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Obtaining stable solutions of optimized offective potential method in basis set representation

Optimized effective potential (OEP) method represents a basis for the rigorous implementation of the orbital-dependent exchange-correlation energy functionals[1] in the context of the Kohn-Sham approach in density functional theory (DFT). The search for a local multiplicative potential such that the eigenfunctions of the resulting single-particle Hamiltonian minimize the orbital-dependent energy functional leads, in a finite basis representation, to an ill-posed algebraic problem. In the present work, the OEP equations in finite basis set of local functions are solved with the use of the incomplete Cholesky decomposition. 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 the occupied-virtual orbital products, stable and numerically accurate solutions of the OEP method can be obtained with the use of the suggested computational approach. The suggested computational approach leads to smooth local potentials for atoms and polyatomic molecules and to the total energies and the Kohn-Sham orbital energies in good agreement with the exact solutions of the OEP method.The utility of the new approach is analysed and an outlook for future developments is presented ​
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