Kernel density function constant

Because the particles are discrete, the probability that a particle is located at a given point X is null. Thus, in order to have a finite sample of particles to estimate the NDE, we need to introduce a kernel density function hwix) centered at x with bandwidth W. Eor example, a constant kernel density function defined by... 

A final set of reactivity indices constitute the so-called nuclear reactivity indices. As can be seen from eqn (26), the Fukui function measures the electron density response due to the change of the number of electrons of the system. However, despite the fact that the electron density determines all ground state properties of an atomic or a molecular system, the response of the nuelei due to this perturbation remains unknown a reponse kernel is needed to translate electron density changes in external potential changes. Cohen et at. circumvented this problem by introducing a nuclear Fukui function, which they defined as the Hellmann-Feynman force F acting on the nuclei due to a perturbation in the number of electrons at a constant external potential ... 

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