Electron Affinity RealQM vs DFT

Chart of electron affinity from 0 to 0.133 Hartree with grey zero affinity.

Electron affinity is a measure of the drop in total energy in energy when a neutral atom A captures an  electron under release of energy forming a negatively charges anion A-  named negative affinity.

An atom with zero affinity has no tendency to capture another electron.  

We consider two basic cases one with zero and one with negative affinity:

• Helium with 2 electrons filling the 1st shell as a noble gas with zero electron affinity.
• Fluorine with negative electron affinity by filling the 2nd shell from 7 to 8 electrons.  

Observed negative electron affinities range from 0.1- 0.3 Hartree with 0.12 for Fluorine. The total energy of Fluorine is -99.7 Hartree, and so to recover a change of 0.1 Hartree in computation requires a precision of 4 correct decimals.  

Here you can run RealQM as essentially a 3-line parameter-free code in 3d with only input the kernel charge giving the following total energies in Hartree:

• Helium    -2.903
• Helium-   -2.906
• Fluorine   -99.4
• Fluorine-  -99.8

We see that RealQM recovers zero affinity for Helium and the trend of negative affinity for Fluorine, if not the exact value with the present resolution of a $50^3$ grid. 

Density Functional Theory DFT as a very complex code, typically gives positive affinity for Helium, and can give values in the range of 0.12 for Fluorine under suitable adjustments of the code. 

PS This is what chatGPT has to say about the role of DFT in years to come:

• DFT will continue to be the dominant method for simulating chemical systems in the foreseeable future. Despite its limitations, it offers the best trade-off between accuracy, computational cost, and scalability. However, machine learning (ML) is emerging as a potential competitor—and in some cases, it might even surpass DFT.

The question is if RealQM can take over this role as a new form of DFT with a collection of one-electron densities instead of just one common density. The investment in DFT has been massive over a period of 50 years, while  RealQM is a spin-off of computational mechanics realised with little manpower. It is thus of interest to compare RealQM and DFT on basic tasks.

Electron Shielding: RealQM vs stdQM

A neutral atom with a kernel of positive charge $Z$ surrounded by $Z$ electrons in some (shell) configuration can attract an outside electron thus forming a negatively charged ion at the release of energy, referred to as (negative) electron affinity. 

For example the electron affinity of Lithium (Z=3) with 2 inner-shell electrons and 1 outer-shell electron has an observed electron affinity of - 0.028 Hartree and Fluorine (Z=9) -0.125 Hartree. 

Ok, so if a Lithium atom can attract a negative electron under release of energy, the kernel must exercise some attraction outside the formally neutral atom, which can be thought of as an effective charge $Z_{eff}$ resulting from incomplete shielding of the kernel by the surrounding electrons. This is referred to as electro-negativity as a qualitative property on a certain empirical scale, see post on electro-negativity.

Because of the physical shell structure of RealQM with non-overlapping electrons, RealQM directly informs that the shielding effect of $N$ inner-shell electrons on outer-shell electrons is $0.5\times N$, so that $Z_{eff} = Z-0.5\times N$ and in particular outside the atom $Z_{eff}=0.5\times Z$, which conforms with about 3 times larger affinity for Fluorine compared to Lithium. The precise shielding effect is directly computable by RealQM. 

StdQM does not deliver any theoretical prediction with the excuse that such a thing must be a very very complicated problem.  

What stdQM offers is Slater's empirical rule to calculate the shielding effect of inner electrons on outer electrons in an atom, which e g says that the shielding effect of the 2 inner electrons of Lithium on the outer electron comes with an empirical factor $0.85$ so that $Z_{eff} =3-2\times 0.85 = 1.30$, while for Fluorine Slater gives $Z_{eff}=4.55$. But Slater says nothing about the shielding effect outside the atom.

On the other hand, RealQM says $Z_{eff} = 3-2\times 0.5=2$ for the outer electron of Lithium and $9-0.5*8=5$ for Fluorine, that is a bit less effective shielding than Slater's rule and so more outside attraction available for electron attraction.  

The reason RealQM gives a direct answer to the shielding effect is its physical shell subdivision without the electron overlapping confusing the picture for stdQM. 

For Helium (Z=2) RealQM gives $Z_{eff}=2-0.5\times 2=1$ and so the anion He- can form even if He is a so called noble gas (with an energy release of $0.8$ Hartree according to code), in agreement with observation. Even He2- with additional energy release of $0.5$ Hartree (code) appears to be possible, but realisation may require very special conditions. 

In stdQM a distinction is being made between electron affinity and electronegativity, with electron affinity the energy release when an single atom adds an electron, and electronegativity rather capacity to share electron in a covalent bond. It is not clear that this distinction is essential and does not appear to be so within RealQM.