7.9.6 Spin-Flip Methods for Di- and Triradicals

The spin-flip method ⁷²⁶ Krylov A. I.
Chem. Phys. Lett.
(2001), 338, pp. 375. Link ^{, 727} Krylov A. I.
Chem. Phys. Lett.
(2001), 350, pp. 522. Link ^{, 728} Krylov A. I.
Acc. Chem. Res.
(2006), 39, pp. 83. Link addresses problems due to small HOMO-LUMO gaps, associated with a single-determinant description of the wave function. Both closed- and open-shell singlet states are described within a single reference as spin-flipping, (e.g., $\alpha \to \beta$) excitations from the triplet reference state, for which both dynamical and non-dynamical correlation effects are smaller than for the corresponding singlet state. This is because the exchange hole, which arises from the Pauli exclusion between same-spin electrons, partially compensates for the poor description of the coulomb hole by the mean-field Hartree–Fock model. Furthermore, because two $\alpha$ electrons cannot form a bond, no bond breaking occurs as the internuclear distance is stretched, and the triplet wave function remains essentially single-reference in character. The spin-flip approach has also proved useful in the description of di- and tri-radicals as well as some problematic doublet states.

The spin-flip method is available for the CIS, CIS(D), CC2, CISD, CISDT, OD, CCSD, EOM-(2,3), and CCSDT levels of theory and the spin complete SF-XCIS (see Section 7.2.3.2). An $𝒪(N^7)$ non-iterative triples corrections are also available—e.g., (dT) and (fT). For the OD and CCSD models, the following non-relaxed properties are also available: dipoles, transition dipoles, SOCs, eigenvalues of the spin-squared operator ($⟨{\widehat{S}}^2⟩$), and densities. Analytic gradients are also for SF-CIS and EOM-SF-CCSD methods. Construction of effective Hamiltonians in Heisenberg and Hubbard spaces from EOM-SF wave functions is described in the Section 13.6. To invoke a spin-flip calculation the SF_STATES $rem should be used, along with the associated $rem settings for the chosen level of correlation by using METHOD (recommended) or using older keywords (CORRELATION, and, optionally, EOM_CORR). Note that the high multiplicity triplet or quartet reference states should be used.

Several double SF methods have also been implemented. ²⁰⁷ Casanova D. et al.
J. Chem. Phys.
(2009), 130, pp. 044103. Link To invoke these methods, use DSF_STATES.