  The starting point to understanding cluster properties is the putative global
minimum and all the nearby local energy minima; however, locating them is
computationally expensive and challenging due to a combinatorial explosion
problem. The relative populations and spectroscopic properties of a molecule
that are a function of temperature can be approximately computed by employing
statistical thermodynamics. Here, we investigate temperature-entropy-driven
isomers distribution on Be$_6$B$_{11}^{-}$ fluxional cluster and the effect of
temperature on their infrared spectroscopy and relative populations. We
identify the vibration modes possessed by the cluster that significantly
contribute to the zero-point energy. A couple of steps are considered for
computing the temperature-dependent relative population: First, using a genetic
algorithm coupled to density functional theory, we performed an extensive and
systematic exploration of the potential/free energy surface of
Be$_6$B$_{11}^{-}$ cluster to locate the putative global minimum and elucidate
the low-energy structures. Second, the relative populations' temperature
effects are determined by considering the thermodynamic properties and
Boltzmann factors. The temperature-dependent relative populations show that the
entropies and temperature are essential for determining the global minimum. We
compute the temperature-dependent total infrared spectra employing the
Boltzmann factor weighted sums of each isomer's infrared spectrum and find that
at finite temperature, the total infrared spectrum is composed of an admixture
of infrared spectra that corresponds to the spectrum of the lowest energy
structure and its isomers located at higher energies. The methodology and
results describe the thermal effects in the relative population and the
infrared spectra.
