Presented is an algorithm for performing the ab initio molecular dynamic (MD) simulations along the predetermined intrinsic reaction paths (TRP). The proposed approach has been implemented within the projector augmented-wave DFT methodology (PAW program). The slow-growth MD simulations along the IRP has been applied for the reactions of (i) the HCN --> CNH isomerization reaction, (ii) the conrotatory ring opening of cyclobutene, (iii) the prototype SN2 reaction Cl- + (CHCl)-Cl-3 --> ClCH3 + Cl-, and (iv) the chloropropene isomerization Cl-CH2-CH=CH2 = CH2=CH-CH2Cl. The results show that the slow-growth MD approach along the predetermined IRP leads to smooth free-energy profiles; use of a well-defined reaction coordinate (RC) reduces the problem of the free-energy hysteresis, Thus, the slow-growth simulations along the IRP typically require less time steps than the standard approach with an a priori chosen RC. The illustrative examples show that the applied methodology works well for the reactions involving concerted changes in many geometrical variables as well as in the cases when the finite-temperature paths strongly deviate from the IRP.