Practical treatment of singlet oxygen with density-functional theory and the multiplet-sum method

Singlet oxygen ( $$^1$$ O $$_2$$ ) comes in two flavors—namely the dominant lower-energy $$a \,^1\Delta _g$$ state and the higher-energy shorter-lived $$b \,^1\Sigma _g^+$$ state—and plays a key role in many photochemical and photobiological reactions. For this reason, and because of the large size of the systems treated, many papers have appeared with density-functional theory (DFT) treatments of the reactions of $$^1$$ O $$_2$$ with different chemical species. The present work serves as a reminder that the common assumption that it is enough to fix the spin multiplicity as unity is not enough to insure a correct treatment of singlet oxygen. We review the correct group theoretical treatment of the three lowest energy electronic states of O $$_2$$ which, in the case of $$^1$$ O $$_2$$ is often so badly explained in the relevant photochemical literature that the explanation borders on being incorrect and prevents, rather than encourages, a correct treatment of this interesting and important photochemical species. We then show how many electronic structure programs, such as a freely downloadable and personal-computer compatible Linux version of deMon2k, may be used, together with the multiplet sum method (MSM), to obtain a more accurate estimation of the potential energy curves (PECs) of the two $$^1$$ O $$_2$$ states. Applications of the MSM DFT method to $$^1$$ O $$_2$$ appear to be extremely rare as we were only able to find one correct application of the DFT MSM (or rather a very similar approach) to $$^1$$ O $$_2$$ in our literature search. Here we treat both the $$a \,^1\Delta _g$$ and $$b \,^1\Sigma _g^+$$ state with a wide variety of density-functional approximations (DFAs). Various strengths and weaknesses of different DFAs emerge through our application of the MSM method. In particular, the quality of the $$a \,^1\Delta _g$$ excitation energy reflects how well functionals are able to describe the spin-flip energy in DFT while the quality of the $$b \,^1\Sigma _g^+$$ excitation energy reflects how well functionals are able to describe the spin-pairing energy in DFT. Finally, we note that improvements in DFT-based excited-state methods will be needed to describe the full PECs of $$^1$$ O $$_2$$ including both the equilibrium bond lengths and dissociation behavior.