We are planning to use free software (Quantum Espresso, VASP or others) because of budget cuts and inability to buy commercial packs. So can we publish these calculations along with the synthetic part for explaining the results obtained?
Completely normal. Quick search brought up many articles using Quantum Espresso specifically published in journals like Journal of Physics D and Physical Review B, even Physical Review Letters well above that impact factor range.
Many would argue that using free (open) code can be even preferable regarding the repeatability of the calculations.
Note that VASP requires a paid institutional license, but maybe you do have access to that.
It's normal. There are a lot publications using free software like Abinit, Elk,....etc. So, a lot of papers have been published in this context in journals with (2-3 impact factor,)