update_shift_damping Subroutine

    subroutine update_shift_damping()
        implicit none
        ! sign convention for imaginary and real time differ
        shift_damping = shift_damping + tau_imag * DiagSft
        if (tDynamicDamping) shift_damping = shift_damping - tau_real &
                                             * real_time_info%damping

    end subroutine update_shift_damping