We studied the initial reaction mechanism of Zn precursors, namely, di-methylzinc (Zn(CH3)2, DMZ) and diethylzinc (Zn(C2H5)2, DEZ), for zinc oxide thin-film growth on a Si (001) surface using density functional theory. We calculated the migration and reaction energy barriers for DMZ and DEZ on a fully hydroxylized Si (001) surface. The Zn atom of DMZ or DEZ was adsorbed on an O atom of a hydroxyl (-OH) due to the lone pair electrons of the O atom on the Si (001) surface. The adsorbed DMZ or DEZ migrated to all available surface sites, and rotated on the O atom with low energy barriers in the range of 0.00-0.13 eV. We considered the DMZ or DEZ reaction at all available surface sites. The rotated and migrated DMZs reacted with the nearest -OH to produce a uni-methylzinc (-ZnCH3, UMZ) group and methane (CH4) with energy barriers in the range of 0.53-0.78 eV. In the case of the DEZs, smaller energy barriers in the range of 0.21-0.35 eV were needed for its reaction to produce a uni-ethylzinc (-ZnC2H5, UEZ) group and ethane (C2H6). Therefore, DEZ is preferred to DMZ due to its lower energy barrier for the surface reaction.