I made this long time ago, did not posted or published anywhere.
I planned to made a more beautiful journal paper in near future, may be this year.
somethings need to be clean up and more detail is needed.
The calculation is based on Hartman-Hahn and Tim Wenckebach, the difference is, they use Fermi-Golden Rule to approximate the polarization transfer rate, but I solved it exactly with computer and also deduced the analytical solution for high-frequency truncated Hamiltonian. This reveal the validity on the frequency truncation. And I will add a comparison with experimental data in the planned-to-do paper.