extend 4body descriptors

[duanzaixu]

Summary

Extend the many‑body descriptors with the new 4‑body terms q_123 and q_233.

Syntax

l_max <l_max_3body> <has_q_222> <has_q_1111> <has_q_112> <has_q_1122> <has_q_123> <has_q_233>

All <has_...> arguments accept any integer value; a non‑zero value means the descriptor is enabled.

• Using l_max 4 1 0 1 0 0 0 means using l_max=4 for 3-body, and l_max=2 for 4-body.
• Using l_max 4 1 0 1 0 1 1 means using l_max=4 for 3-body, and l_max=3 for 4-body.
• Using l_max 4 1 0 1 1 1 1 means using l_max=4 for 3-body, l_max=3 for 4-body, and l_max=2 for 5-body.
• Note on q_1111: This descriptor is simply the square of the 3‑body descriptor: q_1111 = (q_11)^2.
  It is provided only for backward compatibility and its use is not recommended.
• Similarly, q_2222 = (q_22)^2. Therefore, q_1122 is the only independent 5-body descriptor up to l_max=2.