Atomic theory wave mechanical model

From a chemical point of view the most important result is that number theory predicts two alternative periodic classifications of the elements. One of these agrees with experimental observation and the other with a wave-mechanical model of the atom. The subtle differences must be ascribed to a constructionist error that neglects the role of the environment in the wave-mechanical analysis. It is inferred that the wave-mechanical model applies in empty space Z/N = 0.58), compared to the result, observed in curved non-empty space, (Z/N = t). The fundamental difference between the two situations reduces to a difference in space-time curvature. 

Each of the three theories accounts for some, but not all aspects of elemental periodicity. The common ground among the three may well reveal the suspected link with space-time structure. What is required is to combine aspects of the wave-mechanical model of hydrogen, the structure of atomic nuclei and number theory. 

The Schrodinger wave equation In 1926, Austrian physicist Erwin Schrbdinger (1887-1961) furthered the wave-particle theory proposed by de Broglie. Schrbdinger derived an equation that treated the hydrogen atom s electron as a wave. Remarkably, Schrbdinger s new model for the hydrogen atom seemed to apply equally well to atoms of other elements—an area in which Bohr s model failed. The atomic model in which electrons are treated as waves is called the wave mechanical model of the atom or, more commonly, the quantum mechanical model of the atom. Like Bohr s model,... 

As we explore this topic, and as we use theories to explain other types of chemical behavior later in the text, it is important that we distinguish the observation (steel msts) from the attempts to explain why the observed event occurs (theories). The observations remain the same over the decades, but the theories (our explanations) change as we gain a clearer understanding of how nature operates. A good example of this is the replacement of the Bohr model for atoms by the wave mechanical model. 

In 1913 Niels Bohr proposed a system of rules that defined a specific set of discrete orbits for the electrons of an atom with a given atomic number. These rules required the electrons to exist only in these orbits, so that they did not radiate energy continuously as in classical electromagnetism. This model was extended first by Sommerfeld and then by Goudsmit and Uhlenbeck. In 1925 Heisenberg, and in 1926 Schrn dinger, proposed a matrix or wave mechanics theory that has developed into quantum mechanics, in which all of these properties are included. In this theory the state of the electron is described by a wave function from which the electron s properties can be deduced. 

In the modern model of the atom, based on wave mechanics, the conception of electronic orbits in the old model is replaced by the idea of the probability of the occurrence of an electron at a given point. The conclusions, however, which can be drawn from the older model remain the same in the newer conception, and it is important to remember that in this new model the essential points of Bohr s theory have not been discarded, but merely interpreted differently and very greatly refined. 

The wave-mechanical theory of the atomic bond leads to a more detailed picture of the multiple bond (Penney), no longer based on a tetrahedral model. 

Soon after the development of the quantum mechanical model of the atom, physicists such as John H. van Vleck (1928) began to investigate a wave-mechanical concept of the chemical bond. The electronic theories of valency, polarity, quantum numbers, and electron distributions in atoms were described, and the valence bond approximation, which depicts covalent bonding in molecules, was built upon these principles. In 1939, Linus Pauling s Nature of the Chemical Bond offered valence bond theory (VBT) as a plausible explanation for bonding in transition metal complexes. His application of VBT to transition metal complexes was supported by Bjerrum s work on stability that suggested electrostatics alone could not account for all bonding characteristics. 

Before discussing in detail the numerical results of our computational work, we describe the theoretical and computational context of the present calculations apart from deficiencies of models employed in the analysis of experimental data, we must be aware of the limitations of both theoretical models and the computational aspects. Regarding theory, even a single helium atom is unpredictable [14] purely mathematically from an initial point of two electrons, two neutrons and two protons. Accepting a narrower point of view neglecting internal nuclear structure, we have applied for our purpose well established software, specifically Dalton in a recent release 2.0 [9], that implements numerical calculations to solve approximately Schrodinger s temporally independent equation, thus involving wave mechanics rather than quantum... 

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

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