What Are the Electrons Really Doing in Molecules? A Space-Time Picture

This is a fundamental and pedagogical work in quantum physics/chemistry, where we try to illustrate the Mulliken's question, "What are the electrons really doing in molecules?". And we also briefly review the development of the most popular numerical approaches in computational chemistry. We examine in a novel approach, how we can overall describe the electronic interactions in atomic systems with the conceptual help of a space-time picture of quantum mechanics. This is not a research article initially looking for new numerical results, but for the imperative fundamental reinterpretation of the (non-classical and stabilizing) electronic exchange and correlation energies, from the point of view of space-time scattering events between electrons. Consistently, we introduce Feynman type diagrams as pictorial representation of the (abstract) enthalpic integrals, scattering mechanisms, in quantum chemistry. In atomic structures, it is almost impossible to fully understand, covalent bonding, electronic enthalpies, surface science, orbital magnetism, catalysis… without computational chemistry. How well do we know the physical meaning of the quantum mechanisms behind the numerical approaches? We give an educational hit to this question, following the philosophy of R.P. Feynman, "just recognizing old things from a new point of view". The possibility of interpreting Coulomb and Fermi holes with space-time diagrams goes deep into the quantum behaviour of electrons, because the Coulomb forces in atomic systems create interreference patterns and then electrons cannot fill the electrostatic potentials everywhere as in classical mechanics. Quantum mechanics also allows electrons in atoms to collide in scatting events, introducing (dynamic) space-time mechanisms that reduce their repulsion energy; and actual successful computational chemistry methods include an average approximation to these stabilization mechanisms.