A unified picture of weak chemical bonds: hydrogen, halogen, carbon...

Previously I posted about improper hydrogen bonds. These are weak hydrogen bonds that have the unusual property that in the X-H...Y system H-bonding leads to a shortening and hardening (blue shift) of the X-H bond. In contrast, for "proper" bonds, X-H lengthens and softens (red shift).

The past few years has seen a rapid increase in interest in an even broader class of weak bonds such as "halogen bonds",  denoted X-Z...Y where Z can now be not just H but a halogen (F, Cl, Br), chalcogen (O, S, Se, Te), or pnictogen (N, P, As, ..)....

There is an interesting paper that contains the helpful summary figure below
Negative hyperconjugation and red-, blue or zero-shift in X-Z---Y complexes
Jyothish Joy, Eluvathingal D. Jemmis and Kaipanchery Vidya

In trying to understand the paper I found reading the following older paper helpful
Electronic Basis of Improper Hydrogen Bonding:  A Subtle Balance of Hyperconjugation and Rehybridization
Igor V. Alabugin, Mariappan Manoharan, Scott Peabody, and Frank Weinhold

[Aside: note the senior author is Weinhold who has featured in some previous posts]

The basic idea is that there are two competing interactions. "Hyperconjugation" is Weinhold's view of proper H-bonds, via the Natural Bond Orbital donor-acceptor picture where the H-bond arises due to charge transfer from the lone pair orbital on Y to the σ* (anti-bonding) orbital associated with X-H. This lengthens and hardens X-H.
When this interaction is weak there is “X-H bond shortening” due to increase in the s-character (rehybridisation of the atomic orbital on X) and polarization of the X−H bond. This is associated with a shorter and harder X-H bond.

Bent's rule is central. It is one of the most general rules governing structure of organic molecules.

atoms tend to maximize the amount of s-character in hybrid orbitals aimed toward electropositive substituents and direct hybrid orbitals with the larger amount of p-character toward more electronegative substituents.

Increasing s-character generally leads to shorter bonds.
As the donor acceptor distance (X-Y) decreases the X-Z bond becomes more polarised and the s-character increases.
The authors note it should be possible to test predicted trends since the amount of s character in the X-Z bond can be measured from the relevant NMR coupling constant.

My question is whether this subtle competition can be captured by generalising my simple 2 diabatic state model for H-bonds to a 3 state model that includes the ionic character of the X-Z bond.