Quantum Physics, Cell Division and the Nature of Chemical Bonding
By Mario Wingert (May 2019)
Friedrich Hund and Robert Mulliken (founders of molecule orbital theory, R.M. Nobel Prize winner for chemistry 1966) already concluded between 1925 and 1927 on the basis of molecular spectroscopic experiments that the spectra of the hydrogen molecule in principle did not differ much from those of a single hydrogen atom. Based on these findings, Hund and Mulliken designed a new concept of chemical bonding and the 'Aufbau principle' radically different from the additive approach developed simultaneously by Heitler, London and later by Linus Pauling (the concept of electron valence bonding): Heitler, London and Pauling thought that the hydrogen molecule is produced by two single hydrogen atoms coming together by approximation and forming an overlapping electron region between the two nuclei, resulting in a common electron pair. This image was based on a postulated "exchange force" between the two hydrogen atomic orbitals (despite repulsive forces) and was modelled by two overlapping Schrödinger electron wave equations. In contrast, Hund and Mulliken imagined that the diatomic hydrogen molecule would emerge from a monatomic, spherical helium atom by a division transformation: the helium atom nucleus would divide into two nuclei, while the original sphere, two-electron cloud of the helium atom would deform into two interconnected spheres forming the holistic molecule orbital of the hydrogen molecule.*
Here we are confronted with a geometric transformation from a single sphere to a connected double sphere or "dumbbell shape". Can we really interpret this transformation as cell division or branching of field orbitals or whole "atoms" or better, of an integral molecule a la Avogadro, as our reinterpretation of Avogadro's hypothesis, chemical experiments, the hydrogen molecule spectra and quantum experiments with single "particles" suggests? Isn't it surprising to find the same approach and a similar picture in the not so well known molecule orbital theory, which dates back to 1925-1928, the founding period of quantum physics?
The term orbital was originally an extention of Bohr's term "electron orbit", for the classical picture of a circular moving electron around the nucleus - on a trajectory like a planet - was unholdable in the new quantum theory after 1925. The word orbital means now exactly the probability density of possible locations where a point-like electron "could be found", if such kind of measurement would be made. This is the Born-Rule, or better: Max Born's interpretation of a mathematical operation, the squared modulus, which has to be applied to the complex state function amplitudes to modelize local absorption events of a (partial-) wave to get approximated point-like solutions, hence to modelize the location of an "point-like" imagined electron.
But this is some kind of euphemism (therefore the quotation marks), for point-like solutions are excluded on principle: it's a Dirac delta function, consisting of two approaching curves which form a funnel-shaped geometry which has in the middle of course a value of zero, but never a point-like solution. Spacelike thought it would be an open ring, endless shrinking in diameter, but never disappearing - hence the area between the two graphs is by no means part of any solution. To bridge this little logical gap Born spoke vaguely about an "area nearby" where the electron could be found. I mention this problem to make clear that there are indeed some questionable terms and pictures like "location", "point-like", and "electron as a particle", up to the question about the creditibility of this interpretation of the used mathematics as indication of "particles".
Aside the problem of giving the squared modulus operation another physical meaning than a suddenly materializing dimensionless particle (which is no more than a giant leap backwards into mechanics, a philosophical wish list interpretation), the mathematical state description practically serves as a model of a non-local "one-electron-field", smeared out around the nucleus, as Schrödinger described it. It is what the physicist calls a local standing or stationary wave, space-like, that does not move or oscillate.
The energy levels now give us a hint that this stationary wave or field orbital is able to perform spacelike transmutations if light energy is absorbed or emitted. It starts with a simple sphere (the so-called Grundzustand or s-orbital), which is "splitting" - or better, branching or cell dividing itself - into two or more sub-parts, branches, or molecule cells, following distinct symmetry principles (called bonding and anti-bonding orbitals). These are the same structure principles as in Bohr's pseudo-mechanical orbit description of the atom complemented by Pauli's exclusion principle, but with more than one electron we get a hierarchy of electron orbits, which are appearently physically not connected. This is only a consequence of the use of the particle model. The energy hierarchy - and the coherent character of the enantiomorphic field - can better be illustrated operationally as tree-like field branching, where the field state is modeled by branching rays (or vectors). See figure below: the transmutation of chemical elements in the field branching model.
