`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

Atomic Orbitals

Atomic orbitals are the fundamental quantum-mechanical descriptions of regions in an atom where electrons are most likely to be found. They are defined by quantum numbers and have specific shapes and symmetries that determine how they interact with orbitals on other atoms during the formation of molecular bonds.

Molecular Orbital Theory

Molecular orbital theory explains chemical bonding by describing how atomic orbitals combine to form molecular orbitals that are spread out over the entire molecule. These molecular orbitals can be occupied by electrons, and the constructive combination of orbitals leads to bonding orbitals, while destructive combinations result in antibonding orbitals.

Linear Combination of Atomic Orbitals (LCAO)

The LCAO method is a technique used to construct molecular orbitals by mathematically adding (or subtracting) atomic orbitals from different atoms. The success of the combination largely depends on the proper alignment and symmetry of the atomic orbitals, ensuring significant overlap and an energetically favorable (bonding) interaction.

Orbital Symmetry and Overlap

Symmetry plays a crucial role in the combination of atomic orbitals. Only orbitals with compatible symmetry properties can overlap effectively to form a bond. The geometric orientation as well as the presence of nodal planes in the orbitals must align such that constructive interference occurs, leading to the formation of a stabilizing bonding molecular orbital.

Sigma and Pi Molecular Orbitals

Sigma (?) molecular orbitals are formed when the overlap of atomic orbitals is end-to-end along the internuclear axis, resulting in an orbital with cylindrical symmetry about that axis. In contrast, pi (?) molecular orbitals result from the side-to-side overlap of orbitals, where the electron density is concentrated above and below the internuclear axis, typically featuring a nodal plane that contains this axis. The type of orbital (? or ?) formed depends on the directional properties and symmetry of the combining atomic orbitals.

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