The initiation rate of ruthenium metathesis catalysts is one of their most important characteristics from the applicational point of view due to the fact, that initiation is often the rate-limiting step of the entire catalytic cycle. Such initiation rate can be adjusted by introducing various modifications to the commonly used Grubbs-like and Hoveyda-Grubbs-like catalysts. Using a DFT approach, we predicted the initiation rates of the 2nd generation Hoveyda-Grubbs catalyst analogues substituted with electron-withdrawing –NO, –NO2, and –SO2C4F9 groups in all positions of the phenyl ring in the benzylidene part. We show that some of the modifications should result in very fast-initiating catalysts. In particular, the –SO2C4F9-substitued derivatives are predicted to be the fastest-initiating in the series. We also found correlations between the selected computed parameters such as the Gibbs free energy barrier for initiation and ruthenium-oxygen bond strengths which, combined with distortion energy analysis, allowed us to provide an explanation of the main driving force behind fast initiation.