest energy first, according to the Pauli exclusion principle and Hund's rule. The molecular orbital theory provides a way to predict the arrangement of electrons in molecules, the shape of molecules, bond order, magnetic properties, and the stability of the molecules.

How does molecular orbital theory differ from valence bond theory?

Molecular Orbital (MO) Theory and Valence Bond (VB) Theory are two approaches to understanding the bonding in molecules.

MO Theory views electrons as delocalized over the entire molecule, forming molecular orbitals that can extend over all the atoms in the molecule. These molecular orbitals are formed from the linear combination of atomic orbitals (LCAO), and they can be bonding, antibonding, or non-bonding. Electrons in bonding orbitals stabilize the molecule, while electrons in antibonding orbitals can destabilize it. MO Theory can also explain phenomena like resonance, magnetism, and the color of molecules.

On the other hand, VB Theory describes bonds as localized between pairs of atoms, with electrons shared in the overlapping regions of atomic orbitals. It emphasizes the concept of hybridization, where atomic orbitals mix to form new hybrid orbitals suitable for pairing electrons to form covalent bonds. VB Theory is often used to describe the geometry of molecules and the types of bonds (single, double, triple) between atoms.

In summary, MO Theory gives a more global view of electron distribution in molecules, while VB Theory provides a more localized picture of bonding between atoms.

How do you draw an electron orbital diagram?

To draw an electron orbital diagram, you'll need to represent the electrons and orbitals of an atom according to the principles of quantum mechanics. Here's a step-by-step guide:

1. Determine the number of electrons in the atom by looking at the atomic number on the periodic table.
2. Familiarize yourself with the types of orbitals (s, p, d, f) and their shapes, but for a simple diagram, you'll just need to know the order they fill: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc. This is known as the Aufbau principle.
3. Start filling the orbitals with electrons. Each orbital can hold a maximum of two electrons.
4. Apply Hund's rule: when you're filling orbitals of the same energy (like the three p orbitals), place one electron in each orbital before you start pairing them. Electrons in the same orbital must have opposite spins, represented by arrows pointing up or down.
5. Continue filling until all the electrons are placed in the appropriate orbitals.

Your diagram will consist of a series of lines or boxes that represent orbitals, with arrows indicating the electrons. The lines or boxes are labeled with the corresponding orbital designation (e.g. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.).

How do you draw a molecular orbital diagram?

To draw a molecular orbital (MO) diagram, follow these steps:

1. Count the valence electrons of the atoms involved in the molecule.
2. Draw the atomic orbitals for each atom. For diatomic molecules, you'll typically deal with 's' and 'p' orbitals.
3. Combine the atomic orbitals to form molecular orbitals. Each atomic orbital can combine with another to form one bonding (lower energy) and one antibonding (higher energy) molecular orbital.
4. Fill the molecular orbitals with the total number of valence electrons, following Hund's rule and the Pauli exclusion principle. Start from the lowest energy level up, and each orbital can hold two electrons with opposite spins.
5. For heteronuclear diatomic molecules, consider the difference in electronegativity between the atoms, which affects the energy levels of the molecular orbitals.
6. Once filled, count the electrons in bonding and antibonding orbitals to determine the bond order: (bonding electrons - antibonding electrons) / 2.
7. The bond order gives you an indication of the stability of the molecule; a higher bond order generally means a stronger bond.

Remember that the specific details can vary depending on the complexity of the molecule, but these steps provide a general framework for constructing a molecular orbital diagram.