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The Structure Lacuna

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The Structure Lacuna Int. J. Mol. Sci. 2012, 13, 9081-9096; doi:10.3390/ijms13079081 OPEN ACCESS International Journal of Molecular Sciences ISSN 1422-0067 www.mdpi.com/journal/ijms Article The Structure Lacuna Jan C.A. Boeyens 1;* and Demetrius C. Levendis 2 1 Unit for Advanced Scholarship, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa 2 Molecular Sciences Institute, School of Chemistry, University of the Witwatersrand, Jan Smuts Avenue, Johannesburg 0001, South Africa; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +27-12-420-4528; Fax: +27-12-362-5288. Received: 6 June 2012; in revised form: 10 July 2012 / Accepted: 12 July 2012 / Published: 20 July 2012 Abstract: Molecular symmetry is intimately connected with the classical concept of three-dimensional molecular structure. In a non-classical theory of wave-like interaction in four-dimensional space-time, both of these concepts and traditional quantum mechanics lose their operational meaning, unless suitably modified. A required reformulation should emphasize the importance of four-dimensional effects like spin and the symmetry effects of space-time curvature that could lead to a fundamentally different understanding of molecular symmetry and structure in terms of elementary number theory. Isolated single molecules have no characteristic shape and macro-biomolecules only develop robust three-dimensional structure in hydrophobic response to aqueous cellular media. Keywords: golden ratio; molecular symmetry; spin function 1. Introduction Most quantum-theoretical concepts of chemistry have their origin in spectroscopy. The atomic spectroscopy of Kirchhoff, Bunsen, Fraunhofer and others resulted in the formulation of Balmer’s mysterious formula, the direct stimulus for the development of quantum mechanics. From molecular spectroscopy, which also dates from the 19th century, developed the concept of molecular symmetry, based on point-group theory. The concept of molecular structure was conjectured to bridge the gap between the two branches of spectroscopy. It is noted in passing that the discipline of quantum molecular theory is based entirely on this postulated, but unproven, concept of molecular structure. Int. J. Mol. Sci. 2012, 13 9082 The analysis of molecular crystals by X-ray diffraction is routinely accepted as final justification of the molecular-structure hypothesis, on assuming that individual molecules maintain their integrity and structure in the solid state. This assumption is demonstrably unjustified. The molecular unit projected from crystallographic analysis is best described as a rigid three-dimensional framework that connects point atoms and is stabilized by crystal-packing interactions. In the absence of such constraints the crystallographic point group no longer represents the shape of the more flexible molecule. Related techniques such as gas-phase electron diffraction define no more than a radial distribution function. Spectroscopists are well aware of the complications associated with defining the symmetry group of non-rigid molecules, but the chemist na¨ıvely accepts that their primitive concept of molecular structure is consistent with the most fundamental theories of physics. It is not. A recently published history of quantum chemistry [1] never mentions the concept “molecular structure”. The classic example of a non-rigid molecule is ammonia, which appears as a bipyramidal arrangement of interconverting polyhedra that reflects by tunneling through the plane of the central N atom [2]. It is pointed out [2] that: As far as the quantum-mechanical formalism is concerned, ammonia is by far no exception. Similar situations can be constructed for all molecules. They do not fit into the molecular-structure theme of traditional chemistry and are considered as “strange” states from a chemical point of view. Neither chemical structures nor chemical bonds do exist any more. On the other extreme, molecules such as the adamantane-derived bispidine ligands have been demonstrated in synthetic studies to operate as rigid units with apparently well-defined classical structure [3]. We contend that the difference between ammonia and bispidine is one of degree only. In both cases the equilibrium molecular geometry is essentially non-classical. Only in the case of bispidine is there a striking correspondence with the structure predicted by classical concepts of valency. Molecular symmetry is a classical concept based on the hypothetical model of point atoms held together by rigid chemical bonds. There is no experimental evidence for the existence of either point atoms nor chemical bonds. Both of these concepts are postulates to support the assumption of molecules with three-dimensional geometrical structure and molecular symmetry is the mathematical description of this structure. Alternatively molecular symmetry could be defined in line with more recent views on atomic and molecular structure. A more appropriate theory, starting from the nature of electrons and atomic nuclei as wave-like distortions of four-dimensional space-time, characterizes