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-to-head overlap along the internuclear axis, resulting in electron density symmetric around this axis. They can form a π molecular orbital through side-to-side overlap, maintaining their orientation perpendicular to the internuclear axis, with electron density accumulating above and below the axis in case of 2px orbitals or in front and behind the axis in case of 2py orbitals.

Step-by-step solution

Understand 2p orbitals characteristics

2p orbitals have two lobes on opposite sides of the nucleus, with a nodal plane passing through the nucleus where the electron probability is zero. There are three 2p orbitals, one along each of the x, y, and z axes: 2px, 2py, and 2pz. In forming molecular orbitals, the orbitals must have the same energy and proper orientation.

Formation of a sigma (σ) molecular orbital

Sigma (σ) molecular orbitals are formed by the head-to-head (or end-to-end) overlap of two atomic orbitals along their internuclear axis. The electron density is symmetric along this axis. For forming σ molecular orbitals using 2p orbitals, we will consider the overlap of two 2pz orbitals: 1. Consider two atoms A and B, each with a 2pz orbital. 2. Align the internuclear axis (the axis connecting the nuclei of both atoms) along the z-axis. 3. Overlap the 2pz orbital of atom A with the 2pz orbital of atom B along the z-axis in a head-to-head fashion. 4. The resulting electron density will be symmetric around the internuclear axis, forming a sigma (σ) molecular orbital.

Formation of a pi (π) molecular orbital

Pi (π) molecular orbitals are formed by the side-to-side overlap of two atomic orbitals, leading to electron density above and below (or in front and behind) the internuclear axis. For forming π molecular orbitals using 2p orbitals, we will consider the overlap of two 2px and two 2py orbitals: 1. Consider two atoms A and B, each with a set of 2px and 2py orbitals. 2. Align the internuclear axis along the z-axis (we will demonstrate with 2px orbitals, but the process is the same for 2py orbitals). 3. Overlap the 2px orbital of atom A with the 2px orbital of atom B in a side-to-side fashion, maintaining their orientation perpendicular to the internuclear axis. 4. With this side-to-side overlap, electron density will be above and below the internuclear axis, forming a pi (π) molecular orbital. The process for 2py orbitals is the same, with electron density accumulating in front and behind the internuclear axis in the resulting π molecular orbital. In summary, two 2p atomic orbitals can combine to form a σ molecular orbital by head-to-head overlap along the internuclear axis, or a π molecular orbital by side-to-side overlap perpendicular to the internuclear axis.

Key concepts

Atomic Orbitals

Atomic orbitals are regions around an atom's nucleus where there is a high probability of finding electrons. These orbitals come in different shapes and sizes, determined by the quantum numbers. Each type of orbital (s, p, d, f) has a distinct shape. For example, s orbitals are spherical, while p orbitals are dumbbell-shaped, having two lobes.

• In our context, we deal with 2p orbitals, which are one type of p orbital.
• Each p orbital has three orientations: along the x, y, and z axes, known as 2px, 2py, and 2pz.

Atomic orbitals play a crucial role in chemical bonding because they can overlap with orbitals from other atoms to form molecular orbitals, which hold the electrons that glue atoms together in molecules.

Sigma Molecular Orbital

A sigma ( σ) molecular orbital arises from the head-on overlap of two atomic orbitals. This overlap occurs along the internuclear axis, the imaginary line connecting the nuclei of the participating atoms.

• When 2p orbitals from two atoms overlap directly as in the case of 2pz orbitals, they form a sigma molecular orbital.
• The resulting electron density is concentrated along the internuclear axis and is symmetric around it.

Sigma bonds, which are the result of this kind of orbital formation, are generally strong and form the backbone of many molecules, holding the atoms firmly along the internuclear axis.

Pi Molecular Orbital

Pi ( π) molecular orbitals are formed through the side-by-side overlap of two atomic orbitals. The overlap occurs perpendicular to the internuclear axis, leading to electron density regions above and below this axis.

• 2px or 2py orbitals can interact in this manner to form π molecular orbitals.
• For example, with 2px orbitals, the electron clouds overlap sideways, leading to electron density regions above and below the axis between the nuclei.

Pi bonds, stemming from π molecular orbitals, often work alongside sigma bonds to further stabilize molecules, but they are usually weaker than sigma bonds due to the nature of their overlap.

2p Orbitals

2p orbitals are a specific type of atomic orbital, representing the second energy level of p orbitals. They are characterized by having two lobes on opposite sides of an atomic nucleus and a nodal plane through the nucleus where the probability of finding an electron is zero.

• The three 2p orbitals — 2px, 2py, and 2pz — are oriented perpendicular to each other, each along one Cartesian axis.
• They are equal in energy for an isolated atom, a concept known as degeneracy.

2p orbitals are crucial in defining how atoms interact in molecules, allowing for the formation of both σ and π molecular orbitals through their strategic overlaps during bond formation.