First principle calculations of the effective exchange integrals (J) in the Heisenberg model for diradical species are presented for both symmetry-adapted multi-reference (MR) and single-reference broken-symmetry (BS) methods. The Mukherjee-type state-specific MR coupled cluster singles and doubles (MkCCSD) method with several different reference orbitals including BS natural orbitals is used to calculate the singlet-triplet energy gaps (S-T energy gap or 2J) and diradical characters for the antiaromatic molecules [a cyclopropenyl anion (CPA), b cyclobutadiene (CBD), and c cyclopentadienyl cation (CPC)], the cyclobutadiene derivatives with polar substitutents [d aminocyclobutadiene (ACBD), e formylcyclobutadiene (FCBD), and f 1-amino-2-formyl-cyclobutadiene (AFCBD)] and finally the cyclobutadine derivatives with radical substitutents [g 1,2-bis(methylene)cyclobutadiene (1,2-BMCBD) and h 1,3-bis(methylene)cyclobutadiene (1,3-BMCBD)]. For the BS methods, the spin-unrestricted Hartree-Fock based CCSD (UHF-CCSD), the CCD with the spin-unrestricted Brueckner determinant (UBD), and BS density functional theory (UDFT) computations are performed. Comparison between MkCCSD and the UHF-CCSD results indicates that spin-contamination of UHF-CCSD solutions still remains. In comparison with UHF-CCSD, the UBD results show that spin-contamination involved in BS solutions is greatly suppressed. To eliminate the spin contamination, an approximate spin-projection (AP) scheme is applied to the BS solutions. The AP procedure with the use of the expectation value of the total-spin operator corresponding to UHF-CCSD and UBD results yields good agreement with the MkCCSD results. As for the AP correction of the UDFT methods, three different computational schemes for predicting the expectation value of the total-spin operator are examined. Systematic comparisons between these methods are presented for the S-T energy gaps (2J). Implications of the present computational results have been discussed in relation to the design of magnetic oligomers and polymers.
- Approximate spin projection procedure
- Diradical character
- Multireference coupled cluster
- Spin contamination
ASJC Scopus subject areas
- Physical and Theoretical Chemistry