Question

Show how two \(2 p\) atomic orbitals can combine to form a \(\sigma\) or a \(\pi\) molecular orbital.

Short answer

Two 2p atomic orbitals can combine to form a σ molecular orbital through head-on or axial overlapping, such as when two 2p_z orbitals overlap along the z-axis (\( 2p_zA + 2p_zB \rightarrow \sigma_{2p_z} \)). They can also combine to form a π molecular orbital through side-wise or parallel overlapping, such as when two 2p_x orbitals overlap along the x-axis (\( 2p_xA + 2p_xB \rightarrow \pi_{2p_x} \)), or when two 2p_y orbitals overlap along the y-axis (\( 2p_yA + 2p_yB \rightarrow \pi_{2p_y} \)).

Step-by-step solution

Understanding atomic orbitals and molecular orbitals

Atomic orbitals are the regions around the nucleus of an atom where there is a high probability of finding an electron. Molecular orbitals, on the other hand, describe the electron distribution in a molecule. The combination of atomic orbitals forms molecular orbitals when atoms bond together in a molecule.

Introduction to 2p atomic orbitals

The 2p atomic orbitals are part of the second energy level and consist of three orbitals, denoted as 2p_x, 2p_y, and 2p_z. These orbitals have a dumbbell shape and are oriented along the x, y, and z axes, respectively.

Overlapping 2p atomic orbitals to form σ molecular orbitals

The σ molecular orbitals are formed by the head-on or axial overlapping of atomic orbitals. For our case, when two 2p_z atomic orbitals from two different atoms overlap along the z-axis, it results in the formation of a σ molecular orbital. The electron cloud is symmetrically distributed around the internuclear axis. This process can be represented as: \[ 2p_zA + 2p_zB \rightarrow \sigma_{2p_z} \] Here, 2p_zA and 2p_zB represent the 2p_z orbitals from two different atoms A and B, and σ_{2p_z} represents the resulting sigma molecular orbital.

Overlapping 2p atomic orbitals to form π molecular orbitals

The π molecular orbitals are formed by the side-wise or parallel overlapping of atomic orbitals. For our case, when a 2p_x atomic orbital from one atom overlaps with a 2p_x atomic orbital from another atom along the x-axis, it results in the formation of a π molecular orbital. Similarly, the overlapping of two 2p_y atomic orbitals along the y-axis also results in a π molecular orbital. The electron cloud is localized above and below the internuclear axis. This process can be represented as: \[ 2p_xA + 2p_xB \rightarrow \pi_{2p_x} \] and \[ 2p_yA + 2p_yB \rightarrow \pi_{2p_y} \] Here, 2p_xA and 2p_xB represent 2p_x orbitals, and 2p_yA and 2p_yB represent 2p_y orbitals from two different atoms A and B, while π_{2p_x} and π_{2p_y} represent the resulting pi molecular orbitals.

Key concepts

Atomic Orbitals

Atomic orbitals are fundamental to understanding molecular orbitals. They are specific regions around an atom's nucleus where the probability of finding electrons is highest.
Think of atomic orbitals as "homes" where electrons live around an atom. These homes have different shapes and sizes depending on their energy levels, signified by the principal and angular quantum numbers.
Specifically, the 2p atomic orbitals we discuss here belong to the second energy level and come in three different orientations:

• 2p_x
• 2p_y
• 2p_z

Each of these orbitals has a dumbbell shape, showing where you’re likely to find that precious electron. They are aligned along different axes (x, y, and z) relative to the atom's nucleus. When these orbitals come close to orbitals from another atom, they can overlap to form a molecular orbital—becoming the "new homes" for electrons in a molecule.

Sigma Orbitals

Sigma (\( \sigma \)) orbitals form when atomic orbitals overlap head-on. Imagine two atoms getting close enough that their electron "homes"—the orbitals—join directly along the line between their nuclei.
This kind of bonding is strongest when you have axial overlapping. In terms of our 2p orbitals, \(2p_z\) from one atom and \( 2p_z \) from another atom meet directly to form a \( \sigma \) molecular orbital.
The significant feature of a \( \sigma \) orbital is that the electron density is focused along the axis connecting the two nuclei. This alignment gives the \( \sigma \) bond its strength and makes it a key player in the stability of many molecules.
So, when you see a molecular formula with a \( \sigma \) bond, you know the electrons are snugly seated in a direct line within the molecule, contributing to its integrity.

Pi Orbitals

Pi (\( \pi \)) orbitals come into play when atomic orbitals overlap side-by-side. Forget the straightforward head-on overlap; \( \pi \) orbitals are all about a parallel meeting, like two cars driving side-by-side on a pair of parallel roads.
In context, think of two \(2p_x\) or two \(2p_y\) orbitals, which don’t align directly like \( \sigma \) orbitals, but rather overlap above and below the internuclear axis.
This placement means the electron cloud in a \( \pi \) bond sits above and below the nuclei, rather than directly in-between them, leading to different physical and chemical properties. These \( \pi \) bonds are quintessential in double and triple bonds, adding layers of strength and influencing how molecules interact. When two atomic orbitals form a \( \pi \) bond, they create a unique interaction that can greatly affect the molecule's shape and reactivity.