| 1. |
- Abbas, Zareen, 1962, et al.
(author)
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From restricted towards realistic models of salt solutions: Corrected Debye–Hückel theory and Monte Carlo simulations
- 2007
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In: Journal of Mathematical Fluid Mechanics. - : Elsevier BV. - 1422-6952 .- 1422-6928 .- 0378-3812. ; 260:2, s. 233-247
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Journal article (peer-reviewed)abstract
- The properties of bulk salt solutions over wide concentration ranges are explored by a combination of simple physical theory and Monte Carlo (MC) simulations. The corrected Debye–Hückel (CDH) theory which incorporates ion size effects in a linear response approximation is extended to yield free energy and other thermodynamic properties by integration of the chemical potential over concentration. Charging integration which is usually used to obtain an electrostatic contribution of total free energy of electrolytes is avoided in this new direct approach. MC simulations are performed with a modified Widom particle insertion method, which also provides directly the ionic activity coefficients. The validity of the CDH theory is tested by comparison with the MC simulation data for 1:1, 2:1, 2:2 and 3:1 restricted primitive model (RPM) electrolytes over a wide concentration range and at various ion sizes. Mean ionic activity and osmotic coefficients calculated by the CDH theory in RPM approximation of electrolyte are fitted to experimental data by adjusting only a mean ionic diameter. Good fits up to 1 molal (m) concentration are obtained for a large number of salt solutions. MC simulations data for unrestricted primitive model (UPM) of 1:1 and 2:1 electrolytes are also fitted to the experimental data by varying the cation radius while keeping the anion radius fixed at a crystallographic value. The success of this approach is found to be salt specific. For example good fits up to 2 and 3.5 m concentrations were obtained for LiCl and LiBr, respectively. However in the case of less dissociated salts such as NaCl and KI the experimental data could only be fitted up to one molal concentration. Possibility of extending the applicability range of the CDH theory to concentrations >2 m is explored by including a concentration dependent dielectric constant as measured in experiments. Mean ionic activity coefficients for a number of salts could successfully be fitted up to 3 m concentration by adjusting only a mean ionic diameter. Difficulties encountered in simultaneously fitting the mean ionic activity and osmotic coefficients at salt concentrations >2 m are discussed.
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| 2. |
- Abbas, Zareen, 1962, et al.
(author)
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Monte Carlo Simulations of Salt Solutions: Exploring the Validity of Primitive Models
- 2009
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In: Journal of Physical Chemistry B. - : American Chemical Society (ACS). - 1520-6106 .- 1520-5207. ; 113:17, s. 5905-5916
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Journal article (peer-reviewed)abstract
- An extensive series of Monte Carlo (MC) simulations were performed in order to explore the validity of simple primitive models of electrolyte solutions and in particular the effect of ion size asymmetry on the bulk thermodynamic properties of real salt solutions. Ionic activity and osmotic coefficients were calculated for 1:1, 2:1, and 3:1 electrolytes by using the unrestricted primitive model (UPM); i.e., ions are considered as charged hard spheres of different sizes dissolved in a dielectric continuum. Mean ionic activity and osmotic coefficients calculated by the MC simulations were fitted simultaneously to the experimental data by adjusting only the cation radius while keeping the anion radius fixed at its crystallographic value. Ionic radii were further optimized by systematically varying the cation and anion radii at a fixed sum of ionic radii. The success of this approach is found to be highly salt specific. For example, experimental data (mean ionic activity and osmotic coefficients) of salts which are usually considered as dissociated such as HCl, HBr, LiCl, LiBr, LiClO4, and KOH were successfully fitted up to 1.9, 2.5, 1.9, 3, 2.5, and 4.5 M concentrations, respectively. In the case of partially dissociated salts such as NaCl, the successful fits were only obtained in a more restricted concentration range. Consistent sets of the best fitted cation radii were obtained for acids, alkali, and alkaline earth halides. A list of recommended ionic radii is also provided. The reliability of the optimized ionic radii was further tested in simulations of the osmotic coefficients of LiCl−NaCl−KCl salt mixtures. A very good agreement between the simulated and experimental data was obtained up to ionic strength of 4.5 M.
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| 3. |
- Abbas, Zareen, 1962, et al.
(author)
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Size-Dependent Surface Charging of Nanoparticles
- 2008
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In: J of Physical Chemistry C. - : American Chemical Society (ACS). - 1932-7447 .- 1932-7455. ; 112:15, s. 5715-5723
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Journal article (peer-reviewed)abstract
- Experimental interest in the possible curvature dependence of particle charging in electrolyte solutions is subjected to theoretical analysis. The corrected Debye-Hückel theory of surface complexation (CDH-SC) and Monte Carlo (MC) simulation are applied to investigate the dependence of surface charging of metal oxide nanoparticles on their size. Surface charge density versus pH curves for spherical metal oxide nanoparticles in the size range of 1-100 nm are calculated at various concentrations of a background electrolyte. The surface charge density of a nanoparticle is found to be highly size-dependent. As the particle diameter drops to below 10 nm there is considerable increase in the surface charge density as compared with the limiting values seen for particles larger than 20 nm. This increase in the surface charge density is due to the enhanced screening efficiency of the electrolyte solution around small nanoparticles, which is most prominent for particles of diameters less than 5 nm. For example, the surface charge densities calculated for 2 nm particles at 0.1 M concentration are very close to the values obtained for 100 nm particles at 1 M concentration. These predictions of the dependence of surface charge density on particle size by the CDH-SC theory are in very good agreement with the corresponding results obtained by the MC simulations. A shift in the pH value of the point of zero charge toward higher pH values is also seen with a decreasing particle size.
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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- Bäck, Andreas, et al.
(author)
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Investigation of ergodic character of quantized vibrational motion
- 2004
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In: Journal of Physical Chemistry A. ; 108:41, s. 8782-8794
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Journal article (peer-reviewed)abstract
- The concept of quantum ergodicity and the degree of ergodic behavior reflected by the bound energy eigenstates are studied for some vibrational systems in two and three dimensions. Different approaches are attempted in order to be able to classify and quantify ergodicity in a given system by investigating the energy eigenfunctions. It is argued that the concept of quantum ergodicity is fundamentally connected to the similarity between eigenstates close in energy and to their globality. Previous investigations and definitions of quantum ergodicity can be seen to connect to this theme; they provide different measures of similarity between eigenstates. Here we propose two practical measures to investigate quantum ergodicity. The systems treated include the famous two-dimensional Henon-Heiles and Barbanis systems, which have previously been investigated both classically and quantum mechanically. As a more realistic three-dimensional example, we consider the vibrations of nonrotating NO2 close to dissociation.
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| 9. |
- 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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| 10. |
- Eek, William, 1976, et al.
(author)
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Simple analysis of atomic reactivity: Thomas-Fermi theory with nonergodicity and gradient correction
- 2006
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In: Theoretical Chemistry Accounts. - : Springer Science and Business Media LLC. - 1432-881X .- 1432-2234. ; 115:4, s. 266-273
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Journal article (peer-reviewed)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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