Is it possible to get a total energy difference for a cubic system around 1 Ry unit with and without including spin-orbit coupling. If any one have references regarding this type please send the link.
As I know, spin-orbit coupling decreases energy. In some systems possible to make such unitary transformation of Hamiltonian to avoid spin-orbit term. For example, in quantum dot with SOC term aps (a - constant, p - momentum, s - Pauli matrix), the difference which you ask is a2m/2 (m - electron mass). So, the difference proportional to the SQUARED spin-orbit strength.