Bilocal Chemical Action

In order to turn the chemical action functional into a current tool for bonding description its reformulation as related with reactivity softness and hardness concepts (Putz, 2003, 2008d, 2012a) seems the appropriate endeavor. It starts with combining the unfolded chemical action variational principle (3.544) the present discussion follows (Putz, 2009a) 

With kernel dependency of electronic density back in chemical action definition the first kernel density Junctional of chemical action yields as (Putz, 2009a) 

Worth noted that the C expression gives the opportunity for understanding chemical action as an interaction quantity due to its close relationship with energy interaction relating polarizability a when the external potential F(r) = E r, with the applied electric field amplitude E, is considered, viz. in polar coordinates 

the formulation can be further refined since considering the chemical hardness and softness kernels, respectively linked by the integration-differentiation chain rule of delta-Dirac bilocal function 5(r -r). Now, making use of the fundamental density functional constraint one gets the local hardness- kernel softness density formulation 

Finally, by comparison of kernel response and softness densities the softness-hardness response bilocal function can be immediately reached out 

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