Consequently, the excitation operator is simply defined as 𝐸 ̂𝑝𝑞 = 𝑎 𝑝 † 𝑎 𝑞 , where p and q refer to molecular spin orbitals, while its non-relativistic definition is 𝐸 ̂𝑝𝑞 = 𝑎 𝑝𝛼 † 𝑎 𝑞𝛼 + 𝑎 𝑝𝛽 † 𝑎 𝑞𝛽, where  and  indicate up and down-spin, respectively, and p and q refer to molecular spatial orbitals. This difference in the excitation operator results in a slightly different energy representation of CASPT2 compared to the non-relativistic method, but the basic concept remains almost the same.