Why Is Chemical Bonding Still a Mystery?

Chemistry is formed by chemical bonding of atoms into molecules, but the physical nature of a chemical bond appears to be unknown even today 100 years after Quantum Mechanics was formed as the physics of atoms and molecules:

• There is no unique way of defining a chemical bond from quantum mechanics. (Roald Hoffmann)
• The concept of the chemical bond is not a real one; it is a figment of our own imagination. A bond does not exist as an observable entity.( Charles Coulson)
• Quantum mechanics does not provide a definition of a chemical bond. (Richard Bader)
• The exact solution of the Schrödinger equation would not solve the chemical problem. (Per-Olov Löwdin)
• Orbitals, bonds, and structures are models imposed on quantum results, not entities delivered by QM itself. (John C. Slater)
• The chemical bond is not a quantum-mechanical observable. (George C. Pimentel)
• Exact quantum dynamics would still not yield chemical concepts such as mechanisms, bonds, or reaction pathways. (William H. Miller)

The lack of a single convincing theoretical explanation of the physics of chemical bonding, questions the credibility of Chemistry as a science, which is met by (instead of one correct theory) a battery of different explanations including Lewis, VB, MO, CFT, LFT, Band Theory, Quantum Chemistry (HF/DFT), supposed to capture different aspects while partly being contradictory.

But in this rather desperate situation of confusion there may be hope the form of  

• Alternative Computational Foundation of Chemistry 

offering an analysis of covalent chemical bond based on a new form of Schrödinger's equation in physical space with clear physical meaning. If you have ever wondered why one neutral Hydrogen atom $H$ can attract another neutral H to form a $H_2$ molecule as a stable relation, this is for you.

Is is natural to trace the unclear physics of covalent chemical bonding back to the lack of clear physics of Schrödinger's equation in its textbook form. Chemical bonding must rely on clear physics to work, and so cannot be explained by unclear physics. 

Chemistry is real physics and cannot rely on a Schrödinger equation without meaning as real physics. RealQM offers a new Schrödinger equation as real physics, and thus a new foundation of chemistry.

 

Chemical Bonding: StdQM vs RealQM

The basic problem of chemistry is how molecules as stable composites are formed through chemical bonding between collections of atoms consisting of positively charged nuclei surrounded by negatively charged electrons. The total energy $TE$ of a stable molecule is smaller than the sum of the energies of the atoms involved, with $TE$ the sum of 

• electron-nucleus potential energy $E_{en}$ negative
• electron-electron potential energy $E_{ee}$ positive
• nucleus-nucleus potential energy $E_{nn}$  positive
• electron kinetic energy $E_{ke}$ positive.

Standard Quantum Mechanics StdQM seeks to explains chemical bonding as an effect of: 

1. Localisation of electrons between nuclei giving maximal decrease of $E_{en}$.
2. Delocalisation of electrons over the whole molecule compensating for increases of $E_{ke}$ from localisation.  

We see a combined process of localisation-delocalisation, which is contradictory and requires intricate explanation to make sense forming a vast literature. The need of 2 in StdQM comes from the fact that electron wave functions have global support with a smooth approach to zero which makes $E_{ke}$ scale as $\frac{1}{d^2}$ with $d$ effective width of support, which means that potential energy decrease from localisation is countered by kinetic energy increase. 

In RealQM as an alternative to StdQM electron wave functions have non-overlapping local supports meeting with continuity without need of approaching zero. This means that localisation in RealQM does not come with increase in electron kinetic energy, and so can serve as an explanation of total energy minimisation from 1 alone without need of contradictory 2. For details see these articles.

Connecting to the previous post, recall that the main role of the Periodic Table is to support understanding of chemical bonding.

Chemical Bond: He2 vs Li+H- vs LiH

1. Li+H-

Let us now let RealQM explain why two Helium He atoms do not bond to a He2 molecule, while a lithium cation Li+ forms a molecule with the anion H- with strong bond. The set up is thus

• Each He has a +2 kernel surrounded by 2 electrons.
• Li+ has a +3 kernel surrounded by 2 electrons and H- has +1 kernel surrounded by 2 electrons.  

