Alternative approach to the optimized effective potential method

We propose an alternative method of calculating so-called optimized effective potentials (OEP’s) by directly exploiting the property of the total energy $E$ of an interacting $N$-electron system to attain a minimum for the true potential of the associated Kohn-Sham equations if $E$ is expressed as a functional of the occupied Kohn-Sham orbitals that solve these equations. The method is based on forming the difference between the sought-for true potential and some local spin-density reference potential corrected to yield the known large $r$ behavior of the OEP. This difference is expanded in terms of attenuated sinusoidal functions that decay exponentially beyond the range of orbital localization. By using this expansion $E$ becomes a function of the expansion coefficients whose values are determined by searching for the minimum of $E.\mathrm{}$ This is achieved by employing a variant of a steepest descent method. Due to the flexibility of the method, the exchange-only virial relation can easily be incorporated by performing the minimization in a suitably modified way. The total energy results for a set of atoms (Be-Xe) differ only by about ${10}^{-3}\mathrm{Ry}$ from those obtained by other authors using different techniques. We have also successfully extended our method to the relativistic case. For the treatment of extended systems we propose a combination of our scheme with an existing approximate OEP method.