Obtaining stable solutions of the optimized-effective-potential method in the basis set representation

Equations of the optimized-effective-potential method in a basis set representation are solved with the use of the incomplete Cholesky decomposition technique. The resulting local potential is expanded in terms of the products of occupied and virtual Kohn-Sham orbitals thus avoiding the use of auxiliary basis sets. It is demonstrated that, for a sufficiently large orbital basis set satisfying the condition of linear dependence of these products, stable and numerically accurate solutions of the OEP method can be obtained with the use of the suggested computational approach.