The white queen needs to get closer to the black king to create a mating possibility. 1.Qh5 or 1.Qh7 (threatening Qg6 mate) and 1.Qe1, Qc1, Qa1 or Qb1 (threatening Qb4 or Qa3) are all well met by 1...d4, giving an escape square on d5. 1.Qg2 looks promising, to meet d4 with Qc6, but Black plays 1...Ng5 or Nd8.
The surprising answer is 1.Qe4! with no direct threat, but 1...fxe4 and 1...dxe4 allow mate by Rf6 and Rd2 respectively. 1...d4 allows 2.Qc6, 1...c3 2.Qb4, 1...f4 2.Qg6 or any knight move is mated by Qxe5.