  We consider the use of pulse-shaped broadband femtosecond lasers to optically
cool rotational and vibrational degrees of freedom of molecules. Since this
approach relies on cooling rotational and vibrational quanta by exciting an
electronic transition, it is most easily applicable to molecules with similar
ground and excited potential energy surfaces, such that the vibrational state
is usually unchanged during electronic relaxation. Compared with schemes that
cool rotations by exciting vibrations, this approach achieves internal cooling
on the orders-of- magnitude faster electronic decay timescale and is
potentially applicable to apolar molecules. For AlH+, a candidate species, a
rate-equation simulation indicates that rovibrational equilibrium should be
achievable in 8 \mu s. In addition, we report laboratory demonstration of
optical pulse shaping with sufficient resolution and power for rotational
cooling of AlH+.
