From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function

Abstract

Important reactivity measures such as the local softness, the Fukui function, and the global hardness have been calculated directly from first principles with the use of the electron density function, beyond the finite difference approximation. Our recently derived density gradient theorem and the principle of nearsightedness of the electronic matter have been instrumental in obtaining the original, albeit approximate, result on the local softness of an atom. By integration of the local softness s(r), we obtain the global softness S and the Fukui function f(r) = s(r)/S. Local and global softness values have also been calculated analytically for the basic hydrogenic orbitals; the general relation to the atomic number S = σZ –2 has been demonstrated, with constants σ characteristic for each orbital type. Global hardness η = 1/S calculated for atoms and ions has been favorably tested against its conventional measure given by the finite difference approximation: (I – A). Calculated test results for atoms and ions in rows 1–4 of the periodic table have been presented.

Enhanced Charge Transfer via S‐Scheme Heterojunction Interface Engineering of Supramolecular SubPc–Br/UiO‐66 Arrays for Efficient Photocatalytic Oxidation

“…In this paper, the degradation path of MC was accurately obtained by using Gaussian calculations in theory and high‐performance liquid chromatography–mass spectrometry (HPLC–MS) to analyze the intermediate products in the experimental process. [ 78 ]…”

“…In this paper, the degradation path of MC was accurately obtained by using Gaussian calculations in theory and high-performance liquid chromatography-mass spectrometry (HPLC-MS) to analyze the intermediate products in the experimental process. [78] Figure 10a shows a diagram of the molecular structure of MC with numbering scheme. Figure 10b,c represents the energy levels of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of MC molecules, which were determined as −0.06879 and −0.1957 eV, respectively.…”

Chemometrics as a valuable tool for evaluating interactions between antiretroviral drugs and food

“…Log P was negatively correlated with the chemical hardness of the molecule (EqualEta). Chemical hardness can be interpreted as the resistance against polarization or deformation of the electron cloud of a molecule 79 . Higher values of chemical hardness are associated with greater stability of a chemical compound 80 .…”

“…Chemical hardness can be interpreted as the resistance against polarization or deformation of the electron cloud of a molecule. 79 Higher values of chemical hardness are associated with greater stability of a chemical compound. 80 There is also an inverse relationship between the hardness of a molecule and its polarizability-the higher the chemical hardness, the lower the polarizability of the molecule.…”

DFT Studies of the Activity and Reactivity of Limonene in Comparison with Selected Monoterpenes

“…Global softness (S) is related to η. Global hardness and softness concern the sensitivity of electron-electron interactions; for example, for anions that are characterized by the lowest hardness value and the highest softness, their susceptibility to changing the number of electrons is low [89]. For the analyzed monoterpenes, molecular hardness η = 0.5•(I -A) and molecular softness S = 0.5/η [86][87][88] were calculated; the η values increase from thymol (with the lowest η value), cymene, pienene, limonene, and menthol (with the highest η value and the lowest S value).…”