Question

Which of the following pairs of atomic orbitals of adjacent nuclei can overlap to form a sigma bond? Which overlap to form a pi bond? Which cannot overlap (no bond)? Consider the \(x\) axis to be the internuclear axis, that is, the line joining the nuclei of the two atoms. (a) \(1 s\) and \(1 s,\) (b) \(1 s\) and \(2 p_{x},\) (c) \(2 p_{x}\) and (f) \(1 s\) and \(2 s\) s. \(2 p_{y},\) (d) \(3 p_{y}\) and \(3 p_{y}\) (e) \(2 p_{x}\) and \(2 p_{x}\)

Short answer

(a), (b), (c), and (f) form sigma bonds; (d) and (e) form pi bonds.

Step-by-step solution

Understanding Orbital Overlap

Atomic orbitals can overlap in two main ways: end-to-end to form sigma (σ) bonds or side-to-side to form pi (π) bonds. Sigma bonds are generally stronger as they involve direct overlap, allowing electron density to be directly between the nuclei. Pi bonds involve side-to-side overlap and are weaker because the overlap is less effective.

Examining Option (a): 1s and 1s

The two 1s orbitals on adjacent nuclei can overlap directly along the internuclear axis to form a sigma bond. As spheres, 1s orbitals provide good electron density overlap, forming a stable sigma bond.

Analyzing Option (b): 1s and 2pₓ

A 1s orbital and a 2pₓ orbital can overlap along the internuclear axis. The 2pₓ orbital has a lobe aligned on the x-axis, enabling end-to-end overlap and forming a sigma bond.

Checking Option (c): 2pₓ and 2pₓ

Two 2pₓ orbitals on adjacent nuclei overlap end-to-end along the x-axis. This direct overlap forms a sigma bond since both lobes of the 2pₓ orbitals are aligned with the internuclear axis.

Considering Option (d): 2p_y and 2p_y

2p_y orbitals are oriented perpendicular to the internuclear (x) axis and hence overlap side-to-side rather than end-to-end. This side-to-side overlap forms a pi bond.

Evaluating Option (e): 3p_y and 3p_y

Similar to option (d), 3p_y orbitals overlap perpendicularly to the x-axis. Such lateral overlap creates a pi bond.

Exploring Option (f): 1s and 2s

Both 1s and 2s orbitals are spherical and can overlap directly as their 's' character facilitates head-on overlap along the internuclear axis, resulting in a sigma bond.

Key concepts

Sigma Bond

A sigma (\(\sigma\)) bond forms from the end-to-end overlap of atomic orbitals. This type of bond involves a head-on approach, allowing for a strong overlap, typically resulting in a direct and stable chemical connection between the two atoms. Sigma bonds are the most common type of covalent bonds found in molecules. The strength of these bonds comes from the fact that the electron density is concentrated directly between the nuclei of the two bonded atoms, facilitating a strong attraction.

• Direct Overlap: The orbitals overlap along the internuclear axis (usually denoted as the x-axis), which is the imaginary line connecting the centers of two atoms in a molecule.


• Involved Orbitals: Common examples include overlapping s orbitals with s orbitals, s orbitals with p orbitals, or p orbitals with p orbitals along the axis.


• Examples: Two 1s orbitals overlapping, as seen in hydrogen molecules, inevitably form a sigma bond.

Pi Bond

Pi (\(\pi\)) bonds arise from the side-to-side overlap of atomic orbitals. Unlike sigma bonds, which align along the internuclear axis, pi bonds occupy a region above and below this axis. This type of overlap typically involves p orbitals that are oriented perpendicular to the axis of the sigma bond that it accompanies.

• Weaker Overlap: Because the overlap occurs in a less direct manner (laterally rather than head-on), the resulting bond is generally weaker than a sigma bond.


• Orbitals Involvement: The p orbitals participating in pi bonds are usually parallel, allowing for the necessary sideways overlap. Particularly, p_y or p_z orbitals overlap in this manner.


• Characteristics: Pi bonds are always found in conjunction with a sigma bond in double and triple bonds. For instance, in ethene, each double bond comprises one sigma and one pi bond.

Internuclear Axis

The internuclear axis is an imaginary line that connects the centers (nuclei) of two atoms involved in a bond. This axis is crucial in determining how atomic orbitals will overlap to form bonds, especially in sigma and pi bonds formation. The orientation of the orbitals relative to this axis dictates the bond type.

• Directly Along: For sigma bonds, orbitals overlap head-to-head along the internuclear axis, ensuring maximum overlapping and bond strength.


• Perpendicular Orientation: For pi bonds, the orbitals involved are positioned parallel to each other but perpendicular to the axis.


• Significance: Understanding the concept of an internuclear axis helps in predicting the type and nature of bond formations between different atomic orbitals.

Chemical Bonding

Chemical bonding is the resulting force that holds atoms together in a compound or molecule. There are various types of bonds, but sigma and pi bonds particularly define covalent bonding through orbital overlap.

• Sigma Bonding: Involves complete fusion of electron clouds through direct orbital overlap along the internuclear axis, resulting in stable bonds.


• Pi Bonding: Formed by lateral overlap in addition to sigma bonds, these provide additional strength and structure, often seen in multiple-bond systems.


• Overall Importance: Understanding chemical bonding is essential to grasp how molecules form, stabilize, and interact in chemical reactions.

By mastering the ideas of sigma and pi bonds, as well as comprehending the role of the internuclear axis, one can predict not just bonding tendencies, but also molecular geometry and reactivity.