Reaction 3 Zr + C 2 H 6 → 3 ZrH ? CH 2 ? CH 3 ? 1 ZrH 2 ? CH 2 = CH 2 → 1 ZrH 3 ? CH = CH 2 $ {}^{\mathbf{3}}\mathrm{Zr}+{\mathrm{C}}_{\mathbf{2}}{\mathrm{H}}_{\mathbf{6}}{\to}^{\mathbf{3}}\mathrm{Zr}\mathrm{H}-{\mathrm{C}\mathrm{H}}_{\mathbf{2}}-{\mathrm{C}\mathrm{H}}_{\mathbf{3}}{\Rightarrow}^{\mathbf{1}}{\mathrm{ZrH}}_2-{\mathrm{C}\mathrm{H}}_2={\mathrm{C}\mathrm{H}}_2{\to}^{\mathbf{1}}{\mathrm{ZrH}}_{\mathbf{3}}-\mathrm{CH}={\mathrm{C}\mathrm{H}}_{\mathbf{2}} $ proceeds via spin-flip surface hopping over several transition states has been investigated. The minimum energy crossing point is determined with the help of the DFT fractional-occupation-number (FON) approach.