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The electronic structure of Ba$_2$Ti$_2$Fe$_2$As$_4$O, a newly discoveredsuperconductor, is investigated using first-principles calculations based onlocal density approximations. Multiple Fermi surface sheets originating fromTi-3$d$ and Fe-3$d$ states are present corresponding to the conductingTi$_2$As$_2$O and Fe$_2$As$_2$ layers respectively. Compared withBaFe$_2$As$_2$, sizeable changes in the related Fermi surface sheets indicatesignificant electron transfer (about 0.12$e$) from Ti to Fe, which suppressesthe stripe-like antiferromagnetism at the Fe sites and simultaneously inducessuperconductivity. Our calculations also suggest that an additionalN\'{e}el-type antiferromagnetic instability at the Ti sites is relativelyrobust against the electron transfer, which accounts for the anomaly at 125 Kin the superconducting Ba$_2$Ti$_2$Fe$_2$As$_4$O.

Self-doping effect and possible antiferromagnetism at titanium-layers in the iron-based superconductor Ba$_2$Ti$_2$Fe$_2$As$_4$O