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Ivan Gutman - One of the best experts on this subject based on the ideXlab platform.
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Limitations of Pauling Bond Order Concept
Polycyclic Aromatic Compounds, 2012Co-Authors: Damir Vukičević, Jelena Đurđević, Ivan GutmanAbstract:It is shown that Kekule structures do not realistically predict the behavior of π-electron properties of those polycyclic hydrocarbons that have many fixed double Bonds. This is caused by the fact that such molecules would be destabilized by delocalization. We analyze a group of polycyclic hydrocarbons with a large number of fixed Bonds, whose geometry was determined by means of an unrestricted symmetry-broken UB3LYP/6-311G(d,p) DFT method. We put forward a new concept, the unpaired Bond Order, and show that it is well correlated with Bond lengths, but poorly correlated with Pauling Bond Orders. Hence, in this way we provide a simple test of the validity of the Pauling-Bond-Order concept for the molecule being considered.
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Vindicating the Pauling-Bond-Order concept
Chemical Physics Letters, 2006Co-Authors: Jelena Sedlar, Ivan Gutman, Ivana Anđelić, Damir Vukičević, Ante GraovacAbstract:Abstract In the Pauling-Bond-Order concept, it is assumed that all Kekule structures of a benzenoid molecule contribute equally to the π-electron contents of the carbon–carbon Bonds. We modified the Pauling-Bond-Order: (a) by increasing the weight of a Kekule structure proportional to the number of Fries-type hexagons and (b) by increasing the weights of the Kekule structures that are compatible with Clar aromatic sextet formulas. Improvements in reproducing experimental carbon–carbon Bond lengths are insignificant, implying that equal weighting of Kekule structures is more justified than one could anticipate.
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Some properties of the topological Bond Order
Chemical Physics Letters, 2005Co-Authors: Ivan Gutman, Slavko Radenković, Boris Furtula, Haruo HosoyaAbstract:Abstract The topological Bond Order is a Bond-Order-like quantity, put forward in the 1970s. It is defined as p rs T = Z ( G rs ) / Z ( G ) , where G is the molecular graph, Grs is obtained from G by deleting from it the adjacent vertices labelled by r and s, and Z stands for the respective topological (Hosoya) index. Because no easy way for the calculation of p rs T is known, its properties were studied only to a limited degree. We now introduce a modified topological Bond Order, p ˜ rs T , that can (easily) be calculated from the eigenvalues of G and Grs. For acyclic systems, p ˜ rs T = p rs T . In the case of polycyclic systems a reasonably accurate linear correlation exists between p ˜ rs T and p rs T . Thus, by studying p ˜ rs T the main properties of p rs T can be established.
David G. Pettifor - One of the best experts on this subject based on the ideXlab platform.
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Non-collinear magnetism with analytic Bond-Order Potentials.
Journal of Physics: Condensed Matter, 2015Co-Authors: Michael E Ford, David G. Pettifor, Ralf DrautzAbstract:The theory of analytic Bond-Order Potentials as applied to non-collinear magnetic structures of transition metals is extended to take into account explicit rotations of Hamiltonian and local moment matrix elements between locally and globally defined spin-coordinate systems. Expressions for the gradients of the energy with respect to the Hamiltonian matrix elements, the interatomic forces and the magnetic torques are derived. The method is applied to simulations of the rotation of magnetic moments in α iron, as well as α and β manganese, based on d-valent orthogonal tight-binding parametrizations of the electronic structure. A new weighted-average terminator is introduced to improve the convergence of the Bond-Order Potential energies and torques with respect to tight-binding reference values, although the general behavior is qualitatively correct for low-moment expansions.
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Valence-dependent analytic Bond-Order potential for magnetic transition metals
Physical Review B, 2011Co-Authors: Ralf Drautz, David G. PettiforAbstract:We extend the analytic Bond-Order potentials for transition metals [Phys. Rev. B 74, 174117 (2006)] to include ferro, antiferro, and noncollinear magnetism and charge transfer. This is achieved by first deriving a suitable tight-binding model through the expansion of the spin-density energy functional to second Order with respect to magnetic and charge fluctuations. The tight-binding model is then approximated locally by the Bond-Order potential expansion, where the variational property of the Bond-Order potential expansion allows us to derive analytic expressions for the forces and torques on the atoms. From the Bond-Order potentials we then extract a hierarchy of multispin interactions beyond the conventional Heisenberg model. The explicit valence dependence of the Bond-Order potentials enables us to characterize the magnetic properties of the 3$d$ transition metals and to reproduce the trend from antiferromagnetic spin Ordering close to the center of the $d$ band through noncollinear spin configurations to ferromagnetic Ordering toward the edges of the $d$ band. The analytic representation of the energy within the Bond-Order potentials is then further expanded in the form of a Ginzburg-Landau expansion, deriving the prefactors explicitly from tight-binding and Bond-Order potentials. Thus, in this paper we present a coherent simplification from fundamental to empirical models of magnetism through coarse graining the electronic structure from spin-density functional theory to tight binding to Bond-Order potentials to the Ginzburg-Landau expansion.
