The promoting mechanism of SO42− on CeO2 for selective catalytic reduction of NO by NH3: A DFT study

Electronegativity: A continuing enigma

“…This problem does not arise with Equation (2) because the number of moles can be a noninteger, nor with Equation ( 4), because ρ(r) is continuous. The differentiability issue has been raised on several occasions, [20][21][22][23] and there have been ingenious rebuttals, [20,[24][25][26][27][28][29][30] but the issue is still being addressed. [31,32] We find it difficult to ignore the fact that Equations (3), (5), and (7) refer to free, ground-state atoms, and molecules, and these can only have integral numbers of electrons.…”

“…This problem does not arise with Equation () because the number of moles can be a non‐integer, nor with Equation (), because ρ( r ) is continuous. The differentiability issue has been raised on several occasions, [ 20‐23 ] and there have been ingenious rebuttals, [ 20,24‐30 ] but the issue is still being addressed. [ 31,32 ]…”

Perturbed reactivity descriptors in the two parabolas model of fractional electron number

“…The extension of density functional theory to fractional electron number based on the three ground states grand canonical ensemble showed also that at zero temperature, the electronic density as a function of 𝑁 is given by a series of straight lines connecting the integer values of 𝑁. [1][2][3][4] Thus, the equivalent of Eqs. ( 1) and ( 2) for the electronic density define the Fukui function and the dual descriptor, respectively,…”

“…The extension of density functional theory to fractional electron number 𝑁, considering the three ground states grand canonical ensemble, showed [1][2][3] that at zero temperature the energy is given by a series of straight lines connecting the integer values of 𝑁. Thus, because of this behavior, [4] the first derivative of the energy 𝐸, with respect to the number of electrons at constant external potential 𝑣(𝐫), the chemical potential 𝜇, is different at the integer values of 𝑁, when evaluated from the left (−) or from the right (+).…”

A conceptual density functional theory approach to substituent effects in fluorescence processes: The case of naphthalimide derivatives

“…In order to analyze the absorption and emission steps in fluorescence as intramolecular charge transfer processes, it is important to consider several aspects of the Fukui function, Equation (). One of them comes from the fact that since the electronic density as a function of , at zero temperature [65–68] and up to temperatures of chemical interest [69], is given by a series of straight lines connecting the integer values of , then the left and right derivatives are given by the expressions [53, 54] where , and are the electron densities, and the three densities are determined at the ground state geometry of the electron system. Also, it has been shown that the Fukui function is the one that minimizes the energy change associated with the removal or addition of charge [70], which implies that and correspond to the places where the charge is removed or added, respectively.…”