What two basic shapes have hybridizations that include \(\bar{d}\) orbitals??

Hybridization in chemistry is a concept that describes the mixing of atomic orbitals to form new, equivalent hybrid orbitals. This process is essential for explaining the shapes of molecular compounds beyond the simple s and p orbital interactions. Hybrid orbitals are able to form more stable and directed bonds to maximize the molecule's stability.

The concept was introduced by chemist Linus Pauling to provide a quantum mechanical explanation for the tetravalency of carbon. Over time, this expanded to account for a variety of atomic combinations in larger and more complex atoms. The inclusion of d orbitals in this process allows atoms with access to the third energy level and beyond to form expanded octets, thereby accommodating more than the typical eight electrons in their outer shells.

Hybridization plays a critical role in predicting molecular geometry because it reflects how atomic orbitals combine when atoms bond together. Different types of hybrid orbitals arise such as sp, sp2, sp3, sp3d, and sp3d2, each corresponding to a particular molecular geometry that defines the molecule's shape.

Trigonal bipyramidal geometry occurs when a central atom is surrounded by five other atoms or groups of atoms in a molecule. The five sp3d hybrid orbitals that form are arranged so that three orbitals lie in a single plane, equidistant from each other at 120-degree angles (in a trigonal planar distribution), with the remaining two orbitals positioned above and below this plane (forming the bipyramidal structure).

This arrangement minimizes electron repulsion and provides an energetically favorable configuration. Common examples of molecules with trigonal bipyramidal geometry are phosphorus pentafluoride (PF5) and sulfur hexafluoride (SF6) after one of the axial positions is occupied.

Octahedral geometry is characteristic of molecules where six groups of electrons or bonds surround a central atom, which is often a metal. The central atom in this configuration is bonded to six other atoms, positioned at the corners of an octahedron.

The hybridization associated with this geometry is sp3d2, which involves one s orbital, three p orbitals, and two d orbitals combining to form six equivalent octahedral hybrid orbitals. These are oriented 90 degrees to each other along the Cartesian axes. The octahedral shape is often seen in coordination compounds, such as sulphur hexafluoride (SF6) or the iron(III) hexaaquacomplex [Fe(H2O)6]3+.

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It is critical to understanding the properties and reactivities of molecules, including their polarity, phase of matter, color, magnetism, and biological activity.

Electron pairs, whether in bonds or as lone pairs, repel each other, and the molecular geometry of a molecule reflects the manner in which these repulsions are minimized. Structural theories like VSEPR (Valence Shell Electron Pair Repulsion) are often used to predict the geometry of a molecule based on the number of electron pairs surrounding the central atom. It’s this geometry that determines hybridization, and not the other way around.

sp3d hybridization involves the mixing of one s orbital, three p orbitals, and one d orbital from the central atom to form five equivalent sp3d hybrid orbitals. This type of hybridization is seen in the trigonal bipyramidal molecular geometry. A perfect example to illustrate this is phosphorus pentachloride (PCl5), where the five chlorine atoms bond with these five hybrid orbitals.

In sp3d hybridization, the electron geometry provides room for five pairs of bonded electrons around the central atom, as in the case of PCl5 with phosphorus at the center surrounded by chlorine atoms, four in the plane and one above and one below this plane. The presence of lone pairs can also influence the bond angles but generally, bond angles in purely sp3d hybridized atoms are 90 and 120 degrees.

The sp3d2 hybridization encompasses the mixing of one s orbital, three p orbitals, and two d orbitals, which results in the formation of six identical sp3d2 hybrid orbitals. These orbitals are then arranged in an octahedral geometry, where all bond angles are 90 degrees, forming an equidistant spatial arrangement around the central atom.

A classic example is sulfur hexafluoride (SF6), where sulfur is the central atom joined to six fluorine atoms. In sp3d2 hybridized molecules, the central atom can accommodate up to 12 electrons, allowing for the formation of complex structures with potentially high coordination numbers. This hybridization is generally found in the central atoms found in the lower periods of the periodic table that have access to d orbitals.