Does Quantum Mechanics Explain the Periodic Table?

A common view among modern physicists is that the Periodic Table is explained by the modern physics of quantum mechanics based on a linear multi-dimensional Schrödinger equation. 

The ground state of the one-electron distribution of a Hydrogen atom can be computed analytically to be given by a spherically symmetric wave function decaying with the distance $r$ from the kernel like $\exp (-r)$, which is referred as a $1S$ state, with energy $-\frac{1}{2}$ Hartree in full agreement with observation.  

The ground state of Helium as the next element in the table with two electrons, is presented to be $1S^2$ in the form of two electrons with the same $1S$ wave function sharing space around the kernel (with different so called spin to coexist). The ground state energy computes to $-2.75$ Hartree, while observed energy is $-2.903$ Hartree. The state $1S^2$ is thus not the ground state. 

When confronted with this fact, ChatGPT gives the following response, after consulting the literature:

• The $1S^2$ state is not fundamentally correct as the ground state of helium because it fails to account for essential electron correlation and yields an incorrect energy. While it can serve as a useful approximation and educational tool, the true ground state is a correlated quantum state that cannot be reduced to $1S^2$. Thus, any claim of its "conceptual correctness" must be qualified and limited to its role as a crude first-order approximation.
• The $1S^2$ concept can be misleading if presented as the full description of helium's ground state. While it serves as a useful approximation and pedagogical tool, it oversimplifies the true quantum nature of the system. To avoid misconceptions, it’s crucial to contextualize $1S^2$ as a starting point in understanding helium, not the definitive or complete description.

We understand that presenting $1S^2$ as the ground state of He is incorrect and so can be seriously misleading, yet it is supposed to be the quantum mechanical explanation of the second element in the periodic table! What then about the rest of the table based on excited states of Hydrogen? 

RealQM presents a different ground state for Helium consisting of two electrons occupying two separate half-spaces through the kernel, for which the energy agrees with observation. More generally, RealQM explains the periodic table as a packing problem of non-overlapping one-electron charge densities meeting at a Bernoulli free boundary, which appears as a better explanation of the period table than the accepted standard.  RealQM is based on a new Schrödinger equation in the form of classical continuum mechanics in 3 space dimensions.

Connecting to the previous post, the idea of a Helium ground state as $1S^2$ came out from the new quantum mechanics emerging 100 year ago as way to understand the atomic world, which today according to ChatGPT however appears to have missed the target. Instead of increasing understanding it fosters mis-understanding. A nice feature of ChatGPT compared to a living scientist heavily invested in a certain school of thought, is that hiding truth/information is not securely built in. 

More precisely: The ground state of Helium as $1S^2$ of the accepted view with incorrect energy, should be compared with the conceptually fundamentally different ground state of RealQM with correct energy. What is your choice?