Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: A new formula for the energy third derivative γ

Abstract

Nuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground state hardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons (N), but is so within constant chemical potential (mu) constraint. The authors apply this feature to evaluate an energy third derivative (gamma). MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model. 11, 312 (2005); J. Chem. Sci. 117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energy-density [A. Tachibana, J. Mol. Mod. 11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.

Variation of the electronic dipole polarizability on the reaction path

“…The calculated electron dipole polarizability corroborates an earlier finding of the softest state in this reaction [8], away from its transition state. However, the present result is obtained beyond the limiting finite difference approximation, which was also tested here in two typical modifications, exploring the computed I ( ξ ) and A ( ξ ) results (MP2 level) or the orbital energies ε ( ξ ) on the HF level.…”

“…1) result formally by taking a derivative of Eq. 4: are reaction force constants calculated for the ionized species, respectively, λ ij stands for the component of the mode softening index introduced in earlier works from this laboratory: [8, 21]…”

“…The hardness stationary points discovered were less sensitive to the calculation technique than those for the energy profile. Ordon and Tachibana presented an analysis for the profile of the molecular stiffness on the reaction path [8]: G ξ = dη / dξ . These authors also presented an effort to determine the electronic flux between the regions in the reacting entity [9].…”

“…An effort is made to escape the tyranny of the finite difference approximation, inevitable in any calculations involving ionization energy ( I ) and electron affinicty ( A ), thus also the chemical potential μ= ½( I + A ) and global hardness, η= ( I-A ). Specifically, the relation between the global softness ( S=η −1 ) and the electronic dipole polarizability changes on the IRC have been studied computationally for the model reaction [8] HF+CO→HCOF.…”

Evolution of the atomic valence observed by the reaction fragility spectra on the reaction path

“…We have studied molecular reactivity modifications along the course of chemical reaction for a long time [1][2][3]. We have developed regional chemical potential evolution and identified the most reactive state along the IRC reaction path [4].…”