Bent molecular geometry arises in molecules that contain lone pairs of electrons due to the repulsion between these electron pairs.

To elaborate, the shape of a molecule is governed by the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory posits that electron pairs surrounding a central atom will orient themselves to minimize repulsion. Since electrons are negatively charged, they repel each other; therefore, they strive to maximize their distance apart.

In molecules that have lone pairs, these unshared pairs of electrons also play a crucial role in determining the molecular shape. Lone pairs consist of valence electrons that are not shared with other atoms and do not participate in chemical bonding. Notably, lone pairs occupy more space than bonding pairs, leading to a stronger repulsive force. As a result, lone pairs push the bonding pairs of electrons closer together, giving the molecule a bent or V-shaped geometry.

A prime example of this phenomenon is the water molecule, denoted as $H_2O$. In water, the oxygen atom has two lone pairs of electrons and two bonding pairs with hydrogen atoms. According to VSEPR theory, the electron pairs will arrange themselves to maximize their separation. However, because the lone pairs occupy more space, they exert a stronger repulsion that pushes the hydrogen atoms closer together, ultimately resulting in a bent molecular geometry.

In summary, the presence of lone pairs in a molecule significantly impacts its shape. The repulsion among electron pairs, particularly the stronger repulsion from lone pairs, causes the molecule to adopt a bent geometry. This concept is essential for understanding the structure and properties of various molecules.