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Most of the work done on the linear response kernel χ(r,r′) has focussed on its atom–atom condensed form χAB. Our previous work [Boisdenghien et al., J. Chem. Theory Comput., 2013, 9, 1007] was the first effort to truly focus on the non-condensed form of this function for closed (sub)shell atoms in a systematic fashion. In this work, we extend our method to the open shell case. To simplify the plotting of our results, we average our results to a symmetrical quantity χ(r,r′). This allows us to plot the linear response kernel for all elements up to and including argon and to investigate the periodicity throughout the first three rows in the periodic table and in the different representations of χ(r,r′). Within the context of Spin Polarized Conceptual Density Functional Theory, the first two-dimensional plots of spin polarized linear response functions are presented and commented on for some selected cases on the basis of the atomic ground state electronic configurations. Using the relation between the linear response kernel and the polarizability we compare the values of the polarizability tensor calculated using our method to high-level values.

Although a lot of work has been done on the chemical relevance of the atom-condensed linear response kernel chi(AB) regarding inductive, mesomeric, and hyperconjugative effects as well as (anti)aromaticity of molecules, the same cannot be said about its not condensed form chi(r,r'). Using a single Slater determinant KS type ansatz involving second order perturbation theory, we set out to investigate the linear response kernel for a number of judiciously chosen closed (sub)shell atoms throughout the periodic table and its relevance, e.g., in relation to the shell structure and polarizability. The numerical results are to the best of our knowledge the first systematic study on this noncondensed linear response function, the results for He and Be being in line with earlier work by Savin. Different graphical representations of the kernel are presented and discussed. Moreover, a frontier orbital approach has been tested illustrating the sensitivity of the nonintegrated kernel to the nodal structure of the orbitals. As a test of our method, a numerical integration of the linear response kernel was performed, yielding an accuracy of 10(-4). We also compare calculated values of the polarizability tensor and their evolution throughout the periodic table to high-level values found in the literature.

s,p-Aromaticity and anti-aromaticity as retrieved by the linear responde kernel