What are the electron-domain and molecular geometries of a molecule that has the following electron domains on its central atom? (a) three bonding domains and no nonbonding domains, (b) three bonding domains and one nonbonding domain, (c) two bonding domains and two nonbonding domains.

Valence Shell Electron Pair Repulsion (VSEPR) theory is the cornerstone concept for understanding molecular shape and geometry. It proposes a practical method to predict the arrangement of electron pairs around a central atom in a molecule based on the principle that these electron domains will be positioned to minimize repulsion between them. This is due to the negative charges of electron domains naturally repelling each other.

Electron domains include both bonding and nonbonding electron pairs, also known as lone pairs. Under VSEPR theory, the term 'electron-domain geometry' refers to the spatial arrangement of all electron domains, while 'molecular geometry' refers only to the arrangement of atoms, excluding nonbonding electron pairs.

When the central atom in a molecule is surrounded by three bonding domains with no nonbonding domains, the molecule adopts a trigonal planar geometry. Here, the three bonding domains are spaced equally around the central atom in a flat, triangular shape, 120 degrees apart. This maximizes their distance from each other, which is in accordance with the rules of VSEPR theory. The absence of nonbonding domains means that the molecular and electron-domain geometries are the same: trigonal planar.

Trigonal pyramidal geometry occurs in molecules with a central atom surrounded by three bonding domains and one nonbonding domain, causing a total of four electron domains. As per VSEPR theory, these electron domains arrange themselves in a tetrahedral electron-domain geometry for maximum spacing. However, the presence of a single nonbonding domain causes a slight asymmetry, effectively 'pushing down' on the bonding domains and creating a pyramidal structure for the molecule. Thus, the electron-domain geometry is tetrahedral, but the molecular shape is trigonal pyramidal, reflecting the position of the atoms only.

Tetrahedral electron geometry is observed when a central atom is surrounded by four electron domains. These electron domains, whether they are bonding domains or nonbonding domains, arrange themselves at the corners of an imaginary tetrahedron, with bond angles of approximately 109.5 degrees. This shape is the consequence of the domains trying to be as distant from one another as possible, a direct application of VSEPR theory. The molecular geometry, however, may differ if one or more of the domains are nonbonding; only the bonding domains determine the molecular geometry.

Bent molecular geometry arises from a central atom bonded to two other atoms with the presence of two nonbonding electron domains. Using VSEPR theory, we could predict a tetrahedral electron-domain geometry overall. However, because the molecular geometry only considers the placement of the bonded atoms, the shape is 'bent' due to the two lone pairs that occupy more space and repel the bonding pairs closer together. The result is a smaller bond angle than in a perfect tetrahedral geometry, leading to the descriptive term 'bent' or 'angular' for this type of molecular shape.