  We present an ab-initio study of boron nitride as well as carbon allotropes.
Their relative thermodynamic stabilities and structural phase transitions from
low- to high-density phases are investigated. Pressure-temperature phase
diagrams are calculated and compared to experimental findings. The calculations
are performed using quantum chemical wavefunction based as well as density
functional theories. Our findings reveal that predicted energy differences
often depend significantly on the choice of the employed method. Comparison
between calculated and experimental results allows for benchmarking the
accuracy of various levels of theory. The produced results show that quantum
chemical wavefunction based theories allow for achieving systematically
improvable estimates. We find that on the level of coupled cluster theories the
low- and high-density phases of boron nitride become thermodynamically
degenerate at 0 K. This is in agreement with recent experimental findings,
indicating that cubic boron nitride is not the thermodynamically stable
allotrope at ambient conditions. Furthermore we employ the calculated results
to assess transition probabilities from graphitic low-density to diamond-like
high-density phases in an approximate manner. We conclude that the stacking
order of the parent graphitic material is crucial for the possible formation of
meta-stable wurtzite boron nitride and hexagonal carbon diamond also known as
lonsdaleite.
