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7.8 Restricted Open-Shell and ΔSCF Methods

7.8.2 Approximate Spin Purification

(September 1, 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.
Theor. Chem. Acc.
(1977), 43, pp. 261.
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, 287 Daul C.
Int. J. Quantum Chem.
(1994), 52, pp. 867.
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, 179 Carter-Fenk K., Herbert J. M.
J. Chem. Theory Comput.
(2020), 16, pp. 5067.
Link

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.

OPSING

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