Introduction

Molecules are system consisting of electrons and nuclei. This definition covers the full range from rather simple molecules like $H_2$ up to extremely complex situations with billions of nuclei, or in principle even solids or fluids although one usually thinks of something like a microscopic object. The question, of course, is what microscopic really means. In principle, one could have molecules with macroscopic large numbers (like $10^{23}$) of electrons and nuclei. Would these behave as quantum or as classical objects?

Even for small molecules, there are in fact some fundamental, conceptual issues in the field of molecular structure, cf. for example the article by B. T. Sutcliffe in ch. 35 of Vol. 1 of the `Handbook of Molecular Physics and Quantum Chemistry', Wiley (2003). These are related to the question of whether or not molecular structure and properties of molecules can be strictly derived from a microscopic Schrödinger equation of an isolated molecule, including all the Coulomb interaction among the constituents. For example, the total Hamiltonian commutes with the parity operator which means that itsd eigenstates are parity eigenstates and therefore cannot must have zero expectation value of the static dipole moment. This would mean that there exist no molecules with static dipole moments, which apparently is in contradiction to what we learn from chemistry. Another such `paradoxon' seems to be isomers of polyatomic molecules, and the concept of the chemical bond (`deconstructing the bond') is not an easy one, either. These seem to be open questions.