  We study the damping of molecular vibrations due to electron-hole pair
excitations in donor-acceptor(D-A) type molecular rectifiers. At finite voltage
additional non-equilibrium electron-hole pair excitations involving both
electrodes become possible, and contribute to the stimulated emission and
absorption of phonons. We point out a generic mechanism for D-A molecules,
where the stimulated emission can dominate beyond a certain voltage due to
inverted position of the D and A quantum resonances. This leads to
current-driven amplification (negative damping) of the phonons similar to
laser-action. We investigate the effect in realistic molecular rectifier
structures using first principles calculations.
