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As all these elements are located in period 3, they can have expanded octets through using their energetically accessible, low-lying d sub-shell for bonding. This is why period 2 elements cannot have an expanded octet, as they don't have access to the d sub-shell.
Yes, it is because of the presence of the d-orbital in the elements staring in period 3! This d-orbital can accommodate the extra electrons! If you look at the formal charge for the elements you mentioned (Si, P, S, and Cl) you can see that having more than the octet minimizes the formal charge and brings it closer to the stable 0, which helps you recognize when an expanded octet would be beneficial.
Rows three and beyond can have an expanded octet (hold more than 8 electrons) because they have access to the s, p AND d orbitals. Having access the the d orbital allows ten electrons to be used in addition to the octet. Rows 2 and above cannot have an expanded octet because they only utilize s and p. Hope this helps!
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