Reduced Scaling Correlated Natural Transition Orbitals\nfor Multilevel Coupled Cluster Calculations

Multilevel coupled\ncluster theory offers reduced scaling computation\nof intensive properties in systems that are too large for standard\ncoupled cluster calculations. A significant benefit of the multilevel\ncoupled cluster framework is the possibility of calculating intensive\nproperties that are not tightly localized if an appropriate set of\nactive orbitals is used. Correlated natural transition orbitals (CNTOs)\nare tailored to describe excitation processes. For multilevel coupled\ncluster singles and doubles (MLCCSD) and singles and perturbative\ndoubles (MLCC2) calculations, the construction of CNTOs generally\nbecomes the computational bottleneck. Here, we demonstrate how CNTOs\ncan be obtained with O(N3) operations, eliminating the O(N5)-scaling steps involved in the original\napproach. This reduction in scaling moves the bottleneck of MLCC2\nand MLCCSD calculations from the active orbital space preparation\nto the MLCC2 and MLCCSD equations with O(N4)-scaling.