Optimized effective potential for calculations with orbital-free potential functionals

Abstract

Approximation of electronic kinetic energy can be naturally expressed in terms of the one-electron effective potential, namely as a potential functional. Such approximate functionals can lead to linear scaling orbital-free calculations of large systems. For calculation within orbital-free potential functionals, a new optimized effective potential (OEP) method has been developed presently for the direct optimization of electronic ground state energy. This approach parallels the development of OEP for the direct optimization of orbital-dependent exchange-correlation functionals within the Kohn–Sham density functional theory (DFT) framework. It uses the effective one-electron potential as the basic computation variable. This potential is further expanded as a linear combination of basis functions plus a fixed reference potential. Thus, the potential optimization is transformed into the optimization of linear coefficients associated with the basis sets. As a key quantity within the orbital-free potential functionals, the chemical potential controls the correct number of electrons and depends on the trial one-electron potential. The derivatives of the chemical potential with respect to the potential variations have been derived and their use leads to a very efficient electron-number conserving update of the trial potential. The calculations of several atoms and diatomic molecules with the simple Thomas–Fermi–Dirac approximate functional has been carried out to demonstrate our approach. The developed OEP approach should be an efficient computational tool for orbital-free potential functionals.