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We develop a method that can constrain any local exchange-correlationpotential to preserve ba-sic exact conditions. Using the method of Lagrangemultipliers, we calculate for each set of given Kohn-Sham orbitals, aconstraint-preserving potential which is closest to the givenexchange-correlation potential. The method is applicable to both thetime-dependent (TD) and independent cases. The exact conditions that areenforced for the time-independent case are: Galilean covariance, zero net forceand torque, and Levy-Perdew virial theorem. For the TD case we enforcetranslational covariance, zero net force, the Levy-Perdew virial theorem andenergy balance. We test our method on the exchange Krieger-Li-Iafrate (xKLI)approximate-optimized effective potential (AOEP), for both cases. For thetime-independent case, we calculated the ground state properties of somehydrogen chains and small sodium clusters, for some constrained xKLI potentialsand Hartree-Fock (HF) exchange. The results indicate that enforcing the exactconditions is not important for these cases. On the other hand, in the case,constraining both energy balance and zero net force yields improved resultsrelative to TDHF calculations. We explored the electron dynamics in smallsodium clusters driven by CW laser pulses. For each laser pulse we comparedcalculations from TD constrained xKLI, TD partially constrained xKLI and TDHF.We found that electron dynamics like elec-tron ionization and moment of inertiadynamics 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 tothe unconstrained xKLI. We also discuss the problems that arise in satisfyingconstraints in the TD case with a non CW driving force.

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