Show how a dx z atomic orbital and a pz atomic orbital...

Show how a $d_{x z}$ atomic orbital and a $p_{z}$ atomic orbital combine to form a bonding molecular orbital. Assume the $x$ -axis is the internuclear axis. Is a $\sigma$ or a $\pi$ molecular orbital formed? Explain.

Key Concepts

Bonding Molecular Orbital Formation

When the d?z and p_z orbitals combine, the lobe of the d?z orbital oriented in the z-direction overlaps with the p_z orbital. This overlap is not directed along the internuclear axis (x-axis) but rather perpendicular to it, thereby forming a bonding molecular orbital that has the characteristics of a pi bond. The constructive overlap lowers the energy of the system and stabilizes the bond between the two atoms.

Sigma versus Pi Molecular Orbitals

Molecular orbitals are classified as ? (sigma) or ? (pi) based on their symmetry relative to the internuclear axis. Sigma orbitals result from head-on overlap with cylindrical symmetry around the internuclear axis, while pi orbitals arise from side-to-side overlap, resulting in a nodal plane that includes the internuclear axis. With the internuclear axis defined along the x-axis, the overlapping parts of the d?z and p_z orbitals lie perpendicular to this axis, leading to a pi-type bonding interaction.

Orbital Overlap and Symmetry

The formation of molecular orbitals involves the linear combination of atomic orbitals whose phases and symmetries allow for constructive interference. For a bonding molecular orbital, the overlapping orbitals must match in phase where they intersect. Here, the portion of the d?z orbital that extends in the z-direction can overlap with the p_z orbital, creating a region of constructive overlap despite the difference in the primary directional orientation of the parent orbitals.

Atomic Orbital Orientation

Atomic orbitals have specific shapes and orientations in space that determine how they can overlap. In this case, the d?z orbital has lobes extending in both the x-direction (the internuclear axis) and the z-direction, while the p_z orbital is oriented along the z-axis. Their relative orientations are crucial because effective overlap depends on the alignment of the lobes with similar phase throughout the region where the atoms interact.

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