Electronic structure, magnetic interactions, and the role of ligands in ${\mathrm{Mn}}_n(n=4,12)$ single-molecule magnets

We report our first principles calculation studies of electronic structure and magnetic properties of the ${\mathrm{Mn}}_n$ $(n=4,12)$ single-molecule magnet, i.e., $\left[{\mathrm{Mn}}_4{\mathrm{O}}_3\mathrm{Cl}{\left(\mathrm{OAc}\right)}_3{\left(\mathrm{dbm}\right)}_3\right]$ $\left(\mathrm{dbmH}=\text{dibenzoyl}\text{−}\text{methane}\right)$ and $\left[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}{\left({\mathrm{CH}}_3\mathrm{COO}\right)}_{16}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]$ molecules. For the calculations, we used the localized pseudoatomic orbital method based on the density functional theory within local density approximation. To investigate the role of ligand and its contribution to the determination of the magnetic properties, we calculated the electronic structures of ${\mathrm{Mn}}_n$ clusters with different ligand configurations. The detailed analysis reveals an important contribution of the bridging carbon atoms, connecting the $\mathrm{Mn}\text{−}\mathrm{O}$ core and the outer ligand complex, to the magnetic ground states of the magnetic molecules. In addition, we calculated the effective exchange-coupling constants among $\mathrm{Mn}$ ions.

Figure 1

Ground state spin configuration and schematic ligand geometry in ${\mathrm{Mn}}_4$. The ${\mathrm{CH}}_3$ with a carbon and two oxygens forms a bridge between $\mathrm{Mn}\left(1\right)$ and $\mathrm{Mn}\left(2\right)$, (3), (4), respectively. Here only the ${\mathrm{CH}}_3$ complex between $\mathrm{Mn}\left(1\right)$ and $\mathrm{Mn}\left(4\right)$ is shown for clarity.

Figure 2

The change of charge and magnetic moment for each type of $\mathrm{Mn}$ in ${\mathrm{Mn}}_4$ by removing three ${\mathrm{CH}}_3$. The data for ${\mathrm{Mn}}_4(N=105,109)$ are not shown for clarity.

Figure 3

The projected density-of-states (pDOS) near the Fermi level at the $\mathrm{Mn}\left(1\right)$ site, corresponding to (a) the original ${\mathrm{Mn}}_4(N=113)$, (b) ${\mathrm{Mn}}_4(N=109)$ with one ${\mathrm{CH}}_3$ removed, and (c) ${\mathrm{Mn}}_4(N=101)$ with three ${\mathrm{CH}}_3$ removed. Note the arrow marks pointing to the states just below the Fermi, the spectral weight of which grow in proportion to the number of ${\mathrm{CH}}_3$ ligands being removed.

Figure 4

(Color online) Spin density distribution of ${\mathrm{Mn}}_4(N=101)$ around the $\mathrm{Mn}\text{−}\mathrm{O}$ core region. Dark (red) color represents negative spin-density (spin-down region), while bright (blue) color represents positive (spin-up region). Note that the carbon atoms are polarized with the same spin as $\mathrm{Mn}\left(1\right)$.

Figure 5

pDOS of Br and Cl in the ${\mathrm{Mn}}_4^{\prime }$ and ${\mathrm{Mn}}_4$, respectively.

Figure 6

Ground state spin configuration in ${\mathrm{Mn}}_{12}$. Inner four circles represent $\mathrm{Mn}\left(1\right)$; outer ones with dark and bright circles are for $\mathrm{Mn}\left(2\right)$ and $\mathrm{Mn}\left(3\right)$, respectively.

Figure 7

Schematic ligand configuration in ${\mathrm{Mn}}_{12}$. Large circles refer to manganese atoms; small dark circles refer to, oxygen atoms.

Figure 8

The change of electronic structure of ${\mathrm{Mn}}_{12}$ by removing 16 ${\mathrm{CH}}_3$ ligands. ${\mathrm{Mn}}_{12}(N=148)$ refers the full system while ${\mathrm{Mn}}_{12}(N=84)$ is the one which 16 ${\mathrm{CH}}_3$’s are removed.

Figure 9

The change of charge and magnetic moment for each type of $\mathrm{Mn}$ in ${\mathrm{Mn}}_{12}$ by removing 16 ${\mathrm{CH}}_3$.