| 1. |
- Bacskay, G. B., et al.
(author)
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Covalent Bonding in the Hydrogen Molecule
- 2017
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In: Journal of Physical Chemistry A. - : American Chemical Society (ACS). - 1089-5639 .- 1520-5215. ; 121:48, s. 9330-9345
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Journal article (peer-reviewed)abstract
- This work addresses the continuing disagreement between two schools of thought concerning the mechanism of covalent bonding. According to Hellmann, Ruedenberg, and Kutzelnigg, covalent bonding is a quantum mechanical phenomenon whereby lowering of the kinetic energy associated with electron sharing, i.e., delocalization, is the key stabilization mechanism. The opposing view of Slater, Feynman, and Bader has maintained that the source of stabilization is electrostatic potential energy lowering due to electron density redistribution to binding regions between nuclei. Following our study of H-2(+) we present an analogous detailed study of H-2 where bonding involves an electron pair with repulsion and correlation playing a significant role in its properties. We use a range of different computational approaches to study and reveal the relevant contributions to bonding as seen in the electron density and corresponding kinetic and potential energy distributions. The energetics associated with the more complex electronic structure of H-2, when examined in detail, clearly agrees with the analysis of Ruedenberg; i.e., covalent bonding is due to a decrease in the interatomic kinetic energy resulting from electronic delocalization. Our results support the view that covalent bonding is a quantum dynamical phenomenon requiring a properly quantized kinetic energy to be used in its description.
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| 2. |
- Bacskay, G. B., et al.
(author)
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Covalent Bonding: The Fundamental Role of the Kinetic Energy
- 2013
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In: Journal of Physical Chemistry A. - : American Chemical Society (ACS). - 1089-5639 .- 1520-5215. ; 117:33, s. 7946-7958
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Journal article (peer-reviewed)abstract
- This work addresses the continuing disagreement between two prevalent schools of thought concerning the mechanism of covalent bonding. According to Hellmann, Ruedenberg, and Kutzelnigg, a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism. The opposing view of Slater, Feynman, and Bader has maintained that the source of stabilization is electrostatic potential energy lowering due to electron density redistribution to binding regions between nuclei. Despite the large body of accurate quantum chemical work on a range of molecules, the debate concerning the origin of bonding continues unabated, even for H-2(+), the simplest of covalently bound molecules. We therefore present here a detailed study of H-2(+), including its formation, that uses a sequence of computational methods designed to reveal the relevant contributing mechanisms as well as the spatial density distributions of the kinetic and potential energy contributions. We find that the electrostatic mechanism fails to provide real insight or explanation of bonding, while the kinetic energy mechanism is sound and accurate but complex or even paradoxical to those preferring the apparent simplicity of the electrostatic model. We further argue that the underlying mechanism of bonding is in fact of dynamical character, and analyses that focus on energy do not reveal the origin of covalent bonding in full clarity.
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| 3. |
- Bacskay, G B, et al.
(author)
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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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In: The Chemical Educator. - 1430-4171. ; 15, s. 42-54
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Journal article (peer-reviewed)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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| 4. |
- Bacskay, G. B., et al.
(author)
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The Virial Theorem and Covalent Bonding
- 2018
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In: Journal of Physical Chemistry A. - : American Chemical Society (ACS). - 1089-5639 .- 1520-5215. ; 122:39, s. 7880-7893
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Journal article (peer-reviewed)
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| 5. |
- Bäck, Andreas, et al.
(author)
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The Mechanism of Covalent Bonding: Analysis within the Hückel Model of Electronic Structure
- 2007
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In: Journal of Chemical Education. ; 84, s. 1201-1203
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Journal article (peer-reviewed)abstract
- The correct description and interpretation of covalent bonding require a quantum mechanical approach. Hückel molecular orbital theory, the simplest quantum mechanical model of molecular electronic structure, is (and in an accompanying online article) shown to be a uniquely useful pedagogical path to the understanding and interpretation of the mechanism of covalent bonding. Using the Hückel model it can be demonstrated that the dynamical character of the molecular orbitals is related simultaneously to the covalent bonding mechanism and to the degree of delocalization of the electron dynamics. The resonance stabilization of conjugated molecules thus corresponds to a special case of the fundamental principle of covalent bonding—the relaxation of dynamical constraints by the delocalization of electronic motion. The covalent bonding mechanism can be seen to arise ultimately from a relaxation of nonergodic constraints on the electron dynamics of the separated atoms leading towards free translation of the valence electrons over two or more atomic centers in a molecule.
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| 6. |
- Eek, William, 1976, et al.
(author)
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The screened Atomic Potential - A Simple Explanation of the Aufbau Model
- 2006
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In: Chem Educator. ; 11, s. 235-242
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Journal article (peer-reviewed)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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| 7. |
- Nordholm, Sture, 1944, et al.
(author)
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The Basics of Covalent Bonding in Terms of Energy and Dynamics
- 2020
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In: Molecules. - : MDPI AG. - 1420-3049. ; 25:11
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Journal article (peer-reviewed)abstract
- We address the paradoxical fact that the concept of a covalent bond, a cornerstone of chemistry which is well resolved computationally by the methods of quantum chemistry, is still the subject of debate, disagreement, and ignorance with respect to its physical origin. Our aim here is to unify two seemingly different explanations: one in terms of energy, the other dynamics. We summarize the mechanistic bonding models and the debate over the last 100 years, with specific applications to the simplest molecules: H-2(+) and H-2. In particular, we focus on the bonding analysis of Hellmann (1933) that was brought into modern form by Ruedenberg (from 1962 on). We and many others have helped verify the validity of the Hellmann-Ruedenberg proposal that a decrease in kinetic energy associated with interatomic delocalization of electron motion is the key to covalent bonding but contrary views, confusion or lack of understanding still abound. In order to resolve this impasse we show that quantum mechanics affords us a complementary dynamical perspective on the bonding mechanism, which agrees with that of Hellmann and Ruedenberg, while providing a direct and unifying view of atomic reactivity, molecule formation and the basic role of the kinetic energy, as well as the important but secondary role of electrostatics, in covalent bonding.
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