# Comment on ‘‘Electron flow and electronegativity equalization in the process of bond formation’’ [J. Chem. Phys. 99, 5151 (1993)]

01 Apr 1994-Journal of Chemical Physics (American Institute of Physics)-Vol. 100, Iss: 7, pp 5390-5390

TL;DR: The implications of the concepts of bond hardness and electronegativity equalization to the density functional theory of Jahn-Teller systems and superconductivity are discussed in this article.

Abstract: The implications of the concepts of bond hardness and electronegativity equalization to the density functional theory of Jahn–Teller systems and superconductivity are discussed.

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TL;DR: In this article, a density-based treatment of Born Couplings is derived from first-principles quantum mechanics beyond the Born-Oppenheimer approximation, which leads to the dynamical Jahn-Teller problem, namely, the coupling of electronic and nuclear motions through the Born coupling terms.

Abstract: The dynamics of Jahn-Teller systems has recently been discussed in terms of generalized electronic charge and current densities in nuclear-coordinate space. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, was a crucial component of this formulation. Here, a density-based treatment of Born Couplings is derived from first-principles quantum mechanics beyond the Born-Oppenheimer approximation. Because of the degenerate electronic configuration of a Jahn-Teller molecule, there are an infinite number of waves in which the charge distribution can be oriented for the same energy, leading to a vanishing bond hardness for the molecular in the symmetric nuclear configuration. Further, the moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, leading to unhindered rotation of the charge cloud. This leads to the dynamical Jahn-Teller problem, namely, the Coupling of electronic and nuclear motions through the Born coupling terms. Applications to superconductivity theory are discussed. 69 refs., 3 figs.

3 citations

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01 Jan 1954

TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.

Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.

7,417 citations

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TL;DR: In this paper, the second-order perturbation theory was used to analyze electron flow and electronegativity equalization in the process of bond formation, and it was shown that the bond hardness is related to the matrix elements of the fragment-electron count operator.

Abstract: Charge‐constrained calculations make it possible to rigorously analyze electron flow and electronegativity equalization in the process of bond formation. Such an analysis is performed for the prototypical H2, HF, and LiH molecules. As the bonds are stretched, the dependence of the electronegativity difference on the extent of charge transfer undergoes a transition from approximate linearity to a steplike discontinuous character. With the help of the second‐order perturbation theory, the bond hardness is related to the matrix elements of the fragment‐electron‐count operator and is shown to increase exponentially with the bond length R at the dissociation limit. For polar bonds, the magnitude of the in situ electronegativity difference ΔχAB decreases quickly with R due to the decreasing polarization of the fragments. However, ΔχAB levels off for large distances, and most of the reduction in charge transfer that accompanies bond dissociation can be attributed to the dramatic increase in the bond hardness. Th...

77 citations

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TL;DR: In this article, the Lagrange multiplier terms are added to the electronic Hamiltonian to calculate the electronegativities of atoms and functional groups in molecules, bond hardnesses, and the charge-transfer components of the bond energies.

Abstract: Rigorous definitions for electronegativities of atoms and functional groups in molecules, bond hardnesses, and the charge-transfer components of the bond energies are proposed. The definitions rely upon values of total energies and their derivatives calculated for molecules composed of fragments with a controlled degree of charge transfer. Such calculations, in which the atomic or fragment charges are obtained with the help of the topological theory of atoms in molecules, are easily accomplished by adding appropriate Lagrange multiplier terms to the electronic Hamiltonian. Numerical examples that are given for 23 different systems indicate that the bond hardnesses are mostly transferable, but because of the electric field generated by the molecular environment the electronegativity differences are not. 27 refs., 1 fig., 1 tab.

57 citations

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TL;DR: In this article, the Jahn-Teller theorem is extended to the dynamical case if the nuclei are considered as moving classically and therefore giving rise to time-dependent terms in the electronic Hamiltonian.

Abstract: It is shown that the Jahn-Teller theorem, formulated on the basis of the Hellmann-Feynman theorem, can be extended to the dynamical case if the nuclei are considered as moving classically and therefore giving rise to time-dependent terms in the electronic Hamiltonian. An example is given which corresponds to D/ sub 3h/ spatial symmetry containing energy gradients with respect to the doubly degenerate displacement coordinate 9 = b/sub 1/q/sub 1/ + b/sub 2/q/sub Nuclear displacement coordinates are treated as timedependent perturbations on the electronic state psi. (C.J.G.)

11 citations

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TL;DR: In this paper, a one-particle theory of N-electron systems was proposed, which bears a certain resemblance to density functional (DF) theory and has been put forward by the present author.

Abstract: We review and update a recently developed one-particle theory of N-electron systems that bears a certain resemblance to density functional (DF) theory and has been put forward by the present author. As distinct from DF theory, the new one-particle scheme applies to any N-electron eigenstate including the ground state. For the latter case, the key equations become identical to those familiar from the Kohn–Sham version of DF theory. The theory given here constitutes the basis for a consistent treatment of normal conductivity and superconductivity, which will be discussed in Part II of this article. © 1993 John Wiley & Sons, Inc.

6 citations

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