  We study the optical generation and control of coherent phonons in elemental
bismuth (Bi) and antimony (Sb) using a classical equation of motion informed by
first-principles calculations of the potential energy surface and the
frequency-dependent macroscopic dielectric function along the zone-centered
optical phonons coordinates. Using this approach, we demonstrate that phonons
with the largest optomechanical couplings, also have the strongest degree of
anharmonicity among the zone-centered modes, a result of the broken symmetry
structural ground state of Bi and Sb. We show how this anharmonicity,
explaining the light-induced phonon softening observed in experiments, prevents
the application of standard phonon-amplification and annihilation protocols. We
introduce a simple linearization protocol that extends the use of such
protocols to the case of anharmonic phonons in broken symmetry materials, and
demonstrate its efficiency at high displacement amplitudes. Our formalism and
results provide a path for improving optical control in non-linear phononics.
