The influence of molecular parameters on the rate of unimolecular reactions induced by monochormatic infrared radiation (URIMIR) is considered in the range of validity of a Pauli master equation. Solutions of the master equation are obtained for a model series of bond fission reactions. A two parameter activation equation for the time dependent rate coefficient is established. The dependence of the steady state rate coefficient, the activation time, and further relevant rate parameters upon the threshold energy for reaction, the excitation quantum, the number of vibrational modes, and the integrated oscillator strength of the fundamental transition is established and summarized in three simple rules. Quantitative calculation for the case B intensity fall-off are presented.