Chemist Eric Scerri as world authority on the Periodic Table asks in the article Can Quantum Ideas Explain Chemistry's Greatest Icon? (Nature 2019):
- Does Quantum Mechanics QM explain the Periodic Table PT?
Scerri recalls that Swedish chemist Löwdin in 1969 presented this as one of chemistry's major theoretical challenges, and adds that it still is.
To non-expert readers of Nature and also the general public this may sound a bit surprising, since QM in its standard form stdQM based on a linear multi-dimensional Schrödinger Equation SE is viewed as the fundamental mathematical model of modern physics describing in particular the electron configurations of all atoms as the basis of PT.
But Scerri and Löwdin say that stdQM only gives a partial explanation of PT with a lot missing. Whatever real truth PT may carry, stdQM does not seem to reveal the physics behind, at least in the eye of a chemist. But a physicist would without hesitation say that PT is well explained by stdQM, at least in principle, and that it is the job of chemists to supply the petty details.
This state of affairs has added to the crisis of modern physics, which largely is a credibility crisis. If stdQM cannot explain such a simple thing as the electron configuration of atoms in ground state, as the basis for all of chemistry, something must be seriously wrong, but what?
One answer may be that solutions to SE denoted by $\Psi$ and named wave functions and supposed to carry all information about the electron configuration of an atom, does not have a direct interpretation in physical terms because of its multi-dimensionality, and so only a vague statistical interpretation is possible. Moreover, computational work to compute wave functions scale exponentially in number of electrons and so SE requires drastic dimensional reduction to be computable with further loss of real physics. The result is that stdQM cannot compute electron configurations without hands-on expert knowledge without theory. It is not surprising that under these conditions it fails to explain PT.
Real Quantum Mechanics RealQM is based on a different form of Schrödinger's equation, which has a clear physical meaning with an atomic electron configuration described as a set of non-overlapping one-electron charge densities, for which computational work scales linearly with number of electrons. RealQM directly extends to molecules as Real Quantum Chemistry described in these articles.
It seems possible that RealQM can give a better explanation of PT than stdQM, and maybe even correct PT in some details, because it has direct physical meaning and computation is affordable for all atoms.
StdQM seeks to explain the electron configuration of an atom with many electrons in terms of the excited states of the Hydrogen atom with just one electron filling s, p, d shells. To make this Aufbau fit with observation various ad hoc rules have been adopted attributed to e g Madelung and Hund. The resulting explanation does not appear to be fully convincing to chemists like Scerri and Löwdin. Something appears to be missing...
RealQM explains the electron configuration in a different way as an electron packing problem, which has a clear physical meaning and so at least has the potential to offer an explanation of PT on physical grounds or suggest corrections. Preliminary studies show promise and further studies are on the way.
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