Spin Contamination Error in Optimized Geometry of Singlet Carbene (¹A₁) by Broken-Symmetry Method

Abstract

Spin contamination errors of a broken-symmetry (BS) method in optimized structural parameters of the singlet methylene ((1)A(1)) molecule are quantitatively estimated for the Hartree-Fock (HF) method, post-HF methods (CID, CCD, MP2, MP3, MP4(SDQ)), and a hybrid DFT (B3LYP) method. For the purpose, the optimized geometry by the BS method is compared with that of an approximate spin projection (AP) method. The difference between the BS and the AP methods is about 10-20 degrees in the HCH angle. In order to examine the basis set dependency of the spin contamination error, calculated results by STO-3G, 6-31G*, and 6-311++G** are compared. The error depends on the basis sets, but the tendencies of each method are classified into two types. Calculated energy splitting values between the triplet and the singlet states (ST gap) indicate that the contamination of the stable triplet state makes the BS singlet solution stable and the ST gap becomes small. The energy order of the spin contamination error in the ST gap is estimated to be 10(-1) eV.

Approximate spin-projected spin-unrestricted density functional theory method: Application to the diradical character dependences of the (hyper)polarizabilities in p-quinodimethane models

“…Within the broken symmetry (BS), i.e., spin-unrestricted (U), ab initio MO and DFT methods, the c enhancement in the intermediate diradical character region has been shown to originate from the field-induced charge transfer between up and down spin density distributions. Although UDFT with several exchange-correlation (XC) functionals reproduces semi-quantitatively the c versus y results obtained with high-level quantum chemistry approaches that account precisely for electron correlation effects [14,23], the removal of spin contamination effects involved in the BS schemes is often essential for reproducing reliable molecular structures and magnetic properties of openshell systems [25][26][27]. Therefore, in our previous study [28], we have developed within the spin-unrestricted single-determinantal frame an approximate spin-projection scheme based on a correction of the occupation numbers in order to improve the description of the odd electron density [29][30][31] and the evaluation of the (hyper)polarizabilities of delocalized open-shell singlet molecules.…”

Density functional theory of the CuA‐like Cu2S2 diamond core in Cu (NGuaS)2Cl2

“…[116,117] Hence, the NI-KS orbital-based method according to eq. In addition, formula (5) is believed to lead to slightly underestimated singlet-triplet splittings |2J|.…”

Adducts of manganese diketonates with redox-active ligands: Computational modeling of valence tautomeric systems

“…The exchange coupling constants J (in cm -1 ) were calculated by the Yamaguchi equation [40,41]. No additional correction of the energies of BS states for spin contamination has been applied because of the used approximation (B3LYP*/6-311++G(d,p)) has been shown [41] to be the most appropriate for the estimation of the energy of BS states.…”

“…The exchange coupling constants J (in cm -1 ) were calculated by the Yamaguchi equation [40,41]. No additional correction of the energies of BS states for spin contamination has been applied because of the used approximation (B3LYP*/6-311++G(d,p)) has been shown [41] to be the most appropriate for the estimation of the energy of BS states. The search for minimum energy crossing point (MECP) in the spin-forbidden reactions has been made based on the program code developed by Harvey et al [42] and modified for the supercomputer [43].…”