Improving approximate-optimized effective potentials by imposing exact conditions: Theory and applications to electronic statics and dynamics

Abstract

We develop a method that can constrain any local exchange-correlation potential to preserve ba-sic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals, a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are: Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the TD case we enforce translational covariance, zero net force, the Levy-Perdew virial theorem and energy balance. We test our method on the exchange Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential (AOEP), for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters, for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by CW laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI and TDHF. We found that electron dynamics like elec-tron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least an order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non CW driving force.