Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes

Abstract

We demonstrate a block-tensor based implementation of coupled-cluster valence-bond singles and doubles (CCVB-SD) [Small, D. W.; Head-Gordon M. J. Chem. Phys. 2012, 137, 114103] which is a simple modification to restricted CCSD (RCCSD) that provides a qualitatively correct description of valence correlations even in strongly correlated systems. We derive the Λ-equation of CCVB-SD and the corresponding unrelaxed density matrices. The resulting production-level implementation is applied to oligoacenes, correlating up to 318 electrons in 318 orbitals. CCVB-SD shows a qualitative agreement with exact methods for short acenes and reaches the bulk limit of oligoacenes in terms of natural orbital occupation numbers, whereas RCCSD shows nonvariational behavior even for relatively short acenes. A significant reduction in polyradicaloid character is found when correlating all valence electrons instead of only the π-electrons.

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

“…The reason why the results of ref. 80 agree with ours can be understood by analysis of the results of the PH calculations. In the method of ref.…”

“…Famously, DMRG calculations have been used to show that the larger linear polyacenes exhibit strong correlation for their π electrons [55]. Other approaches used have included density functional theory [56][57][58][59][60][61], multiconfiguration pair-density functional theory [62], projected Hartree-Fock theory [63], the random phase approximation [64], configuration interaction [60] (CI), adaptive CI [27], GW theory [65], variational two-electron reduced density matrix (VRDM) theory [66][67][68][69], Møller-Plesset perturbation theory [61,[70][71][72][73], spin-flip methods [74,75], CAS-SCF [53,59,71,72,76] as well as restricted-active space self-consistent field theory [77], valence bond [78] and CC valence bond (CCVB) theory [79,80], CC theory [70][71][72]80] and multireference averaged quadratic CC theory [81,82], an algebraic diagrammatic construction scheme [83], as well as PPH methods with approximate orbitals [50].…”

“…As far as we are aware, the only full-valence calculations on large polyacenes employing a method potentially capable of accurate treatment of strong correlation that have been published are the CCVB calculations performed contemporaneously in our group [79,80]. Thanks to our recent implementation [50], even the larger polyacenes can be treated accurately in full-valence active spaces using PPH methods, yielding an independent way to check the correctness of the recent CCVB results.…”

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

“…The difference between our observations and predictions of polyradical character from previous studies can perhaps be understood by noting that both the SUHF method employed in Ref 59 and the v2RDM method used in Ref 60 tend to predict "more radical-like" NO occupations than CASSCF. At any rate, prior experience with 1D polyacenes suggest that radicaloid character is artificially augmented by pure π space calculations, and inclusion of σ orbitals into the active space reduces radical character [68][69][70] . It is therefore reasonable to view these π space calculations as an upper bound to the true radicaloid character of these molecules, and our results suggest that members of the periacene sequence up to 6-periacene are at best biradical and possess very little polyradical character.…”

An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions

“…With an RHF reference, it has shown catastrophic nonvariationality for strongly correlated systems. 6,107,108 It is possible that RCCSD (and even RCCSDT) is also ex- . 3.…”