Modeling the electron density kernels

Abstract

Existing approximation to the softness kernel, successfully explored in earlier work, has been extended; the normal Gauss distribution function has been used instead of the Dirac delta. The softness kernel becomes continuous functions in space and may be used to calculate the linear response function of the electron density. Three-dimensional visualization of the softness kernel and the linear response function are presented for a nitrogen atom as a working example. By using a single parameter of the spatial Gauss distribution, the novel softness kernel has been adjusted to be consistent with the standard form of the hardness kernel, representing the leading fraction of the electronic interactions in the system.

Reactivity Patterns of Imidazole, Oxazole, and Thiazole As Reflected by the Polarization Justified Fukui Functions

“…Constants b and c are internal parameters of the method, the calculation scheme for the PJFF allows for their direct determinations. They stem from the adopted approximation for the softness kernel: 5,7 δρ δ…”

“…The polarization justified Fukui function is determined from the local polarization function (the computable vector): bold-italicα ( r ) ≡ prefix− false( ∂ ρ ( r ) / ∂ bold-italicε false) N The effect of the density function responding to an external perturbation (uniform electric field ε ) is now included directly in the new FF. − This approach, originally proposed for atoms, has recently been extended to molecules leading to the explicit formulation of the local softness s ( r ) = [∂ρ( r )/∂μ] v : s ( r ) = bold-italicα ( r ) · [ r − M e ( N ) ] − b ρ ( r ) [ M e − N r ] · [ r − M e ( N ) ] ( 1 − c ) false[ boldr − boldM normale false( N false) false] 2 where vectors α ( r ), M e , and M e ( N ) are the local polarization (eq ), the electronic part of the dipole moment, and its derivative over N , respectively. The Fukui function f ( r ) is just the local softness divided by the result of integration thereof ( S = ∫ s ( r )d ...…”

“…The common remedy is to explore the electrophilic FF (( f – ( r )) = (∂ρ( r )/∂ N ) ν – ) and nucleophilic FF (( f + ( r )) = (∂ρ( r )/∂ N ) ν + ) in order to describe the appropriate sensitivity of a molecule . The concept of the polarization justified Fukui functions (PJFF) proposed in this laboratory − overcomes the difficulty in differentiating the local quantity (electron density) over the number of electrons ( N ) by using the second part of the definition (eq ). The similar idea was explored by Ayers et al; the f – ( r ) and f + ( r ) Fukui functions have been deduced from the change in Kohn–Sham orbital energies induced by perturbations in molecular external potential.…”

Critical Study of the Charge Transfer Parameter for the Calculation of Interaction Energy Using the Local Hard–Soft Acid–Base Principle

“…However, the interaction between molecules occurs through particular atoms (definite site) within the molecule, and thus, the interaction is always local. Therefore, to explain the interactions between molecules, we need local reactivity descriptors (LRD) − such as Fukui function and local softness. The Fukui function and local softness relate the change of electron density to the number of electrons and chemical potential respectively.…”

Chemical reactivity in the framework of pair density functional theories

“…[1] However, little is known about the nature of these kernels and only some approximations have been examined. [9–16]…”