We study the formation and destruction of molecules in the ejecta of Population III supernovae (SNe) using a chemical kinetic approach to follow the evolution of molecular abundances from day 100 to day 1000 after explosion. The chemical species included range from simple di-atomic molecules to more complex dust precursor species. All relevant chemical processes that are unique to the SN environment are considered. Our work focuses on zero-metallicity progenitors with masses of 20, 170, and 270 Msun, and we study the effect of different levels of heavy element mixing and the inward diffusion of hydrogen on the ejecta chemistry. We show that the ejecta chemistry does not reach a steady state within the relevant time-span for molecule formation. The primary species formed are O2, CO, SiS, and SO. The SiO, formed as early as 200 days after explosion, is rapidly depleted by the formation of silica molecular precursors in the ejecta. The rapid conversion of CO to C2 and its thermal fractionation at temperatures above 5000 K allow for the formation of carbon chains in the oxygen-rich zone of the unmixed models, providing an important pathway for the formation of carbon dust in hot environments where the C/O ratio is less than 1. We show that the fully-mixed ejecta of a 170 Msun progenitor synthesizes 11.3 Mun of molecules whereas 20 Msun and 270 Msun progenitors produce 0.78, and 3.2 Msun of molecules, respectively. The admixing of 10 % of hydrogen into the fully-mixed ejecta of the 170 Msun progenitor increases its molecular yield to ~ 47Msun. The unmixed ejecta of a 170 Msun progenitor supernova without hydrogen penetration synthesizes ~37 Msun of molecules, whereas its 20 Msun counterpart produces ~ 1.2 Msun. Finally, we discuss the cosmological implication of molecule formation by Pop. III SNe in the early universe.
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