Spin polarization and annihilation for radicals and diradicals

Abstract

ABSTRACT:The extent of spin polarization in unrestricted Hartree-Fock and density functional B3LYP calculations has been determined for a few monoradicals as well as the corresponding diradicals containing these monoradicals as functional groups. Simple relations are found that explain the very high value for the average spin after projecting out the triplet component from a broken-spin calculation on the singlet state. The implications of these results for estimating the energy of the low-spin diradical by spin projection or by the Heisenberg Hamiltonian are discussed.

Variational fractional-spin density-functional theory for diradicals

“…The c p optimization to minimize the total energy can be performed efficiently with this derivative information in Eq. (15). Such degeneracy is also consistent with previous research.…”

“…Accurate predictions of the singlet-triplet (ST) energy gaps remains a challenge for conventional density-functional theory because of the multireference nature of the singlet state. 12,13 Therefore, most computational studies involving singlet diradicals utilize ab initio multireference methods, such as complete active space self-consistent field (CASSCF), [14][15][16] complete active space with second-order perturbation theory, 17,18 or multireference coupled cluster theory. 19,20 Unfortunately, all these multireference ab initio methods are extremely computationally demanding for large systems.…”

“…Direct application of DFT usually takes the form of unrestricted calculations and is complicated with spin contamination that leads to overstabilization of singlet states similar to unrestricted Hartree-Fock calculations. 14,15,21,22 Many efforts have been devoted to understanding and correcting spin contamination, 15,[23][24][25][26] and a factor-of-2 correction is normally needed. 27 One can also use spin-projection to improve the accuracy of unrestricted methods for calculating ST gaps, 21, 28-30 but it is not a self-consistent approach and does not provide satisfactory densities.…”

Computational studies of modified [Fe3S4] clusters: Why iron is optimal

“…As expected, adding 10% exact exchange in the form of TPSSh gives results in between B3LYP and TPSS, now with an intermediate spin ground state, but still a large energy gap (46 kJ/mol) to the experimentally observed low-spin state. The inconsistent treatment of spin by DFT functionals is a well-known problem [11,54], and the best-performing functional, in this case BP86, has to be chosen ad hoc.…”

CASSCF version of density functional theory

“…The usual treatment, i.e., spin‐unrestricted KS‐DFT (UKS‐DFT), leads to the symmetry‐broken problem in a similar way in Hartree–Fock (HF) theory in the nearly degenerate problem 3–7. Some spin‐projection approaches following UKS‐DFT (PUKS‐DFT) 4, 7–9 are available for these cases, but it is known that the projection‐after variation approach of PUKS‐DFT leads to a spurious cusp in the computed potential curve 8, as in the case of HF theory 10. Multireference (MR) density functional theory (DFT) enables us to handle the issue 11–41.…”