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.

Perspective on ElectroNegativity

Let us now give more perspective on the electronegativity explored by RealQM in the previous post as the decrease of energy achieved by hypothetically adding one electron to a given atom with kernel charge Z assuming the electron configuration of the next element in the periodic table with charge Z+1. 

For example, RealQM computes a decrease of about 4 Hartree when an electron is added to Fluorine with Z=9 with electron shell configuration 2+4+3 to obtain the configuration 2+4+4 of Neon with Z=10 as the ion F-. 

In a similar way we obtain energy decrease of 0.8 Hartree for Helium- (Z=2), 1.2 for Lithium- (Z=3), 1.7 for Beryllium- (Z=4) and 2.3 for Boron- (Z=5) increasing to 4 for F- (Z=9) as the maximal electronegativity for all elements. 

RealQM gives the very small value 0.06 for H- in opposition to an accepted value of 2.  

We next ask under what conditions the ion F- will be created from F by incorporation of one electron at an energy decrease of 4 Hartree? It directly connects to the nature of the bond of  molecule HF as ionic or covalent. In an ionic bond the F atom would fully capture the electron of H with a decrease of energy of more than 3 Hartree. This is very substantial and would correspond to a dissociation energy of HF of more than 3 Hartree which is 10 times bigger than that observed.

We have earlier seen that a HF with a covalent bond has a dissociation energy in accordance with observation.

We conclude that F- appears to be hypothetical and in particular does not combine with H+ to form HF by an ionic bond. In other words, it is not clear what role electronegativity has to play if bonds are rather covalent than ionic. Any idea? Recall that direct measurement is viewed to be impossible, which gives support to a suspicion that electronegativity is more fiction than reality.

PS The accepted electronegativity of H of 2 Hartree stands out as very singular/strange:

 

 

ElectroNegativity by RealQM

Electronegativity (or rather electron affinity, see this post) of an atom measures the decrease of total energy arising from adding an electron. Pauling suggested a scale to measure electronegativity addressing the following values to the elements in the periodic table:

We see in the 2nd row electronegativity increase from 1.0 for Lithium to 4.0 for Fluorine as the maximum over all elements. 

RealQM gives the following electron affinity values measured in Hartree:

• H-    0.04  (code)
• He-   0.8    (code)
• Li-    1.2    (code)
• Ber-  1.7    (code)
• B-     2.3    (code)
• F-      5.0    (code)

We see that the the 2nd row Pauling scale matches the RealQM values in Hartrees, which makes sense to Pauling's scale. 

We note that (i) Helium is missing in the Pauling scale, and (ii) the values for H- differ fundamentally.

The reason the Pauling scale does not take up He is probably the preconceived idea of standard quantum chemistry that He as a noble gas has no incentive at all to catch an electron. RealQM tells a different story, connecting to the previous post showing that He can form a He2 molecule. 

On the other hand, RealQM gives H a very small desire to catch an electron, thus supporting the common idea that H acts as an electron donor, in particular when forming the HF molecule by combining with F with maximal electronegativity in an ionic bond.  

The Pauling value of 2.0 for H- stands out as strange and in conflict with the idea of ionic bond in HF.  

H can form H2 molecule in a covalent bond even with small electronegativity, because no entire capture of an electron is needed, only sharing. RealQM captures the difference in capturing and sharing of electrons, which standard QM does not appear to do.