Theoretical Study of the Vertical Electronic Spectra, Electron-Spin g-Factors and Hyperfine Coupling Constants of the (C_2v) Cyclic Radicals C₃⁺, Si₃⁺, C₃⁻ and Si₃⁻

Abstract

The vertical transition energies and Δg-values of cyclic C₃⁺, Si₃⁺ (X²B₂), C₃⁻ (1²A₁, metastable) and Si₃⁻ (X²A₁) are studied with ROHF MOs, multireference (MRDCI) wavefunctions and 6-311+G(2d) basis sets. Si₃⁻ has at least eight bound states. For each radical, the in-plane components of the g shift, Δg_yy and Δg_zz (with g_ii = g_e + Δg_ii), have similar negative values (about −1200 ppm for C₃⁺, C₃⁻ and about −8000 ppm for Si₃⁺, Si₃⁻). The Δg_xx’s are larger in magnitude, negative for C₃⁺, Si₃⁺ (−11000 and −72000 ppm) but positive for C₃⁻, Si₃⁻ (8000 and 165000 ppm). The hyperfine coupling constants A_iso, A_dip are evaluated with ab initio CISD, QCISD, CCD, MP4SDQ methods as well as with density functional theory (DFT) methods (SVWN, B3LYP, B3PW91, PW91PW91), using a spin-unrestricted formalism; several basis sets are considered. Both approaches give internally consistent A_iso’s and A_dip’s for each X₃⁻ center, with the (positive) s-spin-density at each basal atom (average A_iso (MHz) = 75 for C₃⁻ and −25 for Si₃⁻) being smaller than at the apical center (275 and −95 MHz). The results are less satisfactory for X₃⁺. All treatments agree, more or less, in a larger (positive) s-density at the basal atoms (A_iso(MHz) from 300 to 700 for C₃⁺, and −80 to −150 for Si₃⁺), whereas the s-contribution at the apical center depends on the method: for C₃⁺, it is positive with ab initio but negative with DFT, whereas for Si₃⁺ the opposite trend is found; as well, A_dip(X₃⁺) shows unusually large discrepancies for each center. For these radicals, literature values of A_iso and A_dip are not available, either from experimental or multireference ab initio studies, to allow for comparisons with our results.