Do the atomic orbitals of the same atom have the same energy under different chemical conditions? In other words, can atomic orbital energy be changed by external changes? For example, does Fe(OH)3 have the same atomic orbital energy as Fe in Fe2O3?
Do not. Each orbital has its own energy, and it can be calculated by means of ab initio calculations with the Schrödinger equation. Programs as Gaussian, Gamess, and many others can do it.