Charge Localization and Ordering in A2_2Mn8_8O16_{16} Hollandite Group Oxides: Impact of Density Functional Theory Approaches

The phases of A$_2$Mn$_8$O$_{16}$ hollandite group oxides emerge from the competition between ionic interactions, Jahn-Teller effects, charge ordering, and magnetic interactions. Their balanced treatment with feasible computational approaches can be challenging for commonly used approximations in Density Functional Theory. Three examples (A = Ag, Li and K) are studied with a sequence of different approximate exchange-correlation functionals. Starting from a generalized gradient approximation (GGA), an extension to include van der Waals interactions and a recently proposed meta-GGA are considered. Then local Coulomb interactions for the Mn $3d$ electrons are more explicitly considered with the DFT+$U$ approach. Finally selected results from a hybrid functional approach provide a reference. Results for the binding energy of the A species in the parent oxide highlight the role of van der Waals interactions. Relatively accurate results for insertion energies can be achieved with a low $U$ and a high $U$ approach. In the low $U$ case, the materials are described as band metals with a high symmetry, tetragonal crystal structure. In the high $U$ case, the electrons donated by A result in formation of local Mn$^{3+}$ centers and corresponding Jahn-Teller distortions characterized by a local order parameter. The resulting degree of monoclinic distortion depends on charge ordering and magnetic interactions in the phase formed. The reference hybrid functional results show charge localization and ordering. Comparison to low temperature experiments of related compounds suggests that charge localization is the physically correct result for the hollandite group oxides studied here. . . .Comment: 16 pages, 8 figure

Comparisons of pH, total alkalinity, and O₂ concentration in nested ANOVAs for both the Skallhavet and the Fiskebäckskil sites and in both waterbody types, i.e., bay and baymouth.

<p>Comparisons of pH, total alkalinity, and O₂ concentration in nested ANOVAs for both the Skallhavet and the Fiskebäckskil sites and in both waterbody types, i.e., bay and baymouth.</p

Gross photosynthetic rates of seagrasses in baymouth water, bay water, and CO₂-purged bay water.

<p><i>n</i> = 6; error bars indicate SE.</p

A summary of pH and DIC components of baymouth water and bay water from both sampling sites, i.e., Skallhavet and Fiskebäckskil.

<p>A summary of pH and DIC components of baymouth water and bay water from both sampling sites, i.e., Skallhavet and Fiskebäckskil.</p

Gross photosynthetic rates of seagrasses under natural O₂ concentrations versus O₂-depleted conditions.

<p><i>n</i> = 6; error bars indicate SE.</p

Comparisons of gross photosynthetic rates of seagrasses measured in bay water with two different O₂ levels, i.e., natural and low O₂ concentration for both the Skallhavet and the Fiskebäckskil sites in repeated-measures ANOVA.

<p>Comparisons of gross photosynthetic rates of seagrasses measured in bay water with two different O₂ levels, i.e., natural and low O₂ concentration for both the Skallhavet and the Fiskebäckskil sites in repeated-measures ANOVA.</p

Gross photosynthetic rates as a function of pH under natural versus O₂-depleted conditions.

<p>A) <i>Zostera marina</i>, B) <i>Ruppia maritima</i>, and C) <i>Ulva intestinalis</i>. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083804#pone-0083804-g001" target="_blank">Figure 1</a> for Total DIC and O₂ contents of seawater at each pH value.</p

Total seawater DIC and O₂ contents at the pH values used in the experiments.

<p>Total seawater DIC and O₂ contents at the pH values used in the experiments.</p

Comparisons of gross photosynthetic rates of seagrasses measured in different types of waterbody, i.e., bay water, baymouth water and CO₂-purged bay water for both the Skallhavet and the Fiskebäckskil sites in repeated-measures ANOVA.

<p>Comparisons of gross photosynthetic rates of seagrasses measured in different types of waterbody, i.e., bay water, baymouth water and CO₂-purged bay water for both the Skallhavet and the Fiskebäckskil sites in repeated-measures ANOVA.</p

Percentage reduction of gross photosynthetic rates under photorespiratory conditions as a function of pH.

<p>A) <i>Zostera marina</i> and B) <i>Ruppia maritima</i>. The figure was produced from the data shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083804#pone-0083804-g002" target="_blank">Figure 2</a>. <i>Ulva intestinalis</i> was excluded from regression analysis, as O₂ conditions had no significant effect on its photosynthetic rates. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083804#pone-0083804-g001" target="_blank">Figure 1</a> for DIC and O₂ contents of seawater at each pH value.</p