  First principles calculations were carried out to study the phase stability
and thermoelectric properties of the naturally occurring marcasite phase of
FeS$_2$ at ambient condition as well as under pressure. Two distinct density
functional approaches has been used to investigate the above mentioned
properties. The plane wave pseudopotential approach was used to study the phase
stability and structural, elastic, and vibrational properties. The full
potential linear augment plane wave method has been used to study the
electronic structure and thermoelectric properties. From the total energy
calculations, it is clearly seen that marcasite FeS$_2$ is stable at ambient
conditions, and it undergoes a first order phase transition to pyrite FeS$_2$
at around 3.7 GPa with a volume collapse of about 3$\%$. The calculated ground
state properties such as lattice parameters, bond lengths and bulk modulus of
marcasite FeS$_2$ agree quite well with the experiment. Apart from the above
studies, phonon dispersion curves unambiguously indicate that marcasite phase
is stable under ambient conditions. Further, we do not observe any phonon
softening across the marcasite to pyrite transition and the possible reason
driving the transition is also analyzed in the present study, which has not
been attempted earlier. In addition, we have also calculated the electronic
structure and thermoelectric properties of the both marcasite and pyrite
FeS$_2$. We find a high thermopower for both the phases, especially with p-type
doping, which enables us to predict that FeS$_2$ might find promising
applications as good thermoelectric materials.
