There are lots of higher order time splitting method as shown by the list with real and complex coefficients $a_i, b_i, c_i$:
$$ [e^{c_s \Delta t \hat C}] e^{b_s \Delta t \hat B} e^{a_s \Delta t \hat A} ... [e^{c_1 \Delta t \hat C}] e^{b_1 \Delta t \hat B} e^{a_1 \Delta t \hat A} u $$
It is not clear which one should I choose, so are there any advantage of complex coefficients over real coefficients? Also, which method is better in practices. Intuitively, the least step $s$ and real coefficients seems an easy choice.