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#### The static response function in Kohn-Sham theory: An appropriate basis for its matrix representation in case of finite AO basis sets

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##### Citation

Kollmar, C., & Neese, F. (2014). The static response function in Kohn-Sham theory:
An appropriate basis for its matrix representation in case of finite AO basis sets.* The Journal of
Chemical Physics,* *141*(13): 134106. doi:10.1063/1.4896897.

Cite as: https://hdl.handle.net/21.11116/0000-0007-A248-1

##### Abstract

The role of the static Kohn-Sham (KS) response function describing the response of the electron density to a change of the local KS potential is discussed in both the theory of the optimized effective potential (OEP) and the so-called inverse Kohn-Sham problem involving the task to find the local KS potential for a given electron density. In a general discussion of the integral equation to be solved in both cases, it is argued that a unique solution of this equation can be found even in case of finite atomic orbital basis sets. It is shown how a matrix representation of the response function can be obtained if the exchange-correlation potential is expanded in terms of a Schmidt-orthogonalized basis comprising orbitals products of occupied and virtual orbitals. The viability of this approach in both OEP theory and the inverse KS problem is illustrated by numerical examples.