We describe the implementation of orbital optimisation for the models in the perfect pairing hierarchy. Orbital optimisation, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the π space. While local minima and σ-π symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the π subspace, as well as in the full σπ valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimised orbitals are used. PH is found to yield good agreement with previously published density matrix renormalisation group data in the π space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger basis sets or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

Novel implementations based on dense tensor storage are presented for the singlet-reference perfect quadruples (PQ) [J. A. Parkhill et al., J. Chem. Phys. 130, 084101 (2009)] and perfect hextuples (PH) [J. A. Parkhill and M. 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_nH_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 (H₅₀), 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.

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller-Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.