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

TL;DR

This paper introduces efficient dense tensor implementations of the perfect quadruples and hextuples models, enabling accurate correlation calculations for large systems with hundreds of electrons at manageable computational costs.

Contribution

The paper presents novel dense tensor storage implementations for PQ and PH models, significantly improving their computational efficiency and scalability for large active spaces.

Findings

Able to handle 140 electrons in 140 orbitals in minutes on a single core

Excellent computational scaling demonstrated on polyenes and hydrogen chains

Results compare favorably with density matrix renormalization group methods

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 {\pi} space of the polyenes, in hydrogen chains (H 50 ), and in the {\pi} 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.