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Atomistic modelling of materials with Bond-Order potentials
International Journal of Materials Research, 2009Co-Authors: Thomas Hammerschmidt, Ralf Drautz, David G. PettiforAbstract:Abstract The atomistic modelling of materials with effective model potentials requires a reliable description of the breaking and making of interatomic Bonds in different atomic environments. The Bond-Order potentials provide such a transferable description of atomic Bonding while at the same time they are computationally efficient for application in large-scale atomistic simulations. We give an overview of the fundamentals of Bond-Order potentials and their derivation from the tight-binding electronic structure by linking the atomic structure to the electronic structure. We discuss the application of the structural energy difference theorem for studying trends in crystal phase stability and provide a brief summary of representative examples for modelling metals, hydrocarbons, and semiconductors with analytic and numerical Bond-Order potentials.
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Bond-Order potential for silicon
Physical Review B, 2007Co-Authors: B. Gillespie, Ralf Drautz, D. A. Murdick, Xiaowang Zhou, Haydn N. G. Wadley, David G. PettiforAbstract:The tight-binding description of covalent Bonding is used to propose a four-level, Bond-Order potential for elemental silicon. The potential addresses both the $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ Bonding and the valence of this $sp$-valent element. The interatomic potential is parametrized using ab initio and experimental data for the diamond cubic, simple cubic, face-centered-cubic, and body-centered-cubic phases of silicon. The Bond-Order potential for silicon is assessed by comparing the predicted values with other estimates of the cohesive energy, atomic volume, and bulk modulus for the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Sn}$, bc8, st12, and 46 clathrate structures. The potential predicts a melting temperature of $1650\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in good agreement with the experimental value of $1687\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The energetics of various high-symmetry point defect structures and the structure and energetics of small silicon clusters are investigated. The potential also provides a robust description of surface reconstructions; it notably predicts with high fidelity the surface formation energy of the (111) $7\ifmmode\times\else\texttimes\fi{}7$ dimer adatom stacking fault configuration.
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Analytic Bond-Order potential for the gallium arsenide system
Physical Review B, 2006Co-Authors: D. A. Murdick, Ralf Drautz, Duc Nguyen-manh, Xiaowang Zhou, Haydn N. G. Wadley, David G. PettiforAbstract:An analytic, Bond-Order potential BOP is proposed and parametrized for the gallium arsenide system. The potential addresses primary and secondary Bonding and the valence-dependent character of heteroatomic Bonding, and it can be combined with an electron counting potential to address the distribution of electrons on the GaAs surface. The potential was derived from a tight-binding description of covalent Bonding by retaining the first two levels of an expanded Green’s function for the and Bond-Order terms. Predictions using the potential were compared with independent estimates for the structures and binding energy of small clusters dimers, trimers, and tetramers and for various bulk lattices with coordinations varying from 4 to 12. The structure and energies of simple point defects and melting transitions were also investigated. The relative stabilities of the 001 surface reconstructions of GaAs were well predicted, especially under high-arsenicoverpressure conditions. The structural and binding energy trends of this GaAs BOP generally match experimental observations and ab initio calculations.
Damir Vukičević - One of the best experts on this subject based on the ideXlab platform.
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Limitations of Pauling Bond Order Concept
Polycyclic Aromatic Compounds, 2012Co-Authors: Damir Vukičević, Jelena Đurđević, Ivan GutmanAbstract:It is shown that Kekule structures do not realistically predict the behavior of π-electron properties of those polycyclic hydrocarbons that have many fixed double Bonds. This is caused by the fact that such molecules would be destabilized by delocalization. We analyze a group of polycyclic hydrocarbons with a large number of fixed Bonds, whose geometry was determined by means of an unrestricted symmetry-broken UB3LYP/6-311G(d,p) DFT method. We put forward a new concept, the unpaired Bond Order, and show that it is well correlated with Bond lengths, but poorly correlated with Pauling Bond Orders. Hence, in this way we provide a simple test of the validity of the Pauling-Bond-Order concept for the molecule being considered.
