Question

Draw sketches illustrating the overlap between the following orbitals on two atoms: (a) the \(2 s\) orbital on each atom, (b) the \(2 p_{z}\) orbital on each atom (assume both atoms are on the \(z\) -axis), (c) the \(2 s\) orbital on one atom and the \(2 p_{z}\) orbital on the other atom.

Short answer

In this exercise, we considered the overlap between different orbitals on two atoms: (a) 2s orbital on each atom, (b) 2pz orbital on each atom, and (c) 2s orbital on one atom and 2pz orbital on the other atom. In each case, we created sketches that reflect the electron probability density and the new bonding and antibonding orbitals formed due to the overlap. For case (a), the overlap between two 2s orbitals produced a bonding σ orbital and an antibonding σ* orbital. In case (b), the overlap between two 2pz orbitals also resulted in a σ and σ* orbital. Lastly, case (c) had an overlap between a 2s orbital and a 2pz orbital, forming a π bond and a π* antibonding orbital.

Step-by-step solution

(Understanding the orbitals)

Before drawing the sketches, we need to understand how each type of orbital looks and how they can overlap. In an atom, an electron occupies orbitals, which can be either s or p. The s orbitals have a spherical symmetry, while the p orbitals have a dumbbell shape along the x, y, and z axis, respectively (e.g., px, py, and pz).

(Case a) Overlapping 2s Orbits on Both Atoms)

In this case, the overlap occurs between spherical 2s orbitals on two atoms. When two 2s orbitals come close together, they can overlap to form two new orbitals: a lower-energy bonding orbital (σ), where the electron probability density is between the two nuclei, and a higher-energy antibonding orbital (σ*), where the electron probability density is pushed away from the nuclei. First, draw two 2s orbitals on each atom, such as two spheres. Then, place them next to each other to show the overlapping regions: when the spherical shapes fuse, a bonding region (σ) is formed in between the nuclei, signifying a stronger bond. Draw an additional, more diffuse, shape surrounding the two spheres, representing the antibonding orbital (σ*).

(Case b) Overlapping 2pz Orbits on Both Atoms)

Here, the overlap occurs between two 2pz orbitals on both atoms that are on the z-axis. The dumbbell shape of the pz orbitals represents the electron probability in each region. When they overlap, the electron probability density increases between the nuclei, forming two new orbitals: a lower-energy bonding orbital (σ) and a higher-energy antibonding orbital (σ*). Create a sketch of two 2pz orbitals, both placed parallel to the z-axis. The dumbbell shapes should fit inside each other like puzzle pieces, with the bonding region (σ) increased between the nuclei. Draw an additional inflated area that extends outward to represent the antibonding orbital (σ*).

(Case c) Overlapping 2s Orbital on One Atom and 2pz Orbital on the Other Atom)

In this case, the overlap is between different orbitals: one 2s (spherical shape) and one 2pz (dumbbell shape). The electron probability density is concentrated between the nuclei, creating an asymmetric bonding orbital (π bond) perpendicular to the z-axis. The resulting antibonding orbital (π*) is more spread out and behaves as a lone pair of electrons. Draw a 2s orbital and a 2pz orbital on different atoms approaching each other. The 2s orbital will overlap with one lobe of the dumbbell-shaped 2pz orbital. The bonding area formed between the nuclei represents the π bond.

Key concepts

2s Orbital

The 2s orbital is a type of atomic orbital found in the second principal energy level (n=2) of an atom. It has a unique spherical shape, which means it is symmetrical about the nucleus and does not favor any particular direction in space. Its spherical nature allows for uniform distribution of electron density around the nucleus.

The significance of the 2s orbital in chemical bonding lies in its ability to overlap with other orbitals, particularly another 2s orbital or a 2p orbital, to form covalent bonds. This overlap is a fundamental aspect of molecular formation and is dictated by the principles of quantum mechanics.

When a 2s orbital overlaps with another 2s orbital from a different atom, it creates a sigma (\r{\( \sigma \)}) bond, characterized by head-on overlap. This forms a bond that is symmetrical around the axis connecting the two atomic nuclei, providing a strong cohesive force in a molecular structure.

2pz Orbital

Similar to the 2s orbital, the 2pz orbital is located on the second principal energy level. However, unlike the spherical 2s orbital, the 2pz orbital has a dumbbell-shaped geometry, extending along the z-axis with two lobes on either side of the nucleus and a nodal plane passing through the nucleus where the probability of finding an electron is zero.

The orientation of the 2pz orbital is crucial when considering orbital overlap in molecular bonding. Its shape is optimized for side-by-side overlap, which can lead to the formation of pi (\r{\( \pi \)}) bonds when the lobes of two 2pz orbitals from adjacent atoms align parallel to one another. These pi bonds are essential in enabling double bonding and unsaturated hydrocarbon structures, which are vital for understanding the chemistry of organic compounds.

Sigma Bonding

Sigma bonding (\r{\( \sigma \)}) is a type of covalent bond that is formed by the direct overlap of orbitals along the axis connecting two atomic nuclei. It is the strongest type of covalent bond because the electron density is greatest directly between the two nuclei, leading to a significant electrostatic attraction between the positively charged nuclei and the shared electrons.

In the context of orbitals like the 2s and 2pz, when these orbitals overlap end-to-end, a sigma bond is formed. This can be visualized by considering the overlap of two 2s orbitals, which results in a bonding orbital where the electron density is shared in a space directly between the nuclei – the most stable arrangement for the shared pair of electrons.

The Key Characteristics of Sigma Bonds:

• Single covalent bonds in molecules always contain a sigma bond.
• Sigma bonds allow for free rotation about the bond axis since their electron density is cylindrically symmetrical.
• They are created by the head-on overlap of atomic orbitals, including s-s, s-p, or p-p orbitals.

Pi Bonding

Pi bonding (\r{\( \pi \)}) represents a form of covalent bond that is characterized by the side-to-side overlap of adjacent p orbitals, such as two 2pz orbitals. Unlike the sigma bond, pi bonds are formed when the lobes of the p orbitals overlap parallel to the axis joining the two atomic nuclei, creating an electron density cloud above and below the bonding axis.

Pi bonds are of special interest as they contribute to the formation of double and triple bonds in conjunction with sigma bonds. While not as strong as sigma bonds due to less effective overlapping, pi bonds add stability to multiple-bonded structures and restrict rotational freedom, which is a key aspect in the geometry of molecules.

Distinguishing Features of Pi Bonds:

• Pi bonds usually exist alongside a sigma bond between the same two atoms, creating double or triple bonds.
• They arise from the parallel overlap of p orbitals, leading to a more diffuse electron cloud.
• Restriction of rotational movement around the bond axis due to pi bonds gives rise to cis-trans isomerism in certain compounds.