From Geometrical Molecules to Topological Molecules: A Quantum Mechanical View

For the practising chemist the concept of a molecule is based on the classical mechanical concept of spatial localization. Since our imagination is trained on macroscopic objects, it is natural to picture molecules as tiny objects occupying a well defined region of space. Localization, size and shape are macroscopic concepts in their origin, and most novel ideas and models of chemistry find their intuitive conception in macroscopic, classical models, with inherently localized nature. However, classical localization can be generalized to quantum mechanics only in a very limited sense, while most of the associated classical mechanical concepts lose their relevance. The classical description of position and motion is clearly inapplicable: the simultaneous measurements of the position and momentum of a particle are limited by the Heisenberg uncertainty relation. This limitation is of major significance on the molecular-electronic level, which leads to fundamental questions concerning the quantum mechanical concept of molecular structure [1–4], which questions cannot be settled within the classically motivated Born—Oppenheimer approximation [5–9]. The generator-coordinate method [10–15], the phase-space and wave-packet methods [see e.g. 16–43] are alternative formulations, which retain some of the advantages of a few familiar, classical concepts and also imply a revision of the classical interpretation of localization.