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Vindicating the Pauling-Bond-Order concept
Chemical Physics Letters, 2006Co-Authors: Jelena Sedlar, Ivan Gutman, Ivana Anđelić, Damir Vukičević, Ante GraovacAbstract:Abstract In the Pauling-Bond-Order concept, it is assumed that all Kekule structures of a benzenoid molecule contribute equally to the π-electron contents of the carbon–carbon Bonds. We modified the Pauling-Bond-Order: (a) by increasing the weight of a Kekule structure proportional to the number of Fries-type hexagons and (b) by increasing the weights of the Kekule structures that are compatible with Clar aromatic sextet formulas. Improvements in reproducing experimental carbon–carbon Bond lengths are insignificant, implying that equal weighting of Kekule structures is more justified than one could anticipate.
Frank Weinhold - One of the best experts on this subject based on the ideXlab platform.
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natural resonance theory ii natural Bond Order and valency
Journal of Computational Chemistry, 1998Co-Authors: Eric D Glendening, Frank WeinholdAbstract:Resonance weights derived from the Natural Resonance Theory .NRT , introduced in the preceding paper are used to calculate ''natural Bond Order,'' ''natural atomic valency,'' and other atomic and Bond indices reflecting the resonance composition of the wave function. These indices are found to give significantly better agreement with observed properties empirical valency, . Bond lengths than do corresponding MO-based indices. A characteristic feature of the NRT treatment is the description of Bond polarity by a ''Bond ionicity'' . index resonance-averaged NBO polarization ratio , which replaces the ''covalent-ionic resonance'' of Pauling-Wheland theory and explicity exhibits the complementary relationship of covalency and electrovalency that underlies empirical assignments of atomic valency. We present ab initio NRT applications . to prototype saturated and unsaturated molecules methylamine, butadiene , . polar compounds fluoromethanes , and open-shell species: hydroxymethyl . radical to demonstrate the numerical stability, convergence, and chemical reasonableness of the NRT Bond indices in comparison to other measures of valency and Bond Order in current usage. Q 1998 John Wiley & Sons, Inc. J Comput Chem 19: 610)627, 1998
Antonio Laganà - One of the best experts on this subject based on the ideXlab platform.
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Bond Order uniform grids for quantum reactive scattering
International Journal of Quantum Chemistry, 2011Co-Authors: Sergio Rampino, Antonio LaganàAbstract:The adoption of evenly spaced grids in the so-called Bond Order coordinates for the calculation of diatomic eigenfunctions in reactive scattering problems is investigated. These grids (used here for the first time in reactive dynamics) sample the accessible space better than traditional Bond length coordinates. A comparison between the Bond Order and the Bond length method on the test H + H2 system using an asymptotically Morse-like potential singles out the advantages of adopting the former when a limited number of grid points is chosen. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112:1818–1828, 2012
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Eigensolutions for one-dimensional cuts of Bond Order potentials
Chemical Physics Letters, 1997Co-Authors: Antonio Laganà, Paolo Spatola, Guillermo Ochoa De Aspuru, Gianni Ferraro, Osvaldo GervasiAbstract:Abstract The calculation of eigenvalues and eigenfunctions of one-dimensional cuts of Bond Order potentials has been revisited to gain insight on the application of the Bond Order formalism to atom-diatom scattering problems. Different approaches are considered by paying attention to efficiency and accuracy.
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Potential energy representations in the Bond Order space
Chemical Physics, 1992Co-Authors: Antonio Laganà, Gianni Ferraro, Osvaldo Gervasi, Ernesto Garcia, Adriano OttaviAbstract:Abstract Different types of reaction channel coordinates defined in the Bond Order space are formulated. Their use for describing the interaction of reactive processes is also discussed.
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A rotating Bond Order formulation of the atom diatom potential energy surface
The Journal of Chemical Physics, 1991Co-Authors: Antonio LaganàAbstract:The advantage of mapping calculated potential energy values onto the space of the Bond Order coordinates is discussed with special concern for the possibility of designing functional representations of the interaction. A rotating model defined in the Bond Order space is proposed.