Spin-density calculation via the graphical unitary group approach

Figures & data

Figure 1. Phenalenyl valence bond structure with the indication for the carbon positions. Doping is considered in positions 2 and 12. The blue positions can present the open radical in ressonant structures.

Figure 2. Spin-density distributions ${\rho }^{[-;1/2]}\left(\mathbf{r}\right)$ for the pristine phenalenyl computed for the doublet ground state obtained from (a) MCSCF, (b) UHF, (c) ROHF, (d) PBE50, (e) PBE0, (f) PBE, (g) TPSS calculations and (h) 2D structure with Mulliken populations (e) from the MCSCF calculation. Blue denotes positive spin-density and red denotes negative values. The isovalue is $\pm 0.001e\cdot {\text{Å}}^{-3}$ for positive and negative values, respectively.

Figure 3. ${\rho }_{\pm }^{[-;1/2]}\left(\mathbf{r}\right)$ spin-promotion distributions and the natural spin-density orbitals (NSDOs) with their eigenvalues (${\mu }_p^{\left(1/2\right)}$) for the pristine phenalenyl computed for the ${}^2{A}_2\left({}^2{A}_1^{\mathrm{\prime }\mathrm{\prime }}\right)$ ground state obtained from the MCSCF calculation. The isovalue is $\pm 0.001e\cdot {\text{Å}}^{-3}$ for ${\rho }_{\pm }^{[-;1/2]}\left(\mathbf{r}\right)$ and $\pm 0.05{\text{Å}}^{-3/2}$ for the NSDOs. Blue and red represent positive and negative values, respectively.

Figure 4. Spin-density distributions ${\rho }^{[-;1/2]}\left(\mathbf{r}\right)$ for the N-didoped phenalenyl computed for the doublet ground state obtained from (a) MCSCF, (b) TPSS calculations and (c) 2D structure with Mulliken populations (e) from the MCSCF calculation. Blue denotes positive spin density and red denotes negative values. The isovalue is $\pm 0.001e\cdot {\text{Å}}^{-3}$ for positive and negative values, respectively.

Figure 5. Spin-density distributions ${\rho }^{[-;1/2]}\left(\mathbf{r}\right)$ for the N-monodoped phenalenyl computed for the doublet ground state obtained from (a) MCSCF, (b) TPSS calculations and (c) 2D structure with Mulliken populations (e) from the MCSCF calculation. Blue denotes positive spin density and red denotes negative values. The isovalue is $\pm 0.001e\cdot {\text{Å}}^{-3}$ for positive and negative values, respectively.

Figure 6. Spin-density distributions ${\rho }^{[-;1/2]}\left(\mathbf{r}\right)$ for the NH-didoped phenalenyl computed for the doublet ground state obtained from (a) MCSCF, (b) TPSS calculations and (c) 2D structure with Mulliken populations (e) from the MCSCF calculation. Blue denotes positive spin density and red denotes negative values. The isovalue is $\pm 0.001e\cdot {\text{Å}}^{-3}$ for positive and negative values, respectively.