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We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar ^40K^87Rb molecules nphys08,science08. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold ^40K and ^87Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X^1Σ^+ and a^3Σ^+ vibrational levels. We find excellent agreementdoi:10.1088/1367-2630/11/5/055043 fatcat:s6a4jleipjdaxakjfx4u46iawy