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7.8 Restricted Open-Shell and ΔSCF Methods

7.8.2 Approximate Spin Purification

(May 7, 2024)

Singlet biradicals are an important special case, whose description within a single-determinant SCF formalism is typical characterized by significant spin contamination, S^21 (in atomic units), indicating an approximately equal mixture of singlet (S^2=0) and triplet (S^2=2) wave functions. This is a result of the fact that a proper description of two electrons in two half-filled orbitals requires a minimum of two determinants. A simple means to correct for this is to use the approximate spin-purification formula 1460 Ziegler T., Rauk A., Baerends E. J.
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EOpSing2EBS-Etrip, (7.59)

which expresses the open-shell singlet energy (EOpSing) in terms of the energy of the broken-symmetry solution (EBS, meaning the state with S^21) and the triplet energy (Etrip). Evaluation of Eq. (7.59) requires two separate SCF calculations but these can be performed together automatically by specifying OPSING = TRUE in the $rem section; see Example 7.6.1. Analytic gradients have been implemented for this approximate spin-purification approach, which again requires two separate SCF gradient computations. For the specific case of open-shell singlets, the ROKS method that is discussed below can be understood as a fully self-consistent or orbital-optimized version of the formula in Eq. (7.59), using a consistent set of orbitals for both terms in the EOpSing formula, whereas the method that is requested using OPSING = TRUE performs two independent SCF calculations with different orbitals in each.


       Controls whether approximate spin purification will be performed according to Eq. (7.59).
       FALSE Spin purification is not performed. TRUE Spin purification will be performed.
       Set to TRUE if spin purification calculation is desired. Make sure that UNRESTRICTED is set to TRUE Gradients are available.