The effect of single amino acid mutations on the rebinding dynamics of nitrogen monoxide (NO) to myoglobin is investigated using reactive molecular dynamics simulations. In particular, mutations of residues surrounding the heme-active site (Leu29, His64, Val68) were considered. Consistent with experiments, all mutations studied here have a significant effect on the kinetics of the NO-rebinding process, which consists of a rapid (several 10 ps) and a slow (100s of ps) time scale. For all modifications considered, the time scales and rebinding fractions agree to within a few percents with results from experiments by adjusting one single, physically meaningful, conformationally averaged quantity: the asymptotic energy separation between the NO-bound ((2)A) and photodissociated ((4)A) states. It is furthermore shown that the thermodynamic stability of wild-type versus mutant Mb for the ligand-free and ligand-bound variants of the protein can be described by the same computational model. Therefore, ligand kinetics and thermodynamics are related in a direct fashion akin to Phi-value analysis, which establishes a relationship between protein folding rates and thermal stability of proteins.