### 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.

- 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 k^{2}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.

- The binding energy of atom would scale as 1/n
^{2}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.

- 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.

- The Bohr radii of valence electrons of atoms scale as a
_{B}∝ m^{2}/Z_{eff}^{2}, 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 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}∝ (n^{2}/n_{min})^{2}m^{2}/Z_{eff}^{2}, and if nm/(n_{min}Z_{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_{min}Z_{eff}) be true in reasonable approximation also for lattice bonds?

- 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.

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

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