Cost-effective description of strong correlation: efficient implementations of the perfect quadruples and perfect hextuples models

Abstract

Novel implementations based on dense tensor storage are presented for the singlet-reference perfect quadruples (PQ) [Parkhill, Lawler, and Head-Gordon, J. Chem. Phys. 130, 084101 (2009)] and perfect hextuples (PH) [Parkhill and Head-Gordon, J. Chem. Phys. 133, 024103 (2010)] models. The methods are obtained as block decompositions of conventional coupled-cluster theory that are exact for four electrons in four orbitals (PQ) and six electrons in six orbitals (PH), but that can also be applied to much larger systems. PQ and PH have storage requirements that scale as the square, and as the cube of the number of active electrons, respectively, and exhibit quartic scaling of the computational effort for large systems. Applications of the new implementations are presented for full-valence calculations on linear polyenes (C n H n+2 ), which highlight the excellent computational scaling of the present implementations that can routinely handle active spaces of hundreds of electrons. The accuracy of the models is studied in the π space of the polyenes, in hydrogen chains (H 50 ), and in the π space of polyacene molecules. In all cases, the results compare favorably to density matrix renormalization group values. With the novel implementation of PQ, active spaces of 140 electrons in 140 orbitals can be solved in a matter of minutes on a single core workstation, and the relatively low polynomial scaling means that very large systems are also accessible using parallel computing.

13 pages, 7 figures

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• Orbital optimization in the perfect pairing hierarchy. Applications to full-valence calculations on linear polyacenes
• Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
• Demonstrating that the non orthogonal orbital optimized coupled cluster model converges to full configuration interaction
• Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
• Coupled-cluster pairing models for radicals with strong correlations