On the quality of the hardness kernel and the Fukui function to evaluate the global hardness

An approximated hardness kernel, which includes the second derivative with respect to the density of the kinetic energy, the electron-electron coulomb repulsion, and the exchange density functionals, has been tested for the calculation of the global hardness. The results obtained for a series of 40 cations and neutral systems and 16 anions represent in most cases an improvement of the results obtained using the HOMO-LUMO gap approach and indicate the viability of this approach to evaluate global hardness. In addition, the relevance of the Fukui function approximation and the role of the three components of the hardness kernel in the evaluation of the global hardness have been analyzed.     

Analogies and differences between calcium-based and europium-based graphite intercalation compounds

An original method using lithium-based liquid alloys has been developed, allowing studies on bulk graphite intercalation compounds with calcium and europium. We showed that binary and ternary compounds belonging to graphite-lithium-calcium and graphite-lithium-europium systems are synthesized in both cases for equivalent reaction conditions but amazingly with many different structural and physical properties. Concerning CaC₆ and EuC₆, even if their 2D unit cells are hexal, their c-axis stacking sequences lead to different symmetries. Regarding kinetical data, formation mechanisms of these graphite intercalation compounds appear comparable however different, with a first common step before differenciation in the intercalation mechanism. Obviously, their physical properties are strongly different due to the nature of the intercalated metallic element. So, the different ternary compounds from these systems also show very considerable differences concerning their electronic properties: complex magnetic ordering for Eu-based ternary GIC and superconducting behaviour for Ca-based ternary GIC. However, common points are highlighted.     

Analogies between photolysis and mass spectrometry of organocyclopolysilanes

Analogies between photolysis and mass spectrometry of organocyclopentasilane and organocyclohexasilane derivatives are shown and the importance of phenyl substituent is noted in the formation of ions by electron bombardment. The stability of these may be explained by p_π-d_π     

Analogies between point mechanics and chemical reaction kinetics

A few rather interesting analogies are shown between classical point mechanics and chemical reaction kinetics. The approach used is that of the differential geometry.

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Fluctuations in electronegativity and global hardness induced by molecular vibrations

A pair of novel molecular indices has been proved to contain important information on the coupling between atomic displacement and electronic properties based on the electron density function within the Density Functional Theory: the nuclear reactivity (Φ) and nuclear stiffness (G). Appropriate calculation procedure has been developed and their role in describing anharmonicity of diatomic molecules has been demonstrated. This present work provides analysis of this effect for small molecules, unveiling the role of symmetry of molecular vibrational modes in modifying the affinity of a molecule to intermolecular electron transfer. The indices have been found to be a crucial factor determining thermal fluctuations in the molecular energy derivatives: electronegativity (χ) and hardness (η). The fluctuations of hardness play a specific role, as they bring a molecule uniquely to a critical region (η0), when molecule becomes unstable to an electron exchange process, due to its excitation in a selected destructive vibrational mode.     

The Fukui potential and the capacity of charge and the global hardness of atoms

In the course of a reaction it is the shape of the Fukui potential that guides a distant reagent toward the site where an electrophile/nucleophile is willing to accept/donate charge. In this paper we explore the mathematical characteristics of the Fukui potential and demonstrate its relationship to the hardness and the ability of an atom in a molecule to change its charge. The Fukui potential not only determines the active site for electron transfer, but it also approximates the distribution of hardness of a molecule: it is the Coulomb contribution to the frontier local hardness. The Fukui potential at the position of the nuclei is equal to the variation of the chemical potential with the nuclear charge and therefore measures the sensitivity of the system to changes in atom type. In the specific case of atoms and slightly charged ions, the Fukui potential at the nucleus measures the hardness. The strong correlation between the hardness and the Fukui potential at the nucleus suggests that the Fukui potential at the nucleus is an alternative definition for the chemical hardness.     

Analogies between Jahn–Teller and Rashba spin physics

In developing physical theories, analogical reasoning has been found to be very powerful, as attested by a number of important historical examples. An analogy between two apparently different phenomena, once established, allows one to transfer information and bring new concepts from one phenomenon to the other. Here, we discuss an important analogy between two widely different physical problems, namely, the Jahn–Teller distortion in molecular physics and the Rashba spin splitting in condensed matter physics. By exploring their conceptual and mathematical features and by searching for the counterparts between them, we examine the orbital texture in Jahn–Teller systems, as the counterpart of the spin texture of the Rashba physics, and put forward a possible way of experimentally detecting the orbital texture. Finally, we discuss the analogy by comparing the coexistence of linear Rashba + Dresselhaus effects and Jahn–Teller problems for specific symmetries, which allow for nontrivial spin and orbital textures, respectively.     

Affinity capillary electrophoresis to evaluate the complex formation between poliovirus and nanobodies

It was demonstrated that nanobodies with an in vitro neutralizing activity against poliovirus type 1 interact with native virions. Here, the use of capillary electrophoresis was investigated as an alternative technique for the evaluation of the formation of nanobody–poliovirus complexes, and therefore predicting the in vitro neutralizing activity of the nanobodies. The macromolecules are preincubated offline in a specific nanobody‐to‐virus ratio and analyzed by capillary electrophoresis with UV detection. At low nanobody‐to‐virus ratios, a clear shift in migration time of the viral peak was observed. A broad peak was obtained, indicating the presence of a heterogeneous population of nanobody–virion complexes, caused by the binding of different numbers of nanobodies to the virus particle. At elevated nanobody‐to‐virus ratios, a cluster of peaks appeared, showing an additional increase in migration times. It was shown that, at these high molar excesses, aggregates were formed. The developed capillary electrophoresis method can be used as a rapid, qualitative screening for the affinity between poliovirus and nanobodies, based on a clearly visible and measurable shift in migration time. The advantages of this technique include that there is no need for antigen immobilization as in enzyme‐linked immunosorbent assays or surface plasmon resonance for the use of radiolabeled virus or for the performance of labor‐ and time‐intensive plaque‐forming neutralization assays.     

