A Molecular–Structure Hypothesis

The self-similar symmetry that occurs between atomic nuclei, biological growth structures, the solar system, globular clusters and spiral galaxies suggests that a similar pattern should characterize atomic and molecular structures. This possibility is explored in terms of the current molecular structure-hypothesis and its extension into four-dimensional space-time. It is concluded that a quantum molecule only has structure in four dimensions and that classical (Newtonian) structure, which occurs in three dimensions, cannot be simulated by quantum-chemical computation

Study of a confined Hydrogen-like atom by the Asymptotic Iteration Method

The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen-like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no longer bound, are also calculated. The results are compared with those in the literature.Comment: 10 page

Novel synthesis and characterisation of 3,3-dimethyl-50-(2-benzothiazolyl)- spironaphth(indoline-2,30-[3H]naphth[2,1-b] [1,4]oxazine) derivatives

Novel modified spirooxazines (SOs) with additional chelating groups were synthesised and the crystal structure of one of these was determined. UV–vis spectroscopic characterization of the photoisomerization of the SO derivatives shows that the photochromic behaviour is altered with Zn2+ coordination. In particular, addition of a group as in carboxylic acid 5 to the indole section of the SO increases the lifetime of the merocyanine Zn 2+ complex by 20-fold compared to the methylated indole 6

The intersection of archaeology, oral tradition and history in the South African interior

The historical entanglement of indigenous and colonial societies in South Africa created not only multiple points of social and cultural interaction, but also a repository of interconnected material, oral and documentary records. A multi-source, comparative approach across disciplinary boundaries is, therefore, essential to achieve a full and seamless account of late precolonial and early colonial African history. Oral tradition could serve as a bridge between archaeology and text-based history, thereby enabling historically known political lineages to be connected with the archaeological ruins of specific precolonial African towns. Similarly, documentary sources on African societies of the interior are often very limited in scope even deep into the nineteenth century, as a result of which the complementary use of archaeological methods and data becomes a methodological imperative. Three case studies from the South African interior, Marothodi, Kaditshwene and Magoro Hill, are presented to illustrate the explanatory potential of an interdisciplinary approach to the study of the more recent African past

N-(2,6-Diisopropyl­phen­yl)formamide

The title compound, C13H19NO, exhibits a non-planar structure in which the 2,6-diisopropyl­phenyl ring is tilted at a dihedral angle of 77.4 (1)° with respect to the formamide group. This is the largest dihedral angle known among structurally characterized formamides. The mol­ecules are linked via N—H⋯O hydrogen bonds, forming infinite chains which run along the b-axis directions

Chemistry in four dimensions

Some chemical phenomena, awkward to rationalize, are argued to originate in the four-dimensional nature of matter in curved space-time. The problem is traced back to the separation of space and time variables in the analysis of fourdimensional events. Althoughmathematically sound, this operation is not physically valid. It destroys the essential non-classical entanglement of space and time, which is recognized in relativistic theory, but not in quantum mechanics. We show that without this approximation the state functions of quantum theory have the same quaternion structure that describes Lorentz transformation and spin. Hypercomplex formulation of four-dimensional motion eliminates several bothersome concepts, such as wave-particle duality and probability density, by providing the logical basis for non-zero commutators in non-classical systems. It shows why chiral states are undefined in quantum theory and why many solid-state transitions appear to be sterically forbidden. A brief introduction to hypercomplex algebra is given as an Appendix.http://www.springer.com/series/430hj201

Wave-mechanical model for chemistry

The strength and defects of wave mechanics as a theory of chemistry are critically examined. Without the secondary assumption of wave-particle duality, the seminal equation describes matter waves and leaves the concept of point particles undefined. To bring the formalism into line with the theory of special relativity, it is shown to require reformulation in hypercomplex algebra that imparts a new meaning to electron spin as a holistic spinor, eliminating serious current misconceptions in the process. Reformulation in the curved space-time of general relativity requires the recognition of nonlinear effects that invalidate the practice of linear combination of atomic orbitals, ubiquitous in quantum chemistry, and redefines the electron as a nondispersive wave packet, or soliton.http://link.springer.com/journal/106982016-10-30am201

Molecular shape

Molecular shape is recognized as an emergent property that complements the projection fromfour-dimensional space-time to tangent Euclidean space. Projection from hypercomplex algebra to real algebra necessitates the three-dimensional definition of concepts such as chirality, quantum uncertainty and probability density to compensate for errors of abstraction. The emergent alternative description of extranuclear charge density as spherical standing waves, optimized by a golden spiral, reveals atomic structure in line with the periodic table of the elements and underpinning the concepts of bond order, interatomic distance and stretching force constant, related to chemical interaction. The principles giving rise to molecular structure are shown to depend, like bond order, on the constructive interference of atomic wave fields, optimized by minimal adjustment to bond orders. The procedure is shown to be equivalent to the philosophy of molecular mechanics. Arguments based on the traditional interpretation of electronegativity, are presented to relate the parameters of strain-free bond lengths, dissociation energies and harmonic force constants, used in molecular mechanics, to quantum-mechanically defined ionization radii of atoms. Atomic electron densities and a bond-order function, both obtained by number-theory optimization, enable the direct calculation of interatomic distance, dissociation energy and stretching force constant for all pairwise interactions of any order. Torsional interaction determines the final shape of a molecule and presumably can only be understood as a four-dimensional effect.http://www.springer.com/series/430hj201

Whole-genome sequencing for an enhanced understanding of genetic variation among South Africans

The Southern African Human Genome Programme is a national initiative that aspires to unlock the unique genetic character of southern African populations for a better understanding of human genetic diversity. In this pilot study the Southern African Human Genome Programme characterizes the genomes of 24 individuals (8 Coloured and 16 black southeastern Bantu-speakers) using deep whole-genome sequencing. A total of ~16 million unique variants are identified. Despite the shallow time depth since divergence between the two main southeastern Bantu-speaking groups (Nguni and Sotho-Tswana), principal component analysis and structure analysis reveal significant (p < 10−6) differentiation, and FST analysis identifies regions with high divergence. The Coloured individuals show evidence of varying proportions of admixture with Khoesan, Bantu-speakers, Europeans, and populations from the Indian sub-continent. Whole-genome sequencing data reveal extensive genomic diversity, increasing our understanding of the complex and region-specific history of African populations and highlighting its potential impact on biomedical research and genetic susceptibility to disease