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Journal of Modern Physics

Some Success Applications for Local-Realism Quantum Mechanics: Nature of Covalent-Bond Revealed and Quantitative Analysis of Mechanical Equilibrium for Several Molecules

Runsheng Tu

Published Jan 1, 2014• 5 citations
Publisher

Abstract

With local realism quantum mechanics established, we can simply describe an extranuclear electron as a large-scale elastic ring with an elastic phase trajectory. Several small molecules can thus be strictly calculated through the logical method of establishing an accurate mechanical equilibrium equation describing the molecular structure, then solving the strict solutions of this mechanical equation and the corresponding wave equation. The results (bond length and dissociation energy) are in good agreement with observed results—i.e. if it is only coincidence, there should not be such a high probability of agreement between calculated and observed results. The method of local realism quantum mechanics is no longer the semi-empirical method. The method to calculate the electron pairing energy uses a linear regression of the ionization energy obtained through experiment. Nonetheless, it is exciting that there are diatomic molecules such as Na2, K2 and asymmetric HF molecules that possess a non-zero non-bonding electron number in the calculation examples. Moreover, the molecular structures are very intuitive, and the calculation method is much simpler than existing methods.

DOI
10.4236/jmp.2014.56041

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With local realism quantum mechanics established, we can simply describe an extranuclear electron as a large-scale elastic ring with an elastic phase trajectory. Several small molecules can thus be strictly calculated through the logical method of establishing an accurate mechanical equilibrium equation describing the molecular structure, then solving the strict solutions of this mechanical equation and the corresponding wave equation. The results (bond length and dissociation energy) are in good agreement with observed results—i.e. if it is only coincidence, there should not be such a high probability of agreement between calculated and observed results. The method of local realism quantum mechanics is no longer the semi-empirical method. The method to calculate the electron pairing energy uses a linear regression of the ionization energy obtained through experiment. Nonetheless, it is exciting that there are diatomic molecules such as Na2, K2 and asymmetric HF molecules that possess a non-zero non-bonding electron number in the calculation examples. Moreover, the molecular structures are very intuitive, and the calculation method is much simpler than existing methods.
A model of the electronic internal structure has been developed, revealing the specific movement mode of electrons outside the nucleus. Building on this, the Bohr's planetary model of the hydrogen atom has been adapted into the Saturn model, suitable for describing multi-center and multi-electron bound systems. It has been discovered that the mathematical formalism of Bohr's old quantum theory and wave mechanics are compatible. A quantum chemistry method has been established to implement this compatibility (where the Saturn model and wave mechanics can complement each other), using this method, the energy eigenvalues of s electrons in atoms and the binding energies and bond lengths of four diatomic molecules such as hydrogen molecules have been successfully calculated. This provides new insights into material structure theory. The aforementioned compatibility could lead to the birth of local realism quantum mechanics.
The following text develops a new method of solving the eigenvalue problem of the quantum mechanical harmonic oscillator. Thereby are introduced new notions, like that of a reduced basis or that of a huge algebra. Furthermore are presented formulas for iterated commutation relations. Commutation Relation and Hamilton Function Oscillatory properties of a diatomic molecule, a carbon-monoxide molecule for example, can be modelled by a linear elastic oscillator. The observables for describing the oscillatory states of the oscillator are taken to be the dis- �� location from the equilibrium state and the relative momentum of the two masses.
Studying complex molecular systems, whether in the gas or a condensed phase, requires highly accurate quantum chemistry methods whose computational effort remains tractable when treating realistic systems. Commonly used ab initio methods such as Coupled Cluster (CC) or Density Functional Theory (DFT) generally provide reliable results when the underlying approximations and parameterizations are appropriate for the systems being studied. Among the less popular quantum chemistry methods, Valence Bond (VB) theory and Quantum Monte Carlo (QMC) methods, each provides different unique advantages and disadvantages. Ab initio VB, while usually only qualitative for energetic properties such as enthalpies of formation, has the distinct advantage of providing very compact wave functions that can be readily mapped into the intuitive Lewis structures that chemists very often use when qualitatively describing the valence electronic structure of atoms and molecules. QMC using trial wave functions based on multireference ab initio quantum methods can give some of the most accurate energies and related properties, however, this is often at a great computational cost. Furthermore, the large wave function expansions in the trial function are often difficult to qualitatively interpret. In this lecture, we will present the Valence-Bond Quantum Monte Carlo methods (VB-QMC) which retain the interpretability of VB and the high accuracy of QMC. We will show a few applications which demonstrate their accuracy for molecules in the gas phase and we will examine areas where innovations could be made.
All the experiments that prove that Einstein is wrong and Bohr won have a serious flaw or loophole that is difficult to overcome — Have to subjectively judge the state of the system before the measurement. Undoubtedly, the establishment of quantum mechanics of local realism is a strong support for Einstein. Many people are dissatisfied with the quantum mechanics of non-local realism and want to establish the quantum mechanics of local realism. But they did not break through the bottleneck. The concept of wave function is widely used in existing quantum mechanics. However, the nature of the wave function is unanswerable. The model of "real wave curling inside the particle" determines that the wave function is the motion equation of localized real wave. The wave mechanics based on such wave functions is quantum mechanics of localized realism. The mathematical formal system of local realism quantum mechanics is the same as the existing one. Explanation of double slit diffraction can be experiment by directional quantization. The explanation system of local realism quantum mechanics is established, and it is guaranteed that this system can also be organically combined with the existing mathematical formal systems of quantum mechanics. Local realism quantum mechanics has all the elements of a valuable new theory, and its birth conforms to the law of theoretical development.
The belief that quantum mechanics (QM) does not admit a realistic interpretation is widespread. According to some scholars concerned with the foundations of QM all existing interpretations of this theory (except for the statistical interpretation) presuppose instead a form of realism which consists in assuming that QM deals with individual objects and their properties. We uphold in the present paper that the arguments supporting the contextuality and the nonlocality of QM are a significant clue to the implicit adoption of stronger forms of realism (realism of theoretical entities and realism of theories). If these kinds of realism are substituted by a simpler and more intuitive semantic realism one can contrive a noncontextual and local interpretation of the formalism of QM (SR interpretation). Moreover one can provide a model for such an interpretation (ESR model) in which local realism and QM do not conflict and some fundamental problems of the standard interpretation of QM are avoided.
In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density functional theory of so-called strictly correlated electrons (SCE). We map out the full two-particle wave function for a wide range of bond distances and interaction strengths and obtain analytic results for the two-particle states and eigenenergies in various limits of strong and weak interactions, and in the limit of large bond distance. We then study the so-called Hartree-exchange-correlation (Hxc) kernel of time-dependent density functional theory which is a key ingredient in calculating excitation energies. We study an approximation based on adiabatic SCE (ASCE) theory which was shown to display a particular feature of the exact Hxc kernel, namely, a spatial divergence as function of the bond distance. This makes the ASCE kernel a candidate for correcting a notorious failure of the commonly used adiabatic local density approximation (ALDA) in the calculation of excitation energies of dissociating molecules. Unlike the ALDA, we obtain nonzero excitation energies from the ASCE kernel in the dissociation regime but they do not correspond to those of the true spectrum unless the interaction strength is taken to be very large such that the SCE theory has the right regime of validity, in which case the excitation energies become exact and represent the so-called zero-point oscillations of the strictly correlated electrons. The commonly studied physical dissociation regime, namely, large molecular separation at intermediate interaction strength, therefore remains a challenge for density functional approximations based on SCE theory.