We performed simulations of initial stages of a carbon nanotube growth catalyzed by iron particles using all-electron density functional theory with generalized gradient approximation for the exchange-correlation functional. The systems studied are Fe4 + Cn for n=7-25, Fe10 + C15, and Fe10C15 + 10C. In addition, we performed a detailed study of development of different isomers in the Cn series, n=7-25.