While dot-and-cross diagrams are primarily used to illustrate the arrangement of valence electrons and the type of chemical bonds, they do not directly predict the shapes of molecules. To determine molecular geometry, the Valence Shell Electron Pair Repulsion (VSEPR) theory is typically used. This theory states that electron pairs around a central atom will arrange themselves to minimize repulsion, thus determining the shape of the molecule. For instance, methane (CH₄) has four pairs of shared electrons around the central carbon atom, leading to a tetrahedral shape. Dot-and-cross diagrams provide the foundational information regarding the number and types of bonds, which is a starting point for applying VSEPR theory. However, for an accurate prediction of molecular shape, additional considerations like lone pairs and bond angles based on VSEPR theory are necessary.

Molecules with an odd number of electrons, often known as radicals, are generally highly reactive. The presence of an unpaired electron in these molecules creates a strong tendency to either gain or lose an electron to achieve a stable electronic configuration. This unpaired electron can easily participate in chemical reactions, making the molecule reactive. For example, nitric oxide (NO) and nitrogen dioxide (NO₂) are radicals with an odd number of electrons. Their reactivity is evident in their roles in various chemical processes, such as combustion and atmospheric reactions. The unpaired electron can form new bonds by pairing with an electron from another atom or molecule, leading to a wide range of chemical reactions. Additionally, these odd-electron molecules often exhibit paramagnetism, which is a direct consequence of their unpaired electrons. The high reactivity of radicals is a critical factor in many biological and environmental processes.

Dot-and-cross diagrams, while useful, have limitations in fully explaining chemical bonding. They are excellent for illustrating the arrangement of valence electrons and the type of bonds formed, but they do not convey information about the spatial arrangement of atoms or the strength and length of the bonds. These diagrams also do not show the movement or delocalization of electrons, which is important in understanding the bonding in molecules like benzene or in metallic bonding. Moreover, dot-and-cross diagrams may oversimplify complex bonding situations, such as resonance structures or hybridization of orbitals, which require more advanced theories to explain. While these diagrams provide a fundamental understanding of bonding, they are just one part of a broader set of tools and theories needed to fully grasp the complexity of chemical bonding in molecules.

Expanded octets are more common in elements from Period 3 onwards due to the presence of d-orbitals in their atomic structure. Starting from the third period, elements such as phosphorus, sulfur, and chlorine have empty d-orbitals in addition to their s and p orbitals. This allows these atoms to accommodate more than eight electrons in their valence shell. For instance, sulfur in sulfur hexafluoride (SF₆) can form six bonds, resulting in a total of twelve valence electrons, which is beyond the octet. The presence of d-orbitals provides the spatial and energy capacity to hold extra electrons that exceed the octet rule. This expanded valence capacity is not possible in elements of the second period, like carbon, nitrogen, and oxygen, as they lack d-orbitals. The ability of these larger atoms to expand their octet is crucial in explaining the formation of many complex molecules and their reactivities.

Dot-and-cross diagrams differentiate between polar and non-polar covalent bonds through the arrangement of shared electron pairs. In a non-polar covalent bond, electrons are shared equally between atoms of the same or similar electronegativity, leading to an even distribution of electron density. For example, in a chlorine molecule (Cl₂), the shared pair of electrons is equally distributed between the two chlorine atoms. On the other hand, polar covalent bonds occur between atoms of different electronegativities, resulting in an unequal sharing of electrons. This creates a dipole moment, with partial positive and negative charges on the atoms involved. For instance, in hydrochloric acid (HCl), the shared electrons are more attracted towards the chlorine atom due to its higher electronegativity compared to hydrogen. This results in a partial negative charge on chlorine and a partial positive charge on hydrogen, illustrating a polar covalent bond. The dot-and-cross diagram for HCl would show the shared electrons closer to the chlorine atom, indicating this polarity.