One of the challenges in organic chemistry stems from the numerous approximations we are compelled to use. In general chemistry, you likely learned that the structure of a molecule is fundamentally governed by quantum mechanics (QM)—a highly complex and mathematically rigorous theory. Yet, in practice, we often draw structures or assign charges on a piece of paper, a blackboard, or a computer screen. How can we expect these simplified representations to capture the true nature of a molecule without delving into QM?
Many of the approximations we rely on—such as resonance, valence bond theory, and formal charge—predate quantum mechanics. Despite their simplicity, these models have proven remarkably accurate for predicting molecular structure, reactivity, and electron distribution. They have been rigorously tested and refined over time. However, it’s important to remember that these representations are just approximations of reality. Even quantum mechanics, while more comprehensive, is still a model with its own limitations, many of which arise from the approximations it, too, must employ.
As physicist P.A.M. Dirac famously noted in 1929, "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble." This elegantly captures the essence of why we rely on approximations: while the laws governing chemistry are well understood, their exact application often exceeds our practical capabilities.