In CCSD and for two-body Hamiltonians, how many nested commutators yield nonzero results? Where does the Baker-Campbell-Hausdorff expansion terminate? What is the (many-body) rank of the resulting \( \overline{H_N} \)?
CCSD truncates for two-body operators at four-fold nested commutators, because each of the four annihilation and creation operators in \( \overline{H_N} \) can be knocked out with one term of \( T \).