Chain and Ring Phosphorus Compounds—Analogies between Phosphorus and Carbon Chemistry

Up to about 15 years ago compounds with a skeleton of phosphorus chains or rings were regarded as “exotic” in the field of nonmetal chemistry. Aside from a number of examples of molecules with two P atoms directly bonded to each other and a few sporadically discovered monocyclic ring compounds, only solids of undefined composition and structure were known. Since then the state of our knowledge in this sector has made considerable progress: between PH₃ and its derivatives on the one hand, and the high-molecular modifications of elementary phosphorus on the other, an unexpected variety of well defined compounds have been discovered, showing many similarities to the analogous compounds of carbon. However, surprises can still occur even with “small” phosphorus-containing molecules, as shown by the likewise recently discovered field of phosphorus three-membered ring compounds.     

Hyperconjugative interactions are the main responsible for the anomeric effect: a direct relationship between the hyperconjugative anomeric effect,global hardness and zero-point energy

The correlations between the global hardness (η), hyperconjugative anomeric effect, Pauli exchange-type repulsions, electrostatic model associated with dipole–dipole interaction and structural parameters in 2-fluorotetrahydropyran, -thiopyran, -selenopyran (1–3) and their chloro- (4–6) and bromo-analogs (7–9) were investigated by means of the conventional and range-corrected functionals and natural bond orbital (NBO) interpretation. By deletion of the HC-exo-AE and HC-endo-AE, the equatorial conformations of compounds 1–9 become more stable than their corresponding axial forms, revealing that anomeric relationships in compounds 1–9 have the hyperconjugative anomeric effect origins while the electrostatic model associated with dipole–dipole interaction does not play a determining role on the variations of the anomeric relationships in these compounds. The anomeric relationships in compounds 1–3 have no Pauli exchange-type repulsions origin, but it has a significant impact on the conformational preferences in compounds 4–6 and 7–9. A canonical molecular orbital interpretation was conducted to investigate the correlations between the linear combinations of natural bond orbitals in the HOMOs, LUMOs and the global hardness (η) values. There is a direct relationship between the hyperconjugative anomeric effect, global hardness (η) and zero-point energies in compounds 1–3, 4–6 and 7–9. The harder axial conformations with the greater hyperconjugative anomeric effect and zero-point energy values are more stable than their corresponding equatorial forms.     

A variation principle for energy differences between states of two different Hamiltonians

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ??] = 〈X₀| ??_x – W_x|X₁〉 – 〈Y₀|??_y – W_y|y₁〉 + 〈X₀| Δ ??|Y₀〉 · 〈X₀| Y₀〉^?1. Δ ?? = ??_y – ??_x, |X₀〉 and |Y₀〉 are the wave functions for the X and Y states and |X₁〉 and |Y₁〉 are functions defined in the text. The principle is applied to a few simple examples.     

Analogies between the reactivities of an anionic gallium(I) heterocycle and N-heterocyclic carbenes toward metallocenes

The synthesis, spectroscopic and structural characterization of the novel nickel-gallium(I) heterocycle complex, [{Ga[N(Ar)C(H)]2}2Ni(mu-Cp)K(tmeda)(mu-Cp)K(mu-C7H8)0.5]infinity, Ar = C6H3Pri2-2,6, are reported. The compound is polymeric in the solid state and reacts with an N-heterocyclic carbene to give the neutral, square planar complex, trans-[Ni{C[N(Me)C(Me)]2}2{Ga[N(Ar)C(H)]2}2]. Analogies between the reactivities of the gallium(I) heterocycle and isoelectronic N-heterocyclic carbenes are discussed.     

Relationship between solvation energy, chemical potential and hardness variations

Starting from a density functional theory (DFT) formalism describing the energy change from one ground state representing an isolated solute, to another one representing the same solute in the field of the solvent, it is possible to obtain a simple and useful expression for the solvation energy in terms of the variation of the electronic chemical potential and global hardness associated to the change from gas to solution phase. Since both properties may be obtained from an orbital theory within the approximate Self Consistent Reaction Field (SCRF) methodology, the proposed model is expected to be useful for the analysis of chemical reactivity in solution.     

A method to evaluate the Sachs formula

A rule-based method for evaluating the Sachs formula is introduced. For simple molecules, such as linear chains and monocycles, the Sachs formula can be evaluated by directly using the rules. For complex molecular systems, the Sachs formula can be evaluated by first breaking up the molecule into constituent pieces of sufficient simplicity so that data for them are available in the data base and then constructing the molecule from the known data by adding all pieces together, one at a time, via a series of binary rules. The method changes the way of evaluating the Sachs formula from a trial-and-error-type numerical search to a purely algebraic manipulation and thus tremendously reduces the computing times. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 19–36, 1997