Which clusters of orbitals would form a "octahedral" electron geometry and would also be possible within the valence shell of an atom?

d2sp3 but obviously those atoms without d orbitals are not eligible for this.

3p orbitals

2sp and 2p orbitals
6sp3d2 orbitals

An octahedral electron geometry can be formed by the hybridization of d orbitals. In order for an atom to form an octahedral electron geometry, it must have available d orbitals in its valence shell.

The elements that can exhibit an octahedral electron geometry within their valence shell are the transition metals in the d-block of the periodic table, such as iron (Fe), cobalt (Co), and chromium (Cr), among others. These elements have partially filled d orbitals that can be involved in the formation of molecular orbitals, resulting in an octahedral electron geometry.

It is important to note that the octahedral electron geometry is common in coordination compounds, such as transition metal complexes, where a central metal atom or ion is surrounded by six ligands. The ligands can be molecules or ions that donate electron pairs to the central atom, forming coordinate bonds.

To determine the clusters of orbitals that would form an octahedral electron geometry and are possible within the valence shell of an atom, we need to consider the valence electron configuration.

The octahedral electron geometry consists of six electron pairs distributed around a central atom. This geometry is commonly observed in molecules with the formula AX6, where A represents the central atom and X represents the surrounding atoms or lone pairs.

In the case of an atom, the maximum number of valence electrons it can have is determined by its position in the periodic table. For example, in the second period, elements can have a maximum of 8 valence electrons, while elements in the third period can have a maximum of 18 valence electrons.

To determine the atoms that can form an octahedral electron geometry, we need to find atoms with six valence electrons. There are a few possible scenarios:

1. Elements from Group 6A or 16 (Group VIA): These elements have six valence electrons. For example, oxygen (O) has a configuration of 2s²2p⁴, sulfur (S) has a configuration of 3s²3p⁴, and selenium (Se) has a configuration of 4s²4p⁴. These elements can form an octahedral electron geometry by sharing their valence electrons with surrounding atoms or by forming bonds.

2. Transition metals: Transition metals can also form octahedral complexes by using d orbitals. These elements have the ability to expand their valence shell and accommodate more than eight electrons. For example, the d-block elements like chromium (Cr) and molybdenum (Mo) can form octahedral complexes by utilizing their d orbitals.

It is important to note that the specific atoms that can form an octahedral electron geometry may vary depending on the combination of atoms and the type of chemical bonding involved.

In summary, atoms that have six valence electrons, such as elements from Group 6A or 16 and transition metals, have the potential to form an octahedral electron geometry within the valence shell of an atom.