The question was then how to adapt the atomic orbit model and wave-like electron exitations of single-electron-state functions to polyatomic molecules which were much more complicated than a hydrogen atom, with much more electrons influencing each other. The new picture of Hund and Mullikan was now that only the outer electron shell - a one-electron wave function - should be important for bonds, but it should enclose the whole molecule instead to be localized between the two nuclei of the hydrogen atoms. And it should in principle satisfy the same quantum number rules based on Pauli's Ausschließungsprinzip and Schrödinger's one-electron wave function of the atomic hydrogen, except that this one-electron wave function has to be related now to two nuclei, which determine a particular shape of the orbital, and the symmetry relations between the quantum numbers (energy levels). To reflect these symmetry relations, which could be conceived as antisymmetrical or symmetrical branching or "splitting" processes of the "energy levels" of the one-electron state function, the mathematical group theory was used.
If we now discard the particle picture of the electron (experimentally well founded due to the interference condition), and with that the atomic assumption of indivisible entities in general, and take the stationary orbital and its branching transmutations as a model of real existing self-structuring processes of an holistic field, and try to express their connectedness or wholeness physically with enantiomorphic properties, we could adapt the cell division and branching picture of fields without any contradiction to experimentally proved facts or mathematical rules like Paulis Ausschließungsprinzip (Pauli's exclusion principle), originally conceived by himself as a strange "two-valuedness" of the magnetic (spin) properties of the electron. And this is also compatible with the molecule orbital theory of Robert Mulliken and Friedrich Hund, as their model of a division transformation of a single, spheric helium atom into a double-spheric hydrogen molecule already indicates.
In this case we have no reason to think that the stationary branched field orbital oscillates or that there is something moving, like Bohr's electron or de Broglies electron waves, what explains the stability of field matter structures in the absence of interactions (whereas interactions indeed cause structure changes). And we can interprete the real and imaginary part of the "wave function", or better, of the branched field orbital state function, as model-like mathematical representation of the two mirrored parts of an enantiomorphic field entity or molecule.
So the cell division and branching process of field orbitals is able to give us something that was considered impossible in quantum mechanics: a physically comprehensible, visualizable and adequate picture of the elementary structures, experiments and physical processes of nature - the nature of the quantum "mechanism" or its functioning, which does not necessarily mean "mechanics", as the branching process shows. This picture does without mechanics, particles and atoms, quite naturally.
But then we have yet to correct our picture of an "real existing" 3D-space, for we now have to assign to every new branch a new space-like dimension, which is a well known problem of the interpretation of the reality of wave functions of atoms with more electrons than hydrogen. I think this is not really a problem, for we know that the concept of space as a 3D-vessel, real existing physical entity, and reference system causes similar problems, which led to the relativity theories. We can take the branching or cell division process simple as physical generation of a new degree of freedom, which opens a new spacelike dimension - hence a new branch or field cell. This new dimension itself is two-valued (two branches, antisymmetrical, enantiomorphic, and has therefore to be expressed in complex numbers), which we can interpret as internal degrees of freedom of a branched system which is part of a hierarchical organized (branched or cell-divided) holistic field structure. Matter field structures can have multiple space-like dimensions depending of their structure depth, like a tree, a cell compound, or a molecule. The more light energy is bounded, the more structure, mass, and intertia.
Robert Mulliken himself gave a short summary of his molecule orbital concept in 1932:
"The principal novelty in the present viewpoint in regard to molecular structure, aside from the consideration of the effect of symmetry of the molecule on the wave functions, consists in the following: In general no attempt is made to treat the molecule as consisting of atoms or ions. Attempts to regard a molecule as consisting of specific atoms or ionic units held together by discrete numbers of bonding electrons or electron pairs are considered as more or less meaningless, exept as an approximation in special cases, or as a method of calculation."
Source: Robert S. Mulliken: "Electronic Structures of Polyatomic Molecules and Valence (1)". Phys. Rev. 40, 55, p.57, 1932. Contained also in: Selected Papers of Robert S. Mulliken, University of Chikago Press, 1975, p. 451.
*More about the history of chemical bonding and quantum chemistry on this website: "Linus Pauling: The Nature of the Chemical Bond"
*Despite a direct request to the original author of the article on the helium-hydrogen transformation of Hund and Mulliken (on the Linus Pauling page), the original source could not be determined, because the article was written by him many years ago and he could not remember it. I have also contacted the son of Friedrich Hund in Göttingen who gave me insight in some pages of Hund's working diaries, but I didn't found there a hint. If there is some expert who knows in which article or book the helium-hydrogen transformation is described by Hund or Mulliken, please let me know. I think it could be historically valueable. Thanks in advance.