The coupled cluster method CCSD(T), considered the "gold standard" of quantum chemistry, is O(N^7). That's the highest-exponent polynomial time algorithm I'm pe

The coupled cluster method CCSD(T), considered the "gold standard" of quantum chemistry, is O(N^7). That's the highest-exponent polynomial time algorithm I'm personally aware of that sees regular use. The various coupled-cluster variants are all basically approximations to full configuration interaction, which is a much worse O(N!).