Evaluating and Interpreting the Chemical Relevance of the Linear Response Kernel for Atoms

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.