5.2 A concept for improving stability of MnO2 81
and solving the equation explicitly is practically impossible, except for very
simple systems. Especially the repulsive interaction between electrons complicates
the treatment of large systems. These include exchange interaction, which
dictates that fermions can not occupy the same quantum state, and electronic
correlation, describing the interaction between electrons. DFT relies on the
Hohenberg-Kohn theorems which demonstrate that the ground state properties
of a system of electrons can be uniquely determined from the electron density.
In other words, if the electron density of a system is known, all ground state
properties can be determined accurately. This is actually a huge advantage,
since the density is a function of three spatial coordinates while treating every
electron in a system with N electrons would include treating 3N coordinates.
Furthermore, given a specic system of electrons, the correct electron density
minimizes the energy functional. With the Kohn-Sham approach the density
of electrons, and specically exchange and correlation interactions, is approximated
and can be varied slightly until a minimum in ground state energy is
found. The approximation of the electron density to a high degree determines
both the accuracy and the computational cost of the calculation.
5.2.2 Summary of DFT results for for MnO2 modications
Here a brief summary of the most important results from a previously conducted
DFT study will be presented. The focus is on the concept which have been
explored experimentally during the Ph.D. project. For more computational
details the reader is referred to the appended paper III.
Steps and kinks of rutile MnO2 were investigated for termination with Ti, Ge,
Sn, Pt, Ru and Ir dioxides. All of these materials, except Ru, are stable at anodic
potentials in acid. The question is which structure is energetically favourable.
Besides the undercoordinated structures modications of at terrace sites and
the bulk oxide were investigated. The energetics of adding the guest materials
were evaluated as a termination energy, E, based on the following equation:
E = Eterm �� Eref �� (Eunit;guest �� Eunit;ref ) (5.3)
where Eterm is the total energy of the terminated structure, Eref the total energy
of the original MnO2 structure, Eunit;guest the energy of a single unit of the
termination material and Eunit;ref the energy of a single unit of MnO2 which
is replaced. The energies of the single units are calculated as bulk formation
energy of the rutile compound. If this termination energy, E, is negative,
it represents the energy gained by the system when another material is introduced.
If positive, the overall system energy has increased which represents an
unfavourable situation, i.e. a less stable structure.
While none of the materials exhibited favourable mixing into the bulk of MnO2
or surface incorporation, the termination of steps was energetically favoured for