Many compounds of the transition-metal elements contain direct bonds between metal atoms. We will assume that the z-axis is defined as the metal–metal bond axis. (d) Sketch the energylevel diagram for the Sc2 molecule, assuming that only the 3d orbital from part (a) is important.

Verified step by step guidance

1. Identify the 3d orbitals of scandium (Sc) that are involved in bonding. In transition metals like Sc, the 3d orbitals are five in number: $d_{xy}$, $d_{xz}$, $d_{yz}$, $d_{x^2-y^2}$, and $d_{z^2}$. Since the z-axis is the metal-metal bond axis, focus on how these orbitals orient along this axis.
2. Determine the symmetry and overlap of the 3d orbitals along the z-axis. The $d_{z^2}$ orbital is symmetric around the z-axis and will have significant direct overlap, contributing to bonding between the metal atoms. The $d_{xz}$ and $d_{yz}$ orbitals will also interact because they have lobes that point along the z-axis.
3. Sketch the energy level diagram starting with the atomic orbitals of each Sc atom. Place the 3d orbitals at their respective energy levels before bonding.
4. Add the molecular orbitals formed by the overlap of the 3d orbitals. The $d_{z^2}$ orbitals from each Sc atom will overlap to form bonding (lower energy) and antibonding (higher energy) molecular orbitals. Similarly, consider the interactions of $d_{xz}$ and $d_{yz}$ orbitals.
5. Label the molecular orbitals according to their symmetry and bonding characteristics. Bonding orbitals are typically lower in energy due to stabilization from the overlap, while antibonding orbitals are higher in energy due to the repulsion between like phases of the electron clouds.

Key Concepts

Transition Metals

Transition metals are elements found in the d-block of the periodic table, characterized by their ability to form variable oxidation states and complex ions. They have partially filled d-orbitals, which play a crucial role in bonding and the formation of compounds. Understanding their electronic configuration is essential for predicting their chemical behavior and the nature of metal-metal bonds.

Energy Level Diagrams

Energy level diagrams visually represent the arrangement of electrons in an atom or molecule, showing the energy levels of different orbitals. In the context of transition metals, these diagrams help illustrate how d-orbitals are filled and how they interact during bond formation. For Sc2, focusing on the 3d orbital allows for a simplified view of the bonding interactions between the two scandium atoms.

Metal-Metal Bonding

Metal-metal bonding occurs when two metal atoms share electrons, leading to the formation of a bond. In transition metal compounds, these bonds can involve d-orbitals, which contribute to the overall stability and properties of the molecule. Understanding the nature of these bonds is crucial for analyzing the electronic structure and reactivity of metal clusters like Sc2.