Valence bond theory from the hierarchy of Planck constants

The idea that valence bonds, or at least some of them, correspond to non-standard value of h_eff/h=n (see this) is very attractive. It could allow to understand what chemical bonds really are and allow a detailed view about how reductionism fails in the sequence of transitions from atomic physics to molecular physics to chemistry to biochemistry.

1. The standard value of n, call it n_min need not correspond to n_min=1 and the findings of Randell Mills (see this) suggesting that hydrogen atom and possibly also other atoms can have binding energies coming as k² multiples of ordinary ones with k=2,3,6, suggests that n_min=6 could correspond to the standard value of h_eff for atoms. n>n_min would mean reduced binding energy and this would mean the possibility of high energy valence bonds.
   
   
2. The binding energy of atom would scale as 1/n² so that for non-standard values of n>n_min would correspond to smaller binding energy scale. The finding that heating of rare-earth atoms leads to a disappearance of some valence electrons (see this) suggests that the value of n for some valence electrons increases from n_min in these situation. The same effect might be achieved by irradiation at suitable photon energies corresponding to energy difference between ordinary state and dark state of electrons. An entire spectroscopy of atoms with dark valence electrons would be waiting to be discovered.
   
   
3. n>n_min would explain why valence bonds are carriers of metabolic energy liberated in catabolic part of metabolism. The temporary of energy involving temporary reduction of n would in turn make possible bio-catalysis by kicking the reactants over the potential wall making the reaction slow. The shortening of long flux tube bonds between reacts as the value of n is reduced could explain why bio-molecules are able to find each other in the molecular crowd.
   
   
4. The Bohr radii of valence electrons of atoms scale as a_B∝ m²/Z_eff², where m (usually denoted by n) is the principal quantum number determining the value of energy in the model based on Schrödinger equation. Z_eff is in good approximation equal to the unscreened nuclear charge Z_eff=n_V equal to the number of valence electrons. If the superposition of atomic orbitals restricted to valence bonds is the essence in the formation of molecules, one an argue that the lengths of bonds and radii of molecules should decrease rapidly with Z_eff. However, the empirical fact is that the bond lengths vary in a rather narrow range, roughly by factor 2!
   
   

The solution of the problem looks rather unique.

1. The value of n assignable to the valence bond is scaled so that nm/Z_eff is near to unity so that the Bohr radius is near to that for hydrogen atom. Z_eff is naturally the charge unscreened by the closed electron shells and equal to the number Z_eff=n_V of valence electrons. This conforms with the periodicity of the periodic table. Since the value of n is same for both bonded atoms, the value of Bohr radii differ which implies that electronic charge is shifted towards the atom with larger n_V and electro-negativities of atoms parameterizing this behavior are different for the atoms of the bond. This conforms qualitatively with the valence bond theory.
   

   For n>n_min one would have a_B∝ (n²/n_min)²m²/Z_eff², and if nm/(n_minZ_eff) is constant in reasonable approximation, the estimate for bond length does not depend much on Z. Could the weak variation of bond lengths be a direct indication that the reduction of molecular physics to atomic physics fails? Also the size of atoms in lattice about 2a_B(H) (one Angström) depends only weakly on Z_eff: could the constancy of nm/(n_minZ_eff) be true in reasonable approximation also for lattice bonds?
   
   

2. The predicted lengths of valence bonds should be realistic: this forces n>n_H and n∝ Z_eff is a rough guess. One should also understand the values of electro-negativities χ(X) allowing quantitative understanding about the distribution of charge along the bond. The bond lengths assignable to the bonded atoms are in general different and the one one with shorter bond length for electrons is expected to be more electronegative since the electrons for it are less de-localized.
   
   

See the article Mysteriously disappearing valence electrons of rare Earth metals and hierarchy of Planck constants or the chapter Quantum criticality and dark matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

For a summary of earlier postings see Latest progress in TGD.

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