Practical Treatment of Singlet Oxygen with Density-Functional Theory and the Multiplet-Sum Method

Abstract

Singlet oxygen (O2) 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 multipicity 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. 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.