  The first order standard perturbation theory combined with ab initio
projector augmented wave operator challenges the realization of the standard
Sternheimer equation with linear computational efficiency. This efficiency
motivates us to describe the electron-phonon interaction in two-dimensional
(2D) black phosphorous monolayer using generalized density functional
perturbation theory (DFPT) with Boltzmann transport theory (BTE). Subsequently,
linear response phonon dynamic behaviour in terms of conductivities, seebeck
coefficients and transport properties are focused for its thermoelectric
application. The analysis reveals the crystal orientation dependence via
structural anisotropy and the density of states of the monolayer structure.
Momentum dependent phonon population dynamics along with the phonon linewidth
are efficient in terms of reciprocal space electronic states. The optimized
values of thermal conductivities of electrons and Seebeck coefficients act as
driving force to modulate thermoelectric effects. Figure of merit is calculated
to be 0.074 at 300 K and 0.152 at 500 K of the MLBP system as a function of the
power factor. The value of lattice thermal conductivity is 37.15 W/mK at room
temperature and follows the inverse dependency with temperature. With the
anticipated superior performance, profound thermoelectric applications can be
achieved particularly in the monolayer black phosphorous system.
