Final answer:
The central atom in BF3 and BeCl2 cannot complete an octet.
Step-by-step explanation:
The central atom in BF3, BeF2, and OF2 cannot complete an octet. In BF3, the boron atom only has six electrons surrounding it, while the fluorine atoms each have a full octet.
This makes the boron atom electron deficient and reactive. Similarly, in BeCl2, the beryllium atom only has four electrons surrounding it, while the chlorine atoms each have a full octet. Finally, in OF2, the oxygen atom only has six electrons surrounding it, while the fluorine atoms each have a full octet. Therefore, the correct answer is Option 1: Both I and III.