Here we present and test several computational prescriptions for calculating singlet-triplet (ST) gap energies and bond dissociation curves for open-shell singlet diradicals using economical unrestricted single reference type calculations. For ST gap energies from Slipchenko and Krylov's atom and molecule test set (C, O, Si, NH, NF, OH(+), O(2), CH(2), and NH(2)(+)) spin unrestricted Hartree-Fock and MP2 energies result in errors greater than 15 kcal/mol. However, spin-projected (SP) Hartree-Fock theory in combination with spin-component-scaled (SCS) or scaled-opposite-spin (SOS) second-order perturbation theory gives ST gap energies with a mean unsigned error (MUE) of less than 2 kcal/mol. Density functionals generally give poor results for unrestricted energies and only the ωB97X-D, the M06, and the M06-2X functionals provide reasonable accuracy after spin-projection with MUE values of 4.7, 4.3, and 3.0 kcal/mol, respectively, with the 6-311++G(2d,2p) basis set. We also present a new one parameter hybrid density functional, diradical-1 (DR-1), based on Adamo and Barone's modified PW exchange functional with the PW91 correlation functional. This DR-1 method gives a mean error (ME) of 0.0 kcal/mol and a MUE value of 1.3 kcal/mol for ST gap energies. As another test of unrestricted methods the bond dissociation curves for methane (CH(4)) and hydrofluoric acid (H-F) were calculated with the M06-2X, DR-1, and ωB97X-D density functionals. All three of these functionals give reasonable results for the methane C-H bond but result in errors greater than 50 kcal/mol for the H-F bond dissociation. Spin-projection is found to significantly degrade bond dissociation curves past ~2.2 Å. Although unrestricted Hartree-Fock theory provides a very poor description of H-F bond dissociation, unrestricted SCS-MP2 and SOS-MP2 methods give accurate results.

Density functional theory was used to model glycinate enolate binding and enantiomeric allylation transition states mediated by the cinchonidinium phase-transfer catalyst 2. Transition states show oxy-anion-ammonium interactions in contrast to π-face interactions in the ground states. The details of stereoselectivity are described within the quaternary ammonium-tetrahedron face model.