The PNOs are then truncated by occupation number (T CUT PNO , defaulting to 3.33 • 10 -7 ) to form a compact virtual space for pair ij. In addition, energy and trace criteria can be used. After the truncated PNO basis is constructed, the truncated PNOs are canonicalized to give orbital energies for the pair ij. For singles, the virtual space is assigned using PNOs from diagonal pair ii, using a tighter occupation cutoff (T CUT PNO scaled by T DIAG SCALE , with the scaling defaulting to 0.03). For triples, the triplet density is formed as the average of pair densities ij, jk, and ik formed from converged LCCSD doubles amplitudes (converged LMP2, LCEPA0, or LCCD amplitudes for weak pairs), and triples natural orbitals (TNOs) are formed from the eigenvectors of the triples density.