| 1. |
- Bacskay, G B, et al.
(författare)
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Is Covalent Bonding a One-Electron Phenomenon? Analysis of a Simple Potential Model of Molecular Structure
- 2010
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Ingår i: The Chemical Educator. - 1430-4171. ; 15, s. 42-54
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this work is to show that covalent bonding is essentially a one-electron quantum mechanical phenomenon. A correct understanding of the mechanism of covalent bonding in H2+ is therefore vital for the understanding and description of bonding in the more complex many-electron molecules. In addition to a standard molecular orbital treatment of H2+, in this work the molecule is also modeled simply as an electron in a square well potential as well as a molecule with Gaussian potential terms. These studies provide strong evidence that covalent bonding is a quantum mechanical phenomenon and a direct consequence of electron delocalization. For the study of more complex systems with comparable ease, a simple one-electron model is proposed where a given molecule is modeled as a superposition of screened atomic potentials, which can reproduce the appropriate atomic orbitals and their energies in a semi-quantitative manner. Application of this approach to the homonuclear diatomics H2 to F2 predict the existence of stable covalently bonded molecules with bond lengths which are in reasonable agreement with experiment. Comparisons are also made with the results of Hartree-Fock and density functional calculations in establishing support for the view that covalent bonding is indeed a one-electron phenomenon and should therefore be taught as such.
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| 2. |
- Eek, William, 1976, et al.
(författare)
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Simple analysis of atomic reactivity: Thomas-Fermi theory with nonergodicity and gradient correction
- 2006
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Ingår i: Theoretical Chemistry Accounts. - : Springer Science and Business Media LLC. - 1432-881X .- 1432-2234. ; 115:4, s. 266-273
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Tidskriftsartikel (refereegranskat)abstract
- Covalent bonding has been found to be related to the relaxation of dynamical constraints on electronic motion in atoms and molecules. The corresponding strain energy in an atom is therefore a measure of its inherent reactivity. Here, such reactivities of the atoms H through Ne are estimated by the use of the Thomas-Fermi density functional theory which can be simply implemented using parametrized exponential electron densities in two different forms-the traditional form assuming complete ergodicity and a modified form which accounts for nonergodicity and therefore strain. The Thomas-Fermi functional is amended by the incorporation of gradient correction of the kinetic energy according to the von Weizsacker prescription. This correction, implemented within the nonergodic form of the Thomas-Fermi theory, is scaled to yield total atomic energies in agreement with the Hartree-Fock results. The scaling factor shows a variation from around 0.07 for Be to 0.1 for Ne. The reactivity, measured by the stabilization brought by going to the ergodic form of quantization within the Thomas-Fermi theory, is zero for He and Ne and shows a broad peak around oxygen in apparent agreement with chemical intuition. Molecular bonding efficiencies are studied for some small molecules and are found to be relatively large for hydrides and smaller for diatomic molecules such as Be-2 and F-2.
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| 3. |
- Eek, William, 1976, et al.
(författare)
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The screened Atomic Potential - A Simple Explanation of the Aufbau Model
- 2006
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Ingår i: Chem Educator. ; 11, s. 235-242
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Tidskriftsartikel (refereegranskat)abstract
- The hydrogen atom, whose electronic structure is well understood by most students of chemistry, forms the basis for the development of theories and descriptions of many-electron atoms with considerably more complex and less easily understood electronic structures. The common textbook description of many-electron atoms is generally in terms of the empirical Aufbau rules and screened nuclei, while researchers often utilize complex computations where physical transparency and understanding are often lost. In this paper we seek to provide a simple physical understanding of many-electron atoms by developing a simple but remarkably accurate representation of the screening mechanism, which explains in simple terms the crucial role of electron–electron repulsion in the energy and orbital structure of atoms. We briefly review the well-known properties of the hydrogen atom and discuss Slater's rules, formulated in the early days of electronic structure theory. The latter provide insight and understanding of the structure of atoms at a qualitative and semi-quantitative level, achieved via the concept of shell-dependent screened effective nuclear charges. The atomic potential we propose incorporates exponential screening. The effective nuclear charge is exponentially damped, so that it varies from Z to +1 with increasing separation from the nucleus. The resulting orbital energies are not only consistent with the Aufbau rules, but also agree well with Hartree–Fock results. This model of screening is, therefore, well-suited to the study of many-electron atoms, in particular, the role of electron–electron repulsion and its simple treatment via nuclear screening.
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| 4. |
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| 5. |
- Nordholm, Sture, 1944, et al.
(författare)
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Ergodicity and Rapid Electron Delocalization - The Dynamical Mechanism of Atomic Reactivity and Covalent Bonding
- 2011
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Ingår i: INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY. - 0020-7608. ; 111:9, s. 2072-2088
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Tidskriftsartikel (refereegranskat)abstract
- Surprisingly, the historical development of the understanding of the concept of covalent bonding is incomplete and the physical mechanism responsible for bonding is still the subject of debate among chemists. We argue that this is primarily due to the key role played by quantum mechanics and the peculiarity of the Coulomb interaction operating between the electrons and nuclei in molecules. A study of the simplest molecules H and H2 as well as the π-electron structure of planar conjugated hydrocarbon molecules leads to the conclusion that delocalization of electron dynamics is the key mechanism of covalent bonding. We find that the new concept of quantum ergodicity defined in terms of the globality of the energy eigenfunctions relates directly to covalent bonding. This is illustrated in the Höckel model of the π-electrons in polyene molecules. An understanding results associating covalent bonding most fundamentally with the relaxation of nonergodic dynamical constraints upon the electron dynamics in atoms and molecules. The strain energy present due to these constraints can be crudely estimated by the comparison of the results of Thomas-Fermi (TF) density functional calculations, which can be carried out both with and without these constraints. We present results for the light atoms H through Ar indicating that there is a very considerable strain in most atoms with the exception of the inert gas atoms. For the atoms H through Ne, we can verify this picture by direct comparison of ergodic TF and self-consistent field-molecular orbital (SCF-MO) results. Comparison with atomization energies for some small molecules shows that due to repulsive mechanisms only a small fraction of the covalent strain energy is actually realized as binding energy in most molecules. The hydride molecules appear to be most efficient in utilizing the strain energy.
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