a molecule as a 4D standing-wave structure in which individual particles do not have independent existence. The only meaningful symmetry of such a construct must be four- and not three-dimensional. It will be argued that classical molecular structure is the three-dimensional projection of non-classical four-dimensional molecular geometry. Int. J. Mol. Sci. 2012, 13 9083 2. Electron Theory The point atom with mass mn is a remnant of the classically assumed ultimate philosophical limit to the subdivision of matter. It has been used in this form by Newton, Dalton, Mendeleev´ and others, until the end of the 19th century. Following Nagaoka, Rutherford and Bohr the concept of a structureless atom was abandoned and replaced by the planetary model of point-like electrons, with mass me in orbit around a point-like heavy nucleus. With the advent of quantum mechanics the Bohr–Sommerfeld orbits gave way to chemical shells of probabilistic charge density—now defining the electron as a point particle! To account for the behaviour of electrons in diffraction experiments the kabbalistic notion of wave-particle duality was concocted, notwithstanding the wave-mechanical alternative proposed by Schrodinger.¨ As the particle model found its way into textbooks the electronic wave structure was completely forgotten, although the quantum-mechanical model never made any logical sense. In order to rationalize the probability function as representing a single electron it is necessary to integrate over all space. The electron associated with a given hydrogen atom, although likely to occupy the ground-state, has a finite probability to be on the moon. The chemists of the world have been content to live with this assumption for a hundred years. They have been brainwashed so thoroughly as not to tolerate any alternative suggestion that makes logical sense. The most bothersome aspect of electronic quantum mechanics is the failure to account for the most prominent attribute of an electron, known as its spin. Efforts to artificially add a spin function to the three-dimensional state function of an electron have only been partially successful. A common remedy is often proposed through the assertion that spin is a relativistic phenomenon, but a conclusive proof has never been formulated. What has been demonstrated is that the spin function, known as a spinor, occurs naturally as an inherent feature of four-dimensional motion. In order to define an electron with spin it is therefore necessary to describe it as an entity in four-dimensional space-time. This would automatically rule out its definition as a point particle, noting that a point in four-dimensional space-time has, not only zero extension but also zero duration. It cannot exist. With this realization the interminable debate about particle or wave becomes redundant and the remaining option is to consider the electron as a four-dimensional wave structure. In fact, Schrodinger’s¨ equation is a modification of the general wave Equation. It is fashionable to state [4] that ... analogies between geometrical optics and classical mechanics on the one hand, and wave optics and quantum mechanics on the other hand ... can only make the Schrodinger¨ equation seem plausible; they cannot be used to derive or prove this equation. Statements like this are standard textbook fare that derives from the Copenhagen campaign to discredit Schrodinger’s¨ wave interpretation [5]): @2Φ @2Φ @2Φ 1 @2Φ + + − = 0 @x2 @y2 @z2 c2 @t2 1 @2Φ r2Φ = (1) c2 @t2 By defining x0 = ict, etc., this equation rearranges into Int. J. Mol. Sci. 2012, 13 9084 @2Φ @2Φ @2Φ @2Φ 2 + 2 + 2 + 2 = 0 @x1 @x2 @x3 @x0 i.e., 22Φ = 0 (2) The solution of Equation 2 has the hypercomplex form Φ = a + ib + jc + kd p known as a quaternion or the spin function. The coefficients i; j; k are generalizations of −1 with the rule of composition: i2 + j2 + k2 = ijk = −1. In order to obtain Schrodinger’s¨ solution it is necessary to separate the space and time variables on solving Equation 1. The result of this is to describe the electron as a three-dimensional object without spin. The consequence is that the three-dimensional angular momentum defined by Schrodinger’s¨ equation is not a conserved quantity and hence inadequate as a basis on which to construct molecular symmetry functions. The conserved quantity is traditionally defined as J = L + S, a solution of Equation 2. In the quaternion representation an electron can no longer be considered as an entity that moves through space, but rather as a distortion of space-time, or the vacuum. A vivid visualization was proposed by Weingard [6] ... conceiving of the motion of particles on analogy with the motion of the letters on the illuminated news sign in Times Square. The letters move, not by anything moving, but by the sequential blinking of the lights of which the sign is composed. Similarly, we can conceive of the motion of a particle as the motion of a geometrical property. Regions of space do not move, but the geometry of adjacent regions change in such a way that a pattern of geometrical properties—the pattern we identify with a certain particle—moves.
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