Reduced Scaling Correlated Natural Transition Orbitals for Multilevel Coupled Cluster Calculations

Multilevel coupled cluster theory offers reduced scaling computation of intensive properties in systems that are too large for standard coupled cluster calculations. A significant benefit of the multilevel coupled cluster framework is the possibility of calculating intensive properties that are not tightly localized if an appropriate set of active orbitals is used. Correlated natural transition orbitals (CNTOs) are tailored to describe excitation processes. For multilevel coupled cluster singles and doubles (MLCCSD) and singles and perturbative doubles (MLCC2) calculations, the construction of CNTOs generally becomes the computational bottleneck. Here, we demonstrate how CNTOs can be obtained with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> operations, eliminating the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math>-scaling steps involved in the original approach. This reduction in scaling moves the bottleneck of MLCC2 and MLCCSD calculations from the active orbital space preparation to the MLCC2 and MLCCSD equations with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math>-scaling.