The H2 opacity arising from the pure-rotational hexadecapole-induced U0(J) transitions occurring during H2H2 and H2He collisions, and from the hexadecapole-induced U0(J) + S0(J′) and the quadrupole-induced S0(J) + S0(J′) transitions in H2He collisions, has been calculated. The U0(J) and S0(J) + S0(J′) contributions from H2H2 collisions are important H2 opacities in the frequency range from 700–3000 cm−1 for temperatures appropriate to the outer planets. It is concluded that this opacity is needed in addition to the opacity from the extrapolation of the 0-0 and 1-0 H2H2 collisionally induced bands to interpret the spectrum at 5 μm for the outer planets.