Which statements about bonding in metal carbonyls are correct?

The carbon lone pair forms the $\sigma$ bond to the metal (A) and filled metal $d$ orbitals back-donate into ${\pi }^{\ast }(\mathrm{CO})$ (B). Back-donation adds electrons to an antibonding orbital, so it weakens, not strengthens, C-O (C is false). It adds $\pi$ character to the M-C bond, strengthening and shortening it (D). Correct: A, B, D.