The essential difference is thus the two +2 kernels of He2 to be compared with the +3 and +1 kernels of Li+H- with 4 electrons in both cases. We shall below compare Li+H- (solid phase) with LiH (gas phase).

As concerns He2 we refer to this post explaining the lack bond of He2 as a consequence of an outward  shift of the electron charge distribution counteracting the bonding effect from accumulation of charge between the kernels.

We now compare the He2 computation with corresponding computation for Li+H- with thus a change from +2 and +2 kernel charge to +3 and +1 and get the following result running this code:

• 

We obtain a ground state energy of Li+H- = -8.08 Hartree to be compared with the energy of Li+ = -7.28 and H- = -0.527 altogether = -7.807, which indicates a dissociation energy of Li+H- = 0.27. According to chatGPT this matches the value 0.26 by FCI and CCSD(T) as best value using Standard Quantum Mechanics StdQM. 

RealQM and StdQM thus give the same dissociation energy for Li+H- but from different mathematical models: RealQM is based on non-overlapping one-electron charge densities as problem in 3 space dimensions, while StdQM requires 12 space dimensions for the 4 electrons involved. RealQM has a direct deterministic physical meaning, while the physical meaning of StdQM is still an open problem.  

The advantage of RealQM is that an explanation of the binding of Li+H- can be read from the above 2d section through the kernels of Li+ and H-, and the 1d section of the one-electron wave functions in yellow:

1. We see to the left 2 half-spherical electron/wave function distributions around the +3 kernel meeting at a free boundary represented in the meeting of yellow curves.
2. Similarly we see to the right 2 half-spherical electron distributions around the +1 kernel meeting at a free boundary.
3. We see an accumulation of charge between the kernels with wave functions meeting at a free boundary, which creates a bond because the accumulation does not require increase of kinetic energy since the wave functions meet with non-zero common value.
4. We see that the free boundary for H- is shifted to the right which decreases the presence of the left half-spherical electron between the kernels and so decreases the bond.
5. The effect of 3 shows to dominate over 4 and so forms a strong bond. 

We now compare with the finding of this post that the Helium atom He does not form a molecule He2 since there is no binding, because in this case the effect of 3 is cancelled by 4 to no bond. 

RealQM offers a concrete physical explanation of both the strong bond of Li+H- and the no bond of He2.

RealQM agrees with StdQM as concerns dissociation energies in both cases. 

StdQM does not offer any physical explanation because it is based on a non-physical model. 

We see also that even if the Li+H- is viewed to have an ionic bond, because an electron has been transferred for Li to H, the actual bond between Li+ and H- is formed as a covalent bond from electron accumulation between the kernels, or "sharing electrons" in StdQM terminology. It suggest that ultimately all chemical bonds are covalent. In particular, both H- and Li+ participate in covalent bonding and the StdQM idea that they cannot because their two electrons form a "filled shell", does not seem to represent physics.

2. LiH

We compare with the smaller dissociation energy 0.0906 of LiH with a covalent bond between Li and H according to the following list of atoms of the form XH with X an alkaline metal with one valence electron.

We thus let RealQM compute dissociation energies E of molecules of the form XH with X=Li, Na, K, Rb, Cs an Fr the Alkaline Metals, and H Hydrogen, with the computation in 3d reduced to the covalent bond from the valence electron of X meeting inner shell electrons a certain distance R to the kernel, and the valence electron of H.  We obtain the following results using this code:

• R = 0.5     E = 0.13
• R = 0.55   E = 0.087
• R = 0.6     E = 0.08
• R = 0.7     E = 0.06
• R = 0.8     E = 0.047
• R = 0.9     E = 0.034 
• R = 1.0.    E = 0.02

with R in atomic units and E in Hartree.

We compare with the following list values:

• LiH   E = 0.0906
• NaH   E = 0.0769
• KH     E = 0.0701
• RbH   E = 0.0655
• CsH   E = 0.0609
• FrH   E = 0.0571

We see a match over the column LiH - FrH with R in the range 0.55 - 0.8.

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3. Transition LiH to Li+H-

Since Li+H- has lower energy than LiH, there is an energy minimisation path from LiH to Li+H- which we seek to capture in this code. We see here the valence electron of Li concentrating charge to the region between the kernels thus forming a form of covalent bond of Li+H- as a new view on the physics.