Which of the following pairs of atomic orbitals of adjacent...

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 $2 p_{x},(\mathrm{c}) 2 p_{x}$ and $2 p_{y},(\mathrm{d}) 3 p_{y}$ and $3 p_{y},(\mathrm{e}) 2 p_{x}$ and $2 p_{x},(\mathrm{f}) 1 s$ and $2 s$.

Key Concepts

Atomic Orbital Shapes and Symmetry

Different types of atomic orbitals, such as s and p orbitals, have distinct shapes and nodal structures that dictate how they interact. S orbitals are spherically symmetric and can overlap with any other orbital in various orientations, while p orbitals have directional lobes that require specific alignments for effective overlap. The shape and symmetry of the orbitals determine whether they can form sigma or pi bonds, or whether their overlap is ineffective for bonding.

Sigma Bond Formation

Sigma bonds are created by the head?on (end-to-end) overlapping of orbitals along the internuclear axis. In this type of bond, the electron density is concentrated directly between the two nuclei, resulting in a strong bond. The ability to form a sigma bond depends on the proper alignment of the lobes or symmetry of the orbitals involved so that maximum electron density is shared along the internuclear axis.

Pi Bond Formation

Pi bonds result from the side-by-side overlap of orbitals that have lobes oriented perpendicular to the internuclear axis. The electron density in a pi bond is located above and below (or in other lateral regions relative to) the internuclear axis, which offers additional bonding strength once a sigma bond is already formed. Effective pi bonding requires specific orbital orientations such that their phase and alignment allow for constructive overlap in these regions.

Orbital Overlap and Orientation

The formation of chemical bonds via orbital overlap is highly dependent on the spatial orientation and symmetry properties of the orbitals involved. Proper overlap requires that the orbitals not only be in physical proximity but also properly aligned with respect to the internuclear axis. Misaligned or orthogonal orbitals may have little or no effective overlap, preventing bond formation.

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