This chapter discusses REKS (spin-Restricted Ensemble Kohn-Sham) calculations for ground and low-lying excited states. REKS can treat states with strong static correlation (J. Phys. Chem. A 104, 6628) and also produces the correct spin symmetry in cases where unrestricted methods suffer from spin contamination. REKS also allows the calculation of, for example, states with multi-reference character as well as the vertical excitation energies between states. REKS can be classified as Single-state REKS, SA-REKS and SI-SA-REKS.

In this chapter we will

  • provide some example calculations of basic energy and gradient evaluation,
  • discuss additional functionality such as level shifting and spin tuning,
  • demonstrate advanced calculations including non-adiabatic couplings between the states and relaxed densities which can be used for QM/MM calculations.

Finally, we will discuss how to diagnose and handle some the problems which can specifically arise in REKS calculations.