Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

Abstract

We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, 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 optimized orbitals are used. PH is found to yield good agreement with previously published density matrix renormalization group (DMRG) 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 bases or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

“…Some of us have recently argued that connected quintuple and hextuple excitations have only a small role in the strong correlation effects, even for the largest acenes. 86 We demonstrate this in the STO-3G basis with the (10e,10o), (14e,14o), (18e,18o) and (26e,26o) ASCI wave functions of 2acene, 3acene, 4acene and 6acene, respectively, shown in figure 4, using geometries from reference 98. For 2acene, a 12k determinant ASCI wave function was used, which is almost FCI for this system.…”

“…As is well known, calculations based on the coupledcluster method converge rapidly with respect to excitation rank used in the calculation, which has also been used recently to construct blazing fast approximate CASSCF approaches. [81][82][83][84][85][86] However, the speed of convergence of coupled-cluster theory may still be too low to be able to cost-efficiently treat challenging strong correlation problems. Our results on Cr 2 lead us to believe that single-reference CC approaches cannot be faithfully applied on challenging problems in transition metal chem-istry, leaving room for alternative approaches.…”

A Combined Selected Configuration Interaction and Many-Body Treatment of Static and Dynamical Correlation in Oligoacenes

“…12,22,54,[65][66][67][68][69][70][71][72][73][74][75][76] In characterizing the ground state, qualitatively different interpretations can arise depending on the degree dynamical correlation included, with recent studies suggesting that pure active-space methods tend to overestimate biradical character in these ground states. [74][75][76][77] An accurate theoretical characterization of the oligoacenes is complicated, however, by (i) strong correlation in the π/π * manifold, (ii) their size, prohibitive for many ab initio methods, and (iii) the large basis sets required for experimental comparisons. For these reasons, a chemically accurate prediction of the singlet-triplet splittings and precise descriptions of the ground states have remained elusive to theoretical techniques.…”

Combining Pair-Density Functional Theory and Variational Two-Electron Reduced-Density Matrix Methods

“…DMRG-or v2RDM-based CASSCF) tend to overestimate the polyradical character of the larger members of the series when correlations among the σ/σ * network are ignored. [131][132][133][134] A detailed history of the progression of these controversies is recounted in Ref. 134.…”