Self-consistent calculations using the Perdew-Zunger self-interaction correction (PZ-SIC) to local density and gradient dependent energy functionals are presented for the binding energy and equilibrium geometry of small molecules as well as energy barriers of reactions. The effect of the correction is to reduce binding energy and bond lengths and increase activation energy barriers when bond breaking is involved. The accuracy of the corrected functionals varies strongly, the correction to the binding energy being too weak for the local density approximation but too strong for the gradient dependent functionals considered. For the Perdew, Burke, and Ernzerhof (PBE) functional, a scaling of the PZ-SIC by one half gives improved results on average for both binding energy and bond lengths. The PZ-SIC does not necessarily give more accurate total energy, but it can result in a better cancellation of errors. An essential aspect of these calculations is the use of complex orbitals. A restriction to real orbitals leads to less accurate results as was recently shown for atoms [S. Klüpfel, P. Klüpfel, and H. Jónsson, Phys. Rev. A 84, 050501 (2011)]. The molecular geometry of radicals can be strongly affected by PZ-SIC. An incorrect, non-linear structure of the C(2)H radical predicted by PBE is corrected by PZ-SIC. The CH(3) radical is correctly predicted to be planar when complex orbitals are used, while it is non-planar when the PZ-SIC calculation is restricted to real orbitals.

The ground state of atoms from H to Ar was calculated using a self-interaction correction to local-and gradient-dependent density functionals. The correction can significantly improve the total energy and makes the orbital energies consistent with ionization energies. However, when the calculation is restricted to real orbitals, application of the self-interaction correction can give significantly higher total energy and worse results, as illustrated by the case of the Perdew-Burke-Ernzerhof gradient-dependent functional. This illustrates the importance of using complex orbitals for systems described by orbital-density-dependent energy functionals.

The Perdew-Zunger self-interaction correction (SIC) to local and semilocal density functionals systematically underestimates molecular bond lengths, yet improves many other ground-state properties. An alternative definition of a SIC is reached by using the Perdew-Zunger energy with a global, multiplicative Kohn-Sham potential instead of the orbital-specific potentials of traditional SIC. Due to the unitary variance of the SIC energy, the most general construction of the SIC Kohn-Sham potential involves a unitary transformation of the Kohn-Sham orbitals. We systematically investigate the Kohn-Sham version of the SIC, in particular with respect to the bond-length question, and present a detailed analysis of the influence of different unitary transformations. Using a complex-valued energy-minimizing transformation appears to be the most favorable approach, and we explain this result by analyzing orbital densities. We discuss how to calculate the transformations efficiently.

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