where E real shift and E imaginary shift are provided as parameters and cannot be non-zero simultaneously, and Ĥ(0) D is the diagonal part of Ĥ(0) . The real and imaginary level shift techniques modify the denominator in the second-order energy expression 1/∆ pqrs by 1/(∆ pqrs +ε) and 1/(∆ pqrs +iε), respectively, where