  Thermodynamic stability and vibrational anharmonicity of single layer black
phosphorene (SLBP) are studied using a spectral energy density (SED) method.
Thermal stability of SLBP sheet is analyzed by computing phonon dispersion at
300 K, which shows that SLBP sheet is dynamically stable at finite temperature
and survives the crumpling transition. Temperature evolution of all zone center
optic phonon modes are extracted, including experimentally forbidden IR and
Raman active modes. Mode resolved phonon frequencies of optic modes shows
significant deviation from quasi-harmonic prediction, which is ascribed to the
effects of inclusion of higher order phonon-phonon scattering processes.
Further, temperature sensitivity of each mode is analyzed by computing their
first order temperature co-efficient (\c{hi}). The quasi-harmonic \c{hi} values
are one order magnitude smaller than the SED and experimental values; which
again substantiate that quasi-harmonic methods are inadequate, and a full
anaharmonic analysis is essential to explain structure and dynamics of SLBP at
finite temperatures.
