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Electronic structure and number theory : bohrs boldest dream

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  • "J.C.A. Boeyens and P. Comba Chemistry by Number TheoryJ.C.A. Boeyens Chemistry in Four DimensionsC.J.H. Schutte Is the Rydberg-Ritz relationship valid?J.C.A. Boeyens Calculation of Atomic Structure J.C.A. Boeyens Covalent InteractionP. Comba and J.C.A. Boeyens Molecular ShapeJ.C.A. Boeyens and D. C. Levendis All is Number"
  • "Whoever reads this volume without rejecting the picture of a point electron that only shows up as a probability distribution has the same problem. In our perception it occurs, like other elementary entities, as a persistent, flexible, wave-like, chiral distortion of space-time. It has mass, charge and spin by virtue of a characteristic wave structure. It disperses into the vacuum on interaction with another of opposite chirality. It is no accident that both wave motion and the fundamental theory of chemistry are best described in terms of natural numbers. However, conventional wave mechanics in three dimensions offers only a partial elucidation of the periodic table of the elements. On the other hand, a detailed reconstruction, also of the more general periodicity of stable nuclides, derives directly from elementary number theory. It shows, in addition, how the periodic function responds to the state of space-time curvature and identifies the golden ratio as a possible parameter that links perceptions in tangent space to the situation in curved space-time. This observation is exploited in the analysis of chemical systems without formal solution of the four-dimensional problem. Most of the work in this volume reports results of this type. To be of practical use the number theory results, which pertain specifically to pairwise diatomic interactions, might be incorporated into algorithms that simulate more complex molecules. Molecular mechanics appears to be an appropriate model to achieve this. In the current quantum chemistry world, molecular mechanics appears to be a "low-level", entirely empirical model which fully ignores the relevant electronic effects [4]. However, via specific atom types, the electronics may be accounted for, and there are a number of recent developments which include specific electronic terms, based on classical quantum chemistry [5-8]. More importantly, in terms of structural modeling, the quality of MM only depends on the force field and its parameterization based on experimental data [9]. The approach presented in this volume suggests that number-theory-based models may significantly reduce the parameter space and, more importantly, produce generic parameters, which might or might not be optimized, based on experimental data in order to obtain a higher accuracy. The development of chemical theory in terms of number theory is not new [10]. What is new is the realization that we are dealing with a four-dimensional problem, the analysis of which requires a fundamentally different mathematical treatment. Physically it means that a 3D analysis in terms of point particles is necessarily incomplete. The analysis by Schutte demonstrates beyond any doubt that the basic assumption of atomic spectroscopy, based on the traditional separation of space and time variables, is not supported by experiment. The most glaring demonstration that a 4D analysis is required is provided by the appearance of electron spin, which never emerges in any 3D model. It is important to understand that spin is not a relativistic effect, but derives from the four-dimensional conservation of angular momentum. These features were not known before and this is the first effort to take their consequences into account. It needs a radically new model of atomic electron distribution, and the exciting thing is that such a model is provided by an optimization by logarithmic spirals. The result is in striking agreement with a standing-wave model of electron density that involves the golden ratio and many other aspects of elementary number theory. Without further assumptions this model of atomic structure can be interpreted directly as the definitive basis of atomic ionization radii and electronegativity. Our reference to previous conclusions about the origin of the periodic table is done to explain the earlier empirical conclusions more logically. What is new in the re-examination of covalent interactions is that the approach in terms of a four-dimensional wave structure leads to a precise definition of bond order, not achieved before. Together with the new free atom ionization radii the parameters of interatomic distance, dissociation energy, stretching force constants and diatomic dipole moments can now be derived as simple functions of the ionization radii and the golden ratio. These results have nothing in common with the more approximate simulations described before. The papers in this volume address a single theme and in order for each of them to constitute a self-contained unit a fair amount of repetition is inevitable, even with generous cross referencing. Many readers, less familiar with the concepts of number theory, the golden mean, logarithmic spirals, hypercomplex numbers, projective geometry, general relativity and quantum field theory, may actually find some reiteration to be of benefit. Not to alienate such readers at the outset the editor in chief, Mike Mingos, patiently guided the composition of the opening paper into the style of Structure and Bonding. His much appreciated advice is gratefully acknowledged. We expect our proposed approach to the understanding of chemically important issues to be rejected by many readers who operate in a comfort zone defined by probability densities, Born-Oppenheimer systems, hybrid orbitals, potential-energy surfaces, ab initio theory and DFT simulations-all of them Copenhagen spinoffs. We realize, of course, that these models have been developed to standards, where they produce a very accurate optimization of structures and properties of molecular compounds and materials in many areas [11], and for application-oriented theoreticians as well as for experimentalists, who use applied theory for predictions and interpretations, there is no immediate need to leave the comfort zone. At the same time it is interesting to note that we are not alone in advocating a rethink of theoretical chemistry. An increasing number of papers in the recent literature (e.g. [12]) call for an update of the teaching of valence theory, for the orbital concept and related ideas to be abandoned and specifically to be removed from undergraduate curricula. We do not fully agree with all those suggestions, but some ideas pioneered in this volume could hopefully find their way into a new paradigm."

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  • "Electronic books"
  • "Aufsatzsammlung"

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  • "Electronic structure and number theory Bohr's boldest dream"
  • "Electronic structure and number theory : bohrs boldest dream"@en
  • "Electronic structure and number theory : bohr's boldest dream"
  • "Electronic structure and number theory : Bohr's boldest dream"
  • "Electronic Structure and Number Theory Bohr's Boldest